TSTP Solution File: SWW349+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW349+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 18:08:06 EDT 2024
% Result : Theorem 173.49s 173.40s
% Output : CNFRefutation 173.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SWW349+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Wed Jun 19 04:15:24 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.13/0.53 start to proof:theBenchmark
% 173.02/173.26 %-------------------------------------------
% 173.02/173.26 % File :CSE---1.7
% 173.02/173.26 % Problem :theBenchmark
% 173.02/173.26 % Transform :cnf
% 173.02/173.26 % Format :tptp:raw
% 173.02/173.26 % Command :java -jar mcs_scs.jar %d %s
% 173.02/173.26
% 173.02/173.26 % Result :Theorem 153.810000s
% 173.02/173.26 % Output :CNFRefutation 153.810000s
% 173.02/173.26 %-------------------------------------------
% 173.02/173.27 %------------------------------------------------------------------------------
% 173.02/173.27 % File : SWW349+1 : TPTP v8.2.0. Released v5.2.0.
% 173.02/173.27 % Domain : Software Verification
% 173.02/173.27 % Problem : Hoare's Logic with Procedures 435261, 5000 axioms selected
% 173.02/173.27 % Version : Especial.
% 173.02/173.27 % English :
% 173.02/173.27
% 173.02/173.27 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 173.02/173.27 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 173.02/173.27 % Source : [Bla11]
% 173.02/173.27 % Names : hoare_435261.5000.p [Bla11]
% 173.02/173.27
% 173.02/173.27 % Status : Theorem
% 173.02/173.27 % Rating : 0.69 v8.2.0, 0.75 v8.1.0, 0.72 v7.5.0, 0.75 v7.4.0, 0.83 v7.3.0, 0.86 v7.1.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.3.0, 0.96 v5.2.0
% 173.02/173.27 % Syntax : Number of formulae : 5228 (1730 unt; 0 def)
% 173.02/173.27 % Number of atoms : 12572 (4522 equ)
% 173.02/173.27 % Maximal formula atoms : 13 ( 2 avg)
% 173.02/173.27 % Number of connectives : 8368 (1024 ~; 154 |; 717 &)
% 173.02/173.27 % ( 878 <=>;5595 =>; 0 <=; 0 <~>)
% 173.02/173.27 % Maximal formula depth : 22 ( 6 avg)
% 173.02/173.27 % Maximal term depth : 19 ( 2 avg)
% 173.02/173.27 % Number of predicates : 139 ( 138 usr; 2 prp; 0-7 aty)
% 173.02/173.27 % Number of functors : 369 ( 369 usr; 63 con; 0-10 aty)
% 173.02/173.27 % Number of variables : 16849 (16701 !; 148 ?)
% 173.02/173.27 % SPC : FOF_THM_RFO_SEQ
% 173.02/173.27
% 173.02/173.27 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 173.02/173.27 % 2011-03-01 12:18:31
% 173.02/173.27 %------------------------------------------------------------------------------
% 173.02/173.27 %----Relevant facts (4985)
% 173.02/173.27 fof(fact_ext,axiom,
% 173.02/173.27 ! [V_g_2,V_f_2] :
% 173.02/173.27 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 173.02/173.27 => V_f_2 = V_g_2 ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com__det,axiom,
% 173.02/173.27 ! [V_u,V_t,V_s,V_c] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 173.02/173.27 => V_u = V_t ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_state__not__singleton__def,axiom,
% 173.02/173.27 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 173.02/173.27 <=> ? [B_s,B_t] : B_s != B_t ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_single__stateE,axiom,
% 173.02/173.27 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 173.02/173.27 => ! [B_t] :
% 173.02/173.27 ~ ! [B_s] : B_s = B_t ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OSkip,axiom,
% 173.02/173.27 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc__elim__cases_I1_J,axiom,
% 173.02/173.27 ! [V_t,V_s] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 173.02/173.27 => V_t = V_s ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OSemi,axiom,
% 173.02/173.27 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 173.02/173.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OIfFalse,axiom,
% 173.02/173.27 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 173.02/173.27 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 173.02/173.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OIfTrue,axiom,
% 173.02/173.27 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 173.02/173.27 ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 173.02/173.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc__elim__cases_I5_J,axiom,
% 173.02/173.27 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 173.02/173.27 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 173.02/173.27 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OWhileFalse,axiom,
% 173.02/173.27 ! [V_ca_2,V_s_2,V_b_2] :
% 173.02/173.27 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_OWhileTrue,axiom,
% 173.02/173.27 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] :
% 173.02/173.27 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2))
% 173.02/173.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2))
% 173.02/173.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I1_J,axiom,
% 173.02/173.27 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I8_J,axiom,
% 173.02/173.27 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 173.02/173.27 <=> ( ( V_a5_2 = V_a2_2
% 173.02/173.27 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 173.02/173.27 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 & ? [B_s1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I7_J,axiom,
% 173.02/173.27 ! [V_a2_2,V_a3_2,V_a1_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 173.02/173.27 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 => ? [B_s1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I6_J,axiom,
% 173.02/173.27 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
% 173.02/173.27 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 173.02/173.27 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I5_J,axiom,
% 173.02/173.27 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
% 173.02/173.27 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 173.02/173.27 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc_Oequations_I4_J,axiom,
% 173.02/173.27 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 173.02/173.27 <=> ? [B_s1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 173.02/173.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I12_J,axiom,
% 173.02/173.27 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I13_J,axiom,
% 173.02/173.27 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I14_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I15_J,axiom,
% 173.02/173.27 ! [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 ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I44_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I45_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I16_J,axiom,
% 173.02/173.27 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I17_J,axiom,
% 173.02/173.27 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I46_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I47_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I53_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I52_J,axiom,
% 173.02/173.27 ! [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) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I5_J,axiom,
% 173.02/173.27 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 173.02/173.27 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 173.02/173.27 <=> ( V_fun_2 = V_fun_H_2
% 173.02/173.27 & V_com_2 = V_com_H_2 ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I4_J,axiom,
% 173.02/173.27 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 173.02/173.27 ( 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)
% 173.02/173.27 <=> ( V_fun_2 = V_fun_H_2
% 173.02/173.27 & V_com1_2 = V_com1_H_2
% 173.02/173.27 & V_com2_2 = V_com2_H_2 ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I3_J,axiom,
% 173.02/173.27 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 173.02/173.27 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 173.02/173.27 <=> ( V_com1_2 = V_com1_H_2
% 173.02/173.27 & V_com2_2 = V_com2_H_2 ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc__elim__cases_I4_J,axiom,
% 173.02/173.27 ! [V_t,V_s,V_c2,V_c1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 173.02/173.27 => ~ ! [B_s1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 173.02/173.27 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_evalc__WHILE__case,axiom,
% 173.02/173.27 ! [V_t_2,V_s_2,V_ca_2,V_b_2] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_t_2))
% 173.02/173.27 => ( ( V_t_2 = V_s_2
% 173.02/173.27 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 173.02/173.27 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.27 => ! [B_s1] :
% 173.02/173.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1))
% 173.02/173.27 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I64_J,axiom,
% 173.02/173.27 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I67_J,axiom,
% 173.02/173.27 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I68_J,axiom,
% 173.02/173.27 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Osimps_I69_J,axiom,
% 173.02/173.27 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Orecs_I1_J,axiom,
% 173.02/173.27 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Orecs_I4_J,axiom,
% 173.02/173.27 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Orecs_I5_J,axiom,
% 173.02/173.27 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_com_Orecs_I6_J,axiom,
% 173.02/173.27 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_WTs__elim__cases_I4_J,axiom,
% 173.02/173.27 ! [V_c2,V_c1] :
% 173.02/173.27 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 173.02/173.27 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 173.02/173.27 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_WTs__elim__cases_I6_J,axiom,
% 173.02/173.27 ! [V_ca_2,V_b_2] :
% 173.02/173.27 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2)))
% 173.02/173.27 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 173.02/173.27
% 173.02/173.27 fof(fact_WTs__elim__cases_I5_J,axiom,
% 173.02/173.27 ! [V_c2_2,V_c1_2,V_b_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 173.02/173.28 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 173.02/173.28 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I6_J,axiom,
% 173.02/173.28 ! [V_a1_2,V_a2_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 173.02/173.28 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_While,axiom,
% 173.02/173.28 ! [V_b_2,V_ca_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I5_J,axiom,
% 173.02/173.28 ! [V_a2_2,V_a1_2,V_a3_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 173.02/173.28 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 173.02/173.28 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OIf,axiom,
% 173.02/173.28 ! [V_b_2,V_c1_2,V_c0_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 173.02/173.28 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I4_J,axiom,
% 173.02/173.28 ! [V_a2_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 173.02/173.28 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 173.02/173.28 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OSemi,axiom,
% 173.02/173.28 ! [V_c1,V_c0] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 173.02/173.28 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OSkip,axiom,
% 173.02/173.28 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I1_J,axiom,
% 173.02/173.28 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WTs__elim__cases_I3_J,axiom,
% 173.02/173.28 ! [V_ca_2,V_a_2,V_Y_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I66_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I71_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I65_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Orecs_I3_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Orecs_I8_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Orecs_I2_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I70_J,axiom,
% 173.02/173.28 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OSkip,axiom,
% 173.02/173.28 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__elim__cases_I1_J,axiom,
% 173.02/173.28 ! [V_t,V_n,V_s] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 173.02/173.28 => V_t = V_s ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OSemi,axiom,
% 173.02/173.28 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 173.02/173.28 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 173.02/173.28 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OWhileTrue,axiom,
% 173.02/173.28 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] :
% 173.02/173.28 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 173.02/173.28 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2))
% 173.02/173.28 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2))
% 173.02/173.28 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OWhileFalse,axiom,
% 173.02/173.28 ! [V_n_2,V_ca_2,V_s_2,V_b_2] :
% 173.02/173.28 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__elim__cases_I5_J,axiom,
% 173.02/173.28 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2))
% 173.02/173.28 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 173.02/173.28 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OIfTrue,axiom,
% 173.02/173.28 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 173.02/173.28 ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 173.02/173.28 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OIfFalse,axiom,
% 173.02/173.28 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 173.02/173.28 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 173.02/173.28 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WTs__elim__cases_I8_J,axiom,
% 173.02/173.28 ! [V_a_2,V_P_2,V_X_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I31_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I62_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I41_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I30_J,axiom,
% 173.02/173.28 ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I32_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I22_J,axiom,
% 173.02/173.28 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I63_J,axiom,
% 173.02/173.28 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I40_J,axiom,
% 173.02/173.28 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I33_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I23_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,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_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I43_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I42_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I6_J,axiom,
% 173.02/173.28 ! [V_pname_H_2,V_pname_2] :
% 173.02/173.28 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 173.02/173.28 <=> V_pname_2 = V_pname_H_2 ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I1_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 173.02/173.28 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 173.02/173.28 <=> ( V_vname_2 = V_vname_H_2
% 173.02/173.28 & V_fun_2 = V_fun_H_2 ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I7_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 173.02/173.28 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2)
% 173.02/173.28 <=> ( V_vname_2 = V_vname_H_2
% 173.02/173.28 & V_pname_2 = V_pname_H_2
% 173.02/173.28 & V_fun_2 = V_fun_H_2 ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I2_J,axiom,
% 173.02/173.28 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 173.02/173.28 ( 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)
% 173.02/173.28 <=> ( V_loc_2 = V_loc_H_2
% 173.02/173.28 & V_fun_2 = V_fun_H_2
% 173.02/173.28 & V_com_2 = V_com_H_2 ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I8_J,axiom,
% 173.02/173.28 ! [V_a3_2,V_a1_2,V_a2_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 173.02/173.28 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OCall,axiom,
% 173.02/173.28 ! [V_a_2,V_X_2,V_pn_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_eval__eq,axiom,
% 173.02/173.28 ! [V_t_2,V_s_2,V_ca_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2))
% 173.02/173.28 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__evalc,axiom,
% 173.02/173.28 ! [V_t,V_n,V_s,V_c] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 173.02/173.28 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I8_J,axiom,
% 173.02/173.28 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2))
% 173.02/173.28 <=> ( ( V_a6_2 = V_a2_2
% 173.02/173.28 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 173.02/173.28 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 & ? [B_s1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I7_J,axiom,
% 173.02/173.28 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2))
% 173.02/173.28 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 => ? [B_s1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I6_J,axiom,
% 173.02/173.28 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2))
% 173.02/173.28 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 173.02/173.28 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I5_J,axiom,
% 173.02/173.28 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2))
% 173.02/173.28 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 173.02/173.28 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I4_J,axiom,
% 173.02/173.28 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2))
% 173.02/173.28 <=> ? [B_s1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 173.02/173.28 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I1_J,axiom,
% 173.02/173.28 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I58_J,axiom,
% 173.02/173.28 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I59_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I54_J,axiom,
% 173.02/173.28 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I55_J,axiom,
% 173.02/173.28 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I48_J,axiom,
% 173.02/173.28 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I49_J,axiom,
% 173.02/173.28 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I19_J,axiom,
% 173.02/173.28 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I18_J,axiom,
% 173.02/173.28 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OAssign,axiom,
% 173.02/173.28 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I2_J,axiom,
% 173.02/173.28 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_Oequations_I3_J,axiom,
% 173.02/173.28 ! [V_a1_2,V_a3_2,V_a2_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 173.02/173.28 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_WT_OLocal,axiom,
% 173.02/173.28 ! [V_a_2,V_Y_2,V_ca_2] :
% 173.02/173.28 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 173.02/173.28 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I29_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I28_J,axiom,
% 173.02/173.28 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I38_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I61_J,axiom,
% 173.02/173.28 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I39_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I60_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I27_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_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_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I26_J,axiom,
% 173.02/173.28 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I36_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I37_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I56_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I57_J,axiom,
% 173.02/173.28 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I25_J,axiom,
% 173.02/173.28 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I24_J,axiom,
% 173.02/173.28 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I9_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I8_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Orecs_I7_J,axiom,
% 173.02/173.28 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I34_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I51_J,axiom,
% 173.02/173.28 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I35_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I50_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I11_J,axiom,
% 173.02/173.28 ! [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 ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I21_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I10_J,axiom,
% 173.02/173.28 ! [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) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_com_Osimps_I20_J,axiom,
% 173.02/173.28 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__elim__cases_I4_J,axiom,
% 173.02/173.28 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t))
% 173.02/173.28 => ~ ! [B_s1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1))
% 173.02/173.28 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evalc_OAssign,axiom,
% 173.02/173.28 ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evalc__elim__cases_I2_J,axiom,
% 173.02/173.28 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 173.02/173.28 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_OAssign,axiom,
% 173.02/173.28 ! [V_n_2,V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__elim__cases_I2_J,axiom,
% 173.02/173.28 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),V_t_2))
% 173.02/173.28 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln__WHILE__case,axiom,
% 173.02/173.28 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_b_2] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_t_2))
% 173.02/173.28 => ( ( V_t_2 = V_s_2
% 173.02/173.28 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 173.02/173.28 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 173.02/173.28 => ! [B_s1] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),V_n_2),B_s1))
% 173.02/173.28 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_n_2),V_t_2)) ) ) ) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evalc__evaln,axiom,
% 173.02/173.28 ! [V_t,V_s,V_c] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 173.02/173.28 => ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),B_n),V_t)) ) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evalc_Oequations_I2_J,axiom,
% 173.02/173.28 ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evaln_Oequations_I2_J,axiom,
% 173.02/173.28 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),V_a4_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ).
% 173.02/173.28
% 173.02/173.28 fof(fact_evalc_OBody,axiom,
% 173.02/173.28 ! [V_s1,V_s0,V_pn] :
% 173.02/173.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 173.02/173.28 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 173.02/173.28
% 173.02/173.29 fof(fact_evalc__elim__cases_I6_J,axiom,
% 173.02/173.29 ! [V_s1,V_s,V_P] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 173.02/173.29 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln__max2,axiom,
% 173.02/173.29 ! [V_t2,V_n2,V_s2,V_c2,V_t1,V_n1,V_s1,V_c1] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n1),V_t1))
% 173.02/173.29 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),V_s2),V_n2),V_t2))
% 173.02/173.29 => ? [B_n] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),B_n),V_t1))
% 173.02/173.29 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),V_s2),B_n),V_t2)) ) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc_Oequations_I9_J,axiom,
% 173.02/173.29 ! [V_a3_2,V_a2_2,V_a1_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 173.02/173.29 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_OBody,axiom,
% 173.02/173.29 ! [V_s1,V_n,V_s0,V_pn] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1))
% 173.02/173.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_Oequations_I9_J,axiom,
% 173.02/173.29 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2))
% 173.02/173.29 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_WT_OBody,axiom,
% 173.02/173.29 ! [V_pn] :
% 173.02/173.29 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 173.02/173.29 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_WT_Oequations_I7_J,axiom,
% 173.02/173.29 ! [V_a_2] :
% 173.02/173.29 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 173.02/173.29 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln__elim__cases_I6_J,axiom,
% 173.02/173.29 ! [V_s1,V_n,V_s,V_P] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 173.02/173.29 => ~ ! [B_n] :
% 173.02/173.29 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 173.02/173.29 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc_OLocal,axiom,
% 173.02/173.29 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 173.02/173.29 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_OLocal,axiom,
% 173.02/173.29 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_n_2),V_s1_2))
% 173.02/173.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc_Oequations_I3_J,axiom,
% 173.02/173.29 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
% 173.02/173.29 <=> ? [B_s1] :
% 173.02/173.29 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 173.02/173.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_Oequations_I3_J,axiom,
% 173.02/173.29 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),V_a5_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
% 173.02/173.29 <=> ? [B_s1] :
% 173.02/173.29 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 173.02/173.29 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),V_a5_2),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_WTs__elim__cases_I7_J,axiom,
% 173.02/173.29 ! [V_P] :
% 173.02/173.29 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 173.02/173.29 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_WT__bodiesD,axiom,
% 173.02/173.29 ! [V_b,V_pn] :
% 173.02/173.29 ( c_Com_OWT__bodies
% 173.02/173.29 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 173.02/173.29 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I2_J,axiom,
% 173.02/173.29 ! [V_loc_H_2,V_loc_2] :
% 173.02/173.29 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 173.02/173.29 <=> V_loc_2 = V_loc_H_2 ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln__Suc,axiom,
% 173.02/173.29 ! [V_s_H,V_n,V_s,V_c] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 173.02/173.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc__elim__cases_I3_J,axiom,
% 173.02/173.29 ! [V_t_2,V_s_2,V_ca_2,V_a_2,V_Y_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_t_2))
% 173.02/173.29 => ~ ! [B_s1] :
% 173.02/173.29 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 173.02/173.29 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln__elim__cases_I3_J,axiom,
% 173.02/173.29 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_a_2,V_Y_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_n_2),V_t_2))
% 173.02/173.29 => ~ ! [B_s1] :
% 173.02/173.29 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 173.02/173.29 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),V_n_2),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_the_Osimps,axiom,
% 173.02/173.29 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 173.02/173.29
% 173.02/173.29 fof(fact_not__None__eq,axiom,
% 173.02/173.29 ! [T_a,V_x_2] :
% 173.02/173.29 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 173.02/173.29 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_not__Some__eq,axiom,
% 173.02/173.29 ! [T_a,V_x_2] :
% 173.02/173.29 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 173.02/173.29 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Osimps_I3_J,axiom,
% 173.02/173.29 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Osimps_I2_J,axiom,
% 173.02/173.29 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Orecs_I2_J,axiom,
% 173.02/173.29 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I6_J,axiom,
% 173.02/173.29 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Oinject,axiom,
% 173.02/173.29 ! [V_a_H_2,V_a_2,T_a] :
% 173.02/173.29 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 173.02/173.29 <=> V_a_2 = V_a_H_2 ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Orecs_I2_J,axiom,
% 173.02/173.29 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Osimps_I5_J,axiom,
% 173.02/173.29 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Orecs_I1_J,axiom,
% 173.02/173.29 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Osimps_I4_J,axiom,
% 173.02/173.29 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_is__none__code_I2_J,axiom,
% 173.02/173.29 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_is__none__code_I1_J,axiom,
% 173.02/173.29 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_is__none__def,axiom,
% 173.02/173.29 ! [V_x_2,T_a] :
% 173.02/173.29 ( c_Option_Ois__none(T_a,V_x_2)
% 173.02/173.29 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I5_J,axiom,
% 173.02/173.29 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Orecs_I1_J,axiom,
% 173.02/173.29 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_n__not__Suc__n,axiom,
% 173.02/173.29 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Suc__n__not__n,axiom,
% 173.02/173.29 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I1_J,axiom,
% 173.02/173.29 ! [V_glb_H_2,V_glb_2] :
% 173.02/173.29 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 173.02/173.29 <=> V_glb_2 = V_glb_H_2 ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I3_J,axiom,
% 173.02/173.29 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_vname_Osimps_I4_J,axiom,
% 173.02/173.29 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Suc__inject,axiom,
% 173.02/173.29 ! [V_y,V_x] :
% 173.02/173.29 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 173.02/173.29 => V_x = V_y ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat_Oinject,axiom,
% 173.02/173.29 ! [V_nat_H_2,V_nat_2] :
% 173.02/173.29 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 173.02/173.29 <=> V_nat_2 = V_nat_H_2 ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc_OCall,axiom,
% 173.02/173.29 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 173.02/173.29 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_OCall,axiom,
% 173.02/173.29 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_n_2),V_s1_2))
% 173.02/173.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 173.02/173.29 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 173.02/173.29 ( class_Rings_Osemiring__1(T_a)
% 173.02/173.29 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc_Oequations_I10_J,axiom,
% 173.02/173.29 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes))))
% 173.02/173.29 <=> ? [B_s1] :
% 173.02/173.29 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 173.02/173.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln_Oequations_I10_J,axiom,
% 173.02/173.29 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2)),V_a2_2),V_a4_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes))))
% 173.02/173.29 <=> ? [B_s1] :
% 173.02/173.29 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 173.02/173.29 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),V_a4_2),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Body__triple__valid__Suc,axiom,
% 173.02/173.29 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
% 173.02/173.29 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_option_Oexhaust,axiom,
% 173.02/173.29 ! [T_a,V_y] :
% 173.02/173.29 ( V_y != c_Option_Ooption_ONone(T_a)
% 173.02/173.29 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat__case__Suc,axiom,
% 173.02/173.29 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__None__iff,axiom,
% 173.02/173.29 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 173.02/173.29 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 173.02/173.29 | ? [B_k_H] :
% 173.02/173.29 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 173.02/173.29 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_bind__lunit,axiom,
% 173.02/173.29 ! [V_f_2,V_x_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_bind__runit,axiom,
% 173.02/173.29 ! [V_x_2,T_a] : hAPP(hAPP(c_Option_Obind(T_a,T_a),V_x_2),c_Option_Ooption_OSome(T_a)) = V_x_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triple_Oinject,axiom,
% 173.02/173.29 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 173.02/173.29 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 173.02/173.29 <=> ( V_fun1_2 = V_fun1_H_2
% 173.02/173.29 & V_com_2 = V_com_H_2
% 173.02/173.29 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triple__valid__def2,axiom,
% 173.02/173.29 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2))
% 173.02/173.29 <=> ! [B_Z,B_s] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 173.02/173.29 => ! [B_s_H] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H))
% 173.02/173.29 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__simps_I1_J,axiom,
% 173.02/173.29 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 173.02/173.29 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__Some__iff,axiom,
% 173.02/173.29 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 173.02/173.29 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
% 173.02/173.29 <=> ? [B_k_H] :
% 173.02/173.29 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 173.02/173.29 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__simps_I2_J,axiom,
% 173.02/173.29 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 173.02/173.29 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 173.02/173.29 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triple__valid__Suc,axiom,
% 173.02/173.29 ! [V_t,V_n,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 173.02/173.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_bind__lzero,axiom,
% 173.02/173.29 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),c_Option_Ooption_ONone(T_b)),V_f_2) = c_Option_Ooption_ONone(T_a) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evalc__elim__cases_I7_J,axiom,
% 173.02/173.29 ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_s1_2))
% 173.02/173.29 => ~ ! [B_s1] :
% 173.02/173.29 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 173.02/173.29 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_evaln__elim__cases_I7_J,axiom,
% 173.02/173.29 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_n_2),V_s1_2))
% 173.02/173.29 => ~ ! [B_s1] :
% 173.02/173.29 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 173.02/173.29 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),V_n_2),B_s1)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triple_Orecs,axiom,
% 173.02/173.29 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triple_Osimps_I2_J,axiom,
% 173.02/173.29 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Body__triple__valid__0,axiom,
% 173.02/173.29 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__Some__iff,axiom,
% 173.02/173.29 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 173.02/173.29 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.02/173.29 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.02/173.29 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__SomeD,axiom,
% 173.02/173.29 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 173.02/173.29 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.02/173.29 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.02/173.29 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_triples__valid__Suc,axiom,
% 173.02/173.29 ! [V_n_2,V_ts_2,T_a] :
% 173.02/173.29 ( ! [B_x] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 173.02/173.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 173.02/173.29 => ! [B_x] :
% 173.02/173.29 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 173.02/173.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_OCall,axiom,
% 173.02/173.29 ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat__rec__Suc,axiom,
% 173.02/173.29 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a,V_f1_2,V_f2_2),V_nat_2)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 173.02/173.29 ! [V_i_2,V_inc_2,T_a] :
% 173.02/173.29 ( class_Rings_Osemiring__1(T_a)
% 173.02/173.29 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__def,axiom,
% 173.02/173.29 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__assoc,axiom,
% 173.02/173.29 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_LoopF,axiom,
% 173.02/173.29 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_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_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__empty,axiom,
% 173.02/173.29 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_empty__map__add,axiom,
% 173.02/173.29 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_derivs__insertD,axiom,
% 173.02/173.29 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
% 173.02/173.29 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_Oinsert,axiom,
% 173.02/173.29 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 173.02/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_cut,axiom,
% 173.02/173.29 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 173.02/173.29 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2)
% 173.02/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 173.02/173.29 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_empty,axiom,
% 173.02/173.29 ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat__rec__0,axiom,
% 173.02/173.29 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 173.02/173.29 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Ass,axiom,
% 173.02/173.29 ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_bind__assoc,axiom,
% 173.02/173.29 ! [V_g_2,V_f_2,V_x_2,T_c,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),hAPP(hAPP(c_Option_Obind(T_c,T_b),V_x_2),V_f_2)),V_g_2) = hAPP(hAPP(c_Option_Obind(T_c,T_a),V_x_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_Option_Ooption(T_a)),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_a)),tc_Option_Ooption(T_a)),T_c),c_Option_Obind(T_b,T_a)),V_f_2)),V_g_2)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Comp,axiom,
% 173.02/173.29 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_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_a),tc_HOL_Obool)))) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_OSkip,axiom,
% 173.02/173.29 ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 173.02/173.29 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_hoare__derivs_OLocal,axiom,
% 173.02/173.29 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 173.02/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.02/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_ca_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_bind__rzero,axiom,
% 173.02/173.29 ! [V_x_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),V_x_2),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Option_Ooption_ONone(T_a) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__empty_I2_J,axiom,
% 173.02/173.29 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__empty_I1_J,axiom,
% 173.02/173.29 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__comp__def,axiom,
% 173.02/173.29 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Suc__neq__Zero,axiom,
% 173.02/173.29 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Zero__neq__Suc,axiom,
% 173.02/173.29 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat_Osimps_I3_J,axiom,
% 173.02/173.29 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Suc__not__Zero,axiom,
% 173.02/173.29 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_nat_Osimps_I2_J,axiom,
% 173.02/173.29 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_Zero__not__Suc,axiom,
% 173.02/173.29 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__None,axiom,
% 173.02/173.29 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 173.02/173.29 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 173.02/173.29 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 173.02/173.29
% 173.02/173.29 fof(fact_map__add__find__right,axiom,
% 173.02/173.29 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 173.02/173.29 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 173.02/173.29 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ).
% 173.02/173.29
% 173.13/173.29 fof(fact_nat__case__0,axiom,
% 173.13/173.29 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 173.13/173.29
% 173.13/173.29 fof(fact_weak__Body,axiom,
% 173.13/173.29 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_BodyN,axiom,
% 173.13/173.29 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 173.13/173.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_triple_Osize_I1_J,axiom,
% 173.13/173.29 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_vname_Osize_I1_J,axiom,
% 173.13/173.29 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_vname_Osize_I2_J,axiom,
% 173.13/173.29 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_triple_Osize_I2_J,axiom,
% 173.13/173.29 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_bot__fun__def,axiom,
% 173.13/173.29 ! [V_x_2,T_b,T_a] :
% 173.13/173.29 ( class_Orderings_Obot(T_a)
% 173.13/173.29 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_vname_Osize_I3_J,axiom,
% 173.13/173.29 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 173.13/173.29 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_vname_Osize_I4_J,axiom,
% 173.13/173.29 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_hoare__valids__def,axiom,
% 173.13/173.29 ! [V_ts_2,V_Ga_2,T_a] :
% 173.13/173.29 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
% 173.13/173.29 <=> ! [B_n] :
% 173.13/173.29 ( ! [B_x] :
% 173.13/173.29 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2))
% 173.13/173.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 173.13/173.29 => ! [B_x] :
% 173.13/173.29 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 173.13/173.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 173.13/173.29
% 173.13/173.29 fof(fact_ball__empty,axiom,
% 173.13/173.30 ! [V_P_2,T_a,B_x] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.30 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_singleton__inject,axiom,
% 173.13/173.30 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.30 => V_a_2 = V_b_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bot__nat__def,axiom,
% 173.13/173.30 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_hoare__sound,axiom,
% 173.13/173.30 ! [V_ts_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__absorb2,axiom,
% 173.13/173.30 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__commute,axiom,
% 173.13/173.30 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__code,axiom,
% 173.13/173.30 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 173.13/173.30 <=> ( V_y_2 = V_x_2
% 173.13/173.30 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 173.13/173.30 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_set__empty__eq,axiom,
% 173.13/173.30 ! [V_xo_2,T_a] :
% 173.13/173.30 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.30 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bot__apply,axiom,
% 173.13/173.30 ! [V_x_2,T_b,T_a] :
% 173.13/173.30 ( class_Orderings_Obot(T_a)
% 173.13/173.30 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_empty__not__insert,axiom,
% 173.13/173.30 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__not__empty,axiom,
% 173.13/173.30 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_doubleton__eq__iff,axiom,
% 173.13/173.30 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.30 <=> ( ( V_a_2 = V_ca_2
% 173.13/173.30 & V_b_2 = V_d_2 )
% 173.13/173.30 | ( V_a_2 = V_d_2
% 173.13/173.30 & V_b_2 = V_ca_2 ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_the__elem__eq,axiom,
% 173.13/173.30 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_MGT__def,axiom,
% 173.13/173.30 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_escape,axiom,
% 173.13/173.30 ! [V_Q_2,V_ca_2,V_Ga_2,T_a,V_P_2] :
% 173.13/173.30 ( ! [B_Z,B_s] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),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_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_conseq1,axiom,
% 173.13/173.30 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.30 => ( ! [B_Z,B_s] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 173.13/173.30 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_conseq2,axiom,
% 173.13/173.30 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.30 => ( ! [B_Z,B_s] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 173.13/173.30 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Option_Omap__def,axiom,
% 173.13/173.30 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_ran__empty,axiom,
% 173.13/173.30 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Loop__sound__lemma,axiom,
% 173.13/173.30 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_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_a),tc_HOL_Obool)))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Least__Suc,axiom,
% 173.13/173.30 ! [V_n_2,V_P_2] :
% 173.13/173.30 ( hBOOL(hAPP(V_P_2,V_n_2))
% 173.13/173.30 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 173.13/173.30 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I1_J,axiom,
% 173.13/173.30 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_LeastI__ex,axiom,
% 173.13/173.30 ! [V_P_2,T_a] :
% 173.13/173.30 ( class_Orderings_Owellorder(T_a)
% 173.13/173.30 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.30 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__comp,axiom,
% 173.13/173.30 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Option_Omap_Ocompositionality,axiom,
% 173.13/173.30 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Option_Omap_Ocomp,axiom,
% 173.13/173.30 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_LeastI,axiom,
% 173.13/173.30 ! [V_k_2,V_P_2,T_a] :
% 173.13/173.30 ( class_Orderings_Owellorder(T_a)
% 173.13/173.30 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 173.13/173.30 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_peek__and__def,axiom,
% 173.13/173.30 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 173.13/173.30 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 173.13/173.30 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__is__None,axiom,
% 173.13/173.30 ! [V_opt_2,V_f_2,T_a,T_b] :
% 173.13/173.30 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 173.13/173.30 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__None,axiom,
% 173.13/173.30 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__eq__Some,axiom,
% 173.13/173.30 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 173.13/173.30 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 173.13/173.30 <=> ? [B_z] :
% 173.13/173.30 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 173.13/173.30 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__Some,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Loop,axiom,
% 173.13/173.30 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_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_a),tc_HOL_Obool)))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_hoare__derivs_OIf,axiom,
% 173.13/173.30 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 173.13/173.30 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_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_a),tc_HOL_Obool))))
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_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_a),tc_HOL_Obool)))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I7_J,axiom,
% 173.13/173.30 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I2_J,axiom,
% 173.13/173.30 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I8_J,axiom,
% 173.13/173.30 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_MGT__alternI,axiom,
% 173.13/173.30 ! [V_ca_2,V_Ga_2] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 173.13/173.30 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_the__elem__def,axiom,
% 173.13/173.30 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__def,axiom,
% 173.13/173.30 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_K__record__comp,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,V_ca_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I4_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I3_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I5_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I6_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_ran__map__upd,axiom,
% 173.13/173.30 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 173.13/173.30 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 173.13/173.30 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Least__Suc2,axiom,
% 173.13/173.30 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 173.13/173.30 ( hBOOL(hAPP(V_P_2,V_n_2))
% 173.13/173.30 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 173.13/173.30 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 173.13/173.30 => ( ! [B_k] :
% 173.13/173.30 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 173.13/173.30 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 173.13/173.30 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2)) ) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I9_J,axiom,
% 173.13/173.30 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__triv,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__def,axiom,
% 173.13/173.30 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 173.13/173.30 ( ( V_x_2 = V_a_2
% 173.13/173.30 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 173.13/173.30 & ( V_x_2 != V_a_2
% 173.13/173.30 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__add__right__cancel,axiom,
% 173.13/173.30 ! [V_n_2,V_k_2,V_m_2] :
% 173.13/173.30 ( 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)
% 173.13/173.30 <=> V_m_2 = V_n_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__add__left__cancel,axiom,
% 173.13/173.30 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.30 ( 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)
% 173.13/173.30 <=> V_m_2 = V_n_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__add__assoc,axiom,
% 173.13/173.30 ! [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)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__add__left__commute,axiom,
% 173.13/173.30 ! [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)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__add__commute,axiom,
% 173.13/173.30 ! [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) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__idem__iff,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 173.13/173.30 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__upd,axiom,
% 173.13/173.30 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__same,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__apply,axiom,
% 173.13/173.30 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 173.13/173.30 ( ( V_z_2 = V_x_2
% 173.13/173.30 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 173.13/173.30 & ( V_z_2 != V_x_2
% 173.13/173.30 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__twist,axiom,
% 173.13/173.30 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] :
% 173.13/173.30 ( V_a_2 != V_ca_2
% 173.13/173.30 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__other,axiom,
% 173.13/173.30 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 173.13/173.30 ( V_z_2 != V_x_2
% 173.13/173.30 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__idem,axiom,
% 173.13/173.30 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 173.13/173.30 ( hAPP(V_f_2,V_x_2) = V_y_2
% 173.13/173.30 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_fun__upd__comp,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__o__map__upd,axiom,
% 173.13/173.30 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__eq__self__zero,axiom,
% 173.13/173.30 ! [V_n,V_m] :
% 173.13/173.30 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 173.13/173.30 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__is__0,axiom,
% 173.13/173.30 ! [V_n_2,V_m_2] :
% 173.13/173.30 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.30 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.30 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Nat_Oadd__0__right,axiom,
% 173.13/173.30 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 173.13/173.30
% 173.13/173.30 fof(fact_plus__nat_Oadd__0,axiom,
% 173.13/173.30 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__Suc__right,axiom,
% 173.13/173.30 ! [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)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__Suc,axiom,
% 173.13/173.30 ! [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)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__Suc__shift,axiom,
% 173.13/173.30 ! [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)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__upd__Some__unfold,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 173.13/173.30 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 173.13/173.30 <=> ( ( V_x_2 = V_a_2
% 173.13/173.30 & V_b_2 = V_y_2 )
% 173.13/173.30 | ( V_x_2 != V_a_2
% 173.13/173.30 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__upd__triv,axiom,
% 173.13/173.30 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 173.13/173.30 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.13/173.30 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__upd__eqD1,axiom,
% 173.13/173.30 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 173.13/173.30 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))
% 173.13/173.30 => V_x_2 = V_y_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_empty__upd__none,axiom,
% 173.13/173.30 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_triple__valid__def,axiom,
% 173.13/173.30 ! [V_t_2,V_n_2,T_a] :
% 173.13/173.30 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 173.13/173.30 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I14_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I13_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I11_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I12_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__is__1,axiom,
% 173.13/173.30 ! [V_n_2,V_m_2] :
% 173.13/173.30 ( 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))
% 173.13/173.30 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.30 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.30 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.30 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_one__is__add,axiom,
% 173.13/173.30 ! [V_n_2,V_m_2] :
% 173.13/173.30 ( 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)
% 173.13/173.30 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.30 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.30 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.30 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__add__upd,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__o__empty,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__upd__nonempty,axiom,
% 173.13/173.30 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__assoc,axiom,
% 173.13/173.30 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__apply,axiom,
% 173.13/173.30 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__eq__dest__lhs,axiom,
% 173.13/173.30 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 173.13/173.30 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2
% 173.13/173.30 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__eq__dest,axiom,
% 173.13/173.30 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 173.13/173.30 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2)
% 173.13/173.30 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_o__eq__elim,axiom,
% 173.13/173.30 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 173.13/173.30 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2)
% 173.13/173.30 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I15_J,axiom,
% 173.13/173.30 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I10_J,axiom,
% 173.13/173.30 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_com_Osize_I16_J,axiom,
% 173.13/173.30 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option_Osize_I2_J,axiom,
% 173.13/173.30 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__0__left,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__0,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_double__zero__sym,axiom,
% 173.13/173.30 ! [V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.30 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 173.13/173.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__0__right,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add_Ocomm__neutral,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__0__iff,axiom,
% 173.13/173.30 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.30 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 173.13/173.30 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 173.13/173.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_double__eq__0__iff,axiom,
% 173.13/173.30 ! [V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_zero__reorient,axiom,
% 173.13/173.30 ! [V_x_2,T_a] :
% 173.13/173.30 ( class_Groups_Ozero(T_a)
% 173.13/173.30 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 173.13/173.30 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__right__imp__eq,axiom,
% 173.13/173.30 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.30 ( class_Groups_Ocancel__semigroup__add(T_a)
% 173.13/173.30 => ( 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)
% 173.13/173.30 => V_b = V_c ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__imp__eq,axiom,
% 173.13/173.30 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 173.13/173.30 => ( 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)
% 173.13/173.30 => V_b = V_c ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__left__imp__eq,axiom,
% 173.13/173.30 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ocancel__semigroup__add(T_a)
% 173.13/173.30 => ( 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)
% 173.13/173.30 => V_b = V_c ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 173.13/173.30 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__right__cancel,axiom,
% 173.13/173.30 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 173.13/173.30 ( class_Groups_Ocancel__semigroup__add(T_a)
% 173.13/173.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)
% 173.13/173.30 <=> V_b_2 = V_ca_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__left__cancel,axiom,
% 173.13/173.30 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Ocancel__semigroup__add(T_a)
% 173.13/173.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)
% 173.13/173.30 <=> V_b_2 = V_ca_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 173.13/173.30 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 173.13/173.30 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Groups_Oab__semigroup__add(T_a)
% 173.13/173.30 => 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)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 173.13/173.30 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 173.13/173.30 ! [V_d,V_c,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 173.13/173.30 ! [V_d,V_c,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 173.13/173.30 ! [V_c,V_a,T_a] :
% 173.13/173.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.30 => 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) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option_Osize_I1_J,axiom,
% 173.13/173.30 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat_Osize_I2_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat_Osize_I4_J,axiom,
% 173.13/173.30 ! [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))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option_Osize_I4_J,axiom,
% 173.13/173.30 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option_Osize_I3_J,axiom,
% 173.13/173.30 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_dom__eq__singleton__conv,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.30 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_the__eq__trivial,axiom,
% 173.13/173.30 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_the__sym__eq__trivial,axiom,
% 173.13/173.30 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bool_Osize_I2_J,axiom,
% 173.13/173.30 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bool_Osize_I1_J,axiom,
% 173.13/173.30 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_option__map__o__sum__case,axiom,
% 173.13/173.30 ! [V_h_2,V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_sum(T_a,T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Sum__Type_Osum_Osum__case(T_a,tc_Option_Ooption(T_d),T_b,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_a,tc_Option_Ooption(T_c),T_b,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_a,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_h_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat__size,axiom,
% 173.13/173.30 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 173.13/173.30
% 173.13/173.30 fof(fact_dom__option__map,axiom,
% 173.13/173.30 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__dom,axiom,
% 173.13/173.30 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 173.13/173.30 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 173.13/173.30 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_dom__eq__empty__conv,axiom,
% 173.13/173.30 ! [V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.30 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_dom__empty,axiom,
% 173.13/173.30 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat_Osize_I3_J,axiom,
% 173.13/173.30 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) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_nat_Osize_I1_J,axiom,
% 173.13/173.30 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_sum__case__KK,axiom,
% 173.13/173.30 ! [V_x_2,V_a_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_a_2),hAPP(c_COMBK(T_a,T_c),V_a_2)),V_x_2) = V_a_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_dom__fun__upd,axiom,
% 173.13/173.30 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 173.13/173.30 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 173.13/173.30 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,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)))) )
% 173.13/173.30 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 173.13/173.30 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__add__upd__left,axiom,
% 173.13/173.30 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 173.13/173.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 173.13/173.30 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_sum__case__weak__cong,axiom,
% 173.13/173.30 ! [V_g_2,V_f_2,T_b,T_c,T_a,V_t_2,V_s_2] :
% 173.13/173.30 ( V_s_2 = V_t_2
% 173.13/173.30 => hAPP(c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f_2,V_g_2),V_t_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_sum__case__inject,axiom,
% 173.13/173.30 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_b,T_c,T_a] :
% 173.13/173.30 ( c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_g1_2,V_g2_2)
% 173.13/173.30 => ~ ( V_f1_2 = V_g1_2
% 173.13/173.30 => V_f2_2 != V_g2_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__imp__upd__le,axiom,
% 173.13/173.30 ! [V_y_2,V_x_2,V_m2_2,V_m1_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2)
% 173.13/173.30 => c_Map_Omap__le(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m1_2),V_x_2),c_Option_Ooption_ONone(T_b)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m2_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bool_Osize_I3_J,axiom,
% 173.13/173.30 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_bool_Osize_I4_J,axiom,
% 173.13/173.30 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_comp__cong,axiom,
% 173.13/173.30 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 173.13/173.30 ( 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))
% 173.13/173.30 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_ospec,axiom,
% 173.13/173.30 ! [V_x_2,V_P_2,V_A_2,T_a] :
% 173.13/173.30 ( ! [B_x] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Option_Oset(T_a,V_A_2)))
% 173.13/173.30 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.30 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 173.13/173.30 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_equalityCE,axiom,
% 173.13/173.30 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 173.13/173.30 ( V_A_2 = V_B_2
% 173.13/173.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.30 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 173.13/173.30 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_emptyE,axiom,
% 173.13/173.30 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insertCI,axiom,
% 173.13/173.30 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 173.13/173.30 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 173.13/173.30 => V_a_2 = V_b_2 )
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insertE,axiom,
% 173.13/173.30 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 173.13/173.30 => ( V_a_2 != V_b_2
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_DiffI,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_DiffE,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.30 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_mem__def,axiom,
% 173.13/173.30 ! [V_A_2,V_x_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.30 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__iff,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.30 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__idemp,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_eqset__imp__iff,axiom,
% 173.13/173.30 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 173.13/173.30 ( V_A_2 = V_B_2
% 173.13/173.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.30 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_eqelem__imp__iff,axiom,
% 173.13/173.30 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 173.13/173.30 ( V_x_2 = V_y_2
% 173.13/173.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.30 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_eq__mem__trans,axiom,
% 173.13/173.30 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 173.13/173.30 ( V_a_2 = V_b_2
% 173.13/173.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_DiffD1,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_DiffD2,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.30 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__refl,axiom,
% 173.13/173.30 ! [V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,V_f_2,V_f_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__antisym,axiom,
% 173.13/173.30 ! [V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 173.13/173.30 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_f_2)
% 173.13/173.30 => V_f_2 = V_g_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__trans,axiom,
% 173.13/173.30 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2)
% 173.13/173.30 => ( c_Map_Omap__le(T_a,T_b,V_m2_2,V_m3_2)
% 173.13/173.30 => c_Map_Omap__le(T_a,T_b,V_m1_2,V_m3_2) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__Diff1,axiom,
% 173.13/173.30 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__Diff__if,axiom,
% 173.13/173.30 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 173.13/173.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) )
% 173.13/173.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_diff__eq__diff__eq,axiom,
% 173.13/173.30 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2)
% 173.13/173.30 => ( V_a_2 = V_b_2
% 173.13/173.30 <=> V_ca_2 = V_d_2 ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__Diff,axiom,
% 173.13/173.30 ! [V_A_2,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.30 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__insert__absorb,axiom,
% 173.13/173.30 ! [V_A_2,V_x_2,T_a] :
% 173.13/173.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_right__minus__eq,axiom,
% 173.13/173.30 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.30 <=> V_a_2 = V_b_2 ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_eq__iff__diff__eq__0,axiom,
% 173.13/173.30 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.30 => ( V_a_2 = V_b_2
% 173.13/173.30 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_diff__self,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_diff__0__right,axiom,
% 173.13/173.30 ! [V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_add__diff__cancel,axiom,
% 173.13/173.30 ! [V_b,V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.30 => 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 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_diff__add__cancel,axiom,
% 173.13/173.30 ! [V_b,V_a,T_a] :
% 173.13/173.30 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.30 => 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 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__cancel,axiom,
% 173.13/173.30 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__empty,axiom,
% 173.13/173.30 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 173.13/173.30
% 173.13/173.30 fof(fact_empty__Diff,axiom,
% 173.13/173.30 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_equals0D,axiom,
% 173.13/173.30 ! [V_a_2,T_a,V_A_2] :
% 173.13/173.30 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.30 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_empty__iff,axiom,
% 173.13/173.30 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_ex__in__conv,axiom,
% 173.13/173.30 ! [V_A_2,T_a] :
% 173.13/173.30 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.30 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_all__not__in__conv,axiom,
% 173.13/173.30 ! [V_A_2,T_a] :
% 173.13/173.30 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__absorb,axiom,
% 173.13/173.30 ! [V_A_2,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.30 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insertI2,axiom,
% 173.13/173.30 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 173.13/173.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__ident,axiom,
% 173.13/173.30 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 173.13/173.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.30 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)
% 173.13/173.30 <=> V_A_2 = V_B_2 ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__iff,axiom,
% 173.13/173.30 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 173.13/173.30 <=> ( V_a_2 = V_b_2
% 173.13/173.30 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insertI1,axiom,
% 173.13/173.30 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__def,axiom,
% 173.13/173.30 ! [V_m_092_060_094isub_0622_2,V_m_092_060_094isub_0621_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_m_092_060_094isub_0621_2,V_m_092_060_094isub_0622_2)
% 173.13/173.30 <=> ! [B_x] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Map_Odom(T_a,T_b,V_m_092_060_094isub_0621_2)))
% 173.13/173.30 => hAPP(V_m_092_060_094isub_0621_2,B_x) = hAPP(V_m_092_060_094isub_0622_2,B_x) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__upd,axiom,
% 173.13/173.30 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 173.13/173.30 => c_Map_Omap__le(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_a_2),V_b_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_a_2),V_b_2)) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__map__add,axiom,
% 173.13/173.30 ! [V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_g_2,V_f_2)) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__iff__map__add__commute,axiom,
% 173.13/173.30 ! [V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2))
% 173.13/173.30 <=> c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2) = c_Map_Omap__add(T_a,T_b,V_g_2,V_f_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__add__le__mapI,axiom,
% 173.13/173.30 ! [V_g_2,V_h_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_h_2)
% 173.13/173.30 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2)
% 173.13/173.30 => ( c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2))
% 173.13/173.30 => c_Map_Omap__le(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2),V_h_2) ) ) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__add__le__mapE,axiom,
% 173.13/173.30 ! [V_h_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.30 ( c_Map_Omap__le(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2),V_h_2)
% 173.13/173.30 => c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_map__le__empty,axiom,
% 173.13/173.30 ! [V_g_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_g_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_insert__Diff__single,axiom,
% 173.13/173.30 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__insert2,axiom,
% 173.13/173.30 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_Diff__insert,axiom,
% 173.13/173.30 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_singletonE,axiom,
% 173.13/173.30 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.30 => V_b_2 = V_a_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_singleton__iff,axiom,
% 173.13/173.30 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.30 <=> V_b_2 = V_a_2 ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_domIff,axiom,
% 173.13/173.30 ! [V_m_2,T_b,V_a_2,T_a] :
% 173.13/173.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 173.13/173.30 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 173.13/173.30
% 173.13/173.30 fof(fact_domI,axiom,
% 173.13/173.30 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 173.13/173.31 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 173.13/173.31 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 173.13/173.31 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 173.13/173.31 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 173.13/173.31 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 173.13/173.31 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 173.13/173.31 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ranI,axiom,
% 173.13/173.31 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 173.13/173.31 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_elem__set,axiom,
% 173.13/173.31 ! [V_xo_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 173.13/173.31 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_upd__None__map__le,axiom,
% 173.13/173.31 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)),V_f_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_dom__minus,axiom,
% 173.13/173.31 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 173.13/173.31 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__diff__def,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.31 ( class_Groups_Ominus(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_bot__empty__eq,axiom,
% 173.13/173.31 ! [V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__upd__None__restrict,axiom,
% 173.13/173.31 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__apply,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.31 ( class_Groups_Ominus(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__upd__restrict__conv,axiom,
% 173.13/173.31 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__fun__upd,axiom,
% 173.13/173.31 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 173.13/173.31 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 173.13/173.31 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__upd__restrict,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 173.13/173.31 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)
% 173.13/173.31 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__upd__image,axiom,
% 173.13/173.31 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pred__equals__eq,axiom,
% 173.13/173.31 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.31 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
% 173.13/173.31 <=> V_R_2 = V_S_2 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__eqI,axiom,
% 173.13/173.31 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 173.13/173.31 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__image,axiom,
% 173.13/173.31 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__ident,axiom,
% 173.13/173.31 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_rev__image__eqI,axiom,
% 173.13/173.31 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_imageI,axiom,
% 173.13/173.31 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__iff,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 173.13/173.31 <=> ? [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.31 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_empty__is__image,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)
% 173.13/173.31 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__empty,axiom,
% 173.13/173.31 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__is__empty,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.31 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__insert,axiom,
% 173.13/173.31 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__compose,axiom,
% 173.13/173.31 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 173.13/173.31 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 173.13/173.31 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diffs0__imp__equal,axiom,
% 173.13/173.31 ! [V_n,V_m] :
% 173.13/173.31 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => V_m = V_n ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__self__eq__0,axiom,
% 173.13/173.31 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__nat_Odiff__0,axiom,
% 173.13/173.31 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__0__eq__0,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__Suc__Suc,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__diff__diff,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__cancel2,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__cancel,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__diff__left,axiom,
% 173.13/173.31 ! [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)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__add__inverse,axiom,
% 173.13/173.31 ! [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 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__add__inverse2,axiom,
% 173.13/173.31 ! [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 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__in,axiom,
% 173.13/173.31 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_insert__image,axiom,
% 173.13/173.31 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__map__empty,axiom,
% 173.13/173.31 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__add__0,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__constant__conv,axiom,
% 173.13/173.31 ! [V_ca_2,T_b,T_a,V_A_2] :
% 173.13/173.31 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.31 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__Suc,axiom,
% 173.13/173.31 ! [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)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__out,axiom,
% 173.13/173.31 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__map__insert,axiom,
% 173.13/173.31 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__map__upd,axiom,
% 173.13/173.31 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__map__def,axiom,
% 173.13/173.31 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__map__to__empty,axiom,
% 173.13/173.31 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__constant,axiom,
% 173.13/173.31 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_eq__mem,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 173.13/173.31 <=> V_x_2 = V_y_2 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Body1,axiom,
% 173.13/173.31 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 173.13/173.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 173.13/173.31 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 173.13/173.31 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 173.13/173.31 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 173.13/173.31 | ? [B_x,B_y] :
% 173.13/173.31 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 173.13/173.31 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 173.13/173.31 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Body__sound__lemma,axiom,
% 173.13/173.31 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.31 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 173.13/173.31 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_hoare__derivs_OBody,axiom,
% 173.13/173.31 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 173.13/173.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 173.13/173.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ran__restrictD,axiom,
% 173.13/173.31 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2))))
% 173.13/173.31 => ? [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.31 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__upd__same,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__complement__singleton__eq,axiom,
% 173.13/173.31 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pair__box_Osize_I1_J,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_b,T_a] : c_Nitpick_Opair__box_Opair__box__size(T_a,T_b,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_a,T_b,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))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__insert,axiom,
% 173.13/173.31 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 173.13/173.31 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Powp__def,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 173.13/173.31 <=> ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup1E,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 173.13/173.31 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup1CI,axiom,
% 173.13/173.31 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 173.13/173.31 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 173.13/173.31 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_UnE,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_UnCI,axiom,
% 173.13/173.31 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 173.13/173.31 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__empty,axiom,
% 173.13/173.31 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__uminus,axiom,
% 173.13/173.31 ! [V_A_2,T_a] :
% 173.13/173.31 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ComplI,axiom,
% 173.13/173.31 ! [V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__Diff__eq,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__commute,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_fun__Compl__def,axiom,
% 173.13/173.31 ! [V_x_2,V_A_2,T_b,T_a] :
% 173.13/173.31 ( class_Groups_Ouminus(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__fun__def,axiom,
% 173.13/173.31 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_double__compl,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup_Oidem,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__idem,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_uminus__apply,axiom,
% 173.13/173.31 ! [V_x_2,V_A_2,T_b,T_a] :
% 173.13/173.31 ( class_Groups_Ouminus(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup_Ocommute,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I5_J,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__commute,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup_Oleft__idem,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I8_J,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__left__idem,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup_Oleft__commute,axiom,
% 173.13/173.31 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I7_J,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__left__commute,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_compl__eq__compl__iff,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 173.13/173.31 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup_Oassoc,axiom,
% 173.13/173.31 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I6_J,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__assoc,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__apply,axiom,
% 173.13/173.31 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup1I1,axiom,
% 173.13/173.31 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 173.13/173.31 ( hBOOL(hAPP(V_A_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup1I2,axiom,
% 173.13/173.31 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 173.13/173.31 ( hBOOL(hAPP(V_B_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.31 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
% 173.13/173.31 <=> V_A_2 = V_B_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__def,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 <=> ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.31 => ! [B_xa] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 173.13/173.31 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 173.13/173.31 => B_x = B_xa ) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_double__complement,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__absorb,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__commute,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__left__absorb,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__left__commute,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__eq__Compl__iff,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)
% 173.13/173.31 <=> V_A_2 = V_B_2 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__assoc,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_bex__Un,axiom,
% 173.13/173.31 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( ? [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 & hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.31 <=> ( ? [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.31 & hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.31 | ? [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 173.13/173.31 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ball__Un,axiom,
% 173.13/173.31 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.31 <=> ( ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.31 & ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__id2,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__minus,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_equation__minus__iff,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 173.13/173.31 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__equation__iff,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 173.13/173.31 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_neg__equal__iff__equal,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 173.13/173.31 <=> V_a_2 = V_b_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pair__box_Oinject,axiom,
% 173.13/173.31 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.31 ( c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_H_2,V_b_H_2)
% 173.13/173.31 <=> ( V_a_2 = V_a_H_2
% 173.13/173.31 & V_b_2 = V_b_H_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__contraD,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( V_x_2 != V_y_2
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.31 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__iff,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 173.13/173.31 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__onD,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.31 => V_x_2 = V_y_2 ) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__Suc,axiom,
% 173.13/173.31 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__imageI2,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2)
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__diff,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_neg__equal__zero,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.31 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 173.13/173.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_neg__equal__0__iff__equal,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_equal__neg__zero,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.31 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 173.13/173.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_neg__0__equal__iff__equal,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 173.13/173.31 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__zero,axiom,
% 173.13/173.31 ! [T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__eq__bot__iff,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 173.13/173.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 173.13/173.31 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 173.13/173.31 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__bot__right,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__bot__left,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__add__cancel,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_add__minus__cancel,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__add,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__add__distrib,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__iff,axiom,
% 173.13/173.31 ! [V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 173.13/173.31 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ComplD,axiom,
% 173.13/173.31 ! [V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 173.13/173.31 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ComplE,axiom,
% 173.13/173.31 ! [V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 173.13/173.31 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__diff__eq,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__Some,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__iff,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_UnI1,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_UnI2,axiom,
% 173.13/173.31 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__empty,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__empty__right,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__empty__left,axiom,
% 173.13/173.31 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__insert__left,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__insert__right,axiom,
% 173.13/173.31 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_image__Un,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,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_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Diff__cancel,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Diff__cancel2,axiom,
% 173.13/173.31 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Diff,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__add__nat,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__Un__eq,axiom,
% 173.13/173.31 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__imageI,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2)
% 173.13/173.31 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_comp__inj__on,axiom,
% 173.13/173.31 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_comp__inj__on__iff,axiom,
% 173.13/173.31 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
% 173.13/173.31 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_right__minus,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 173.13/173.31 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_left__minus,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ab__left__minus,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__unique,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__0,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__minus__eq__add,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Rings_Ocomm__ring__1(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_ab__diff__minus,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__def,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Groups_Ogroup__add(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_insert__is__Un,axiom,
% 173.13/173.31 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__map__add__dom,axiom,
% 173.13/173.31 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2))
% 173.13/173.31 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_dom__map__add,axiom,
% 173.13/173.31 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__fun__updI,axiom,
% 173.13/173.31 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pair__box_Osize_I2_J,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pair__box_Orecs,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__rec(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_pair__box_Osimps_I2_J,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__case(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__comp,axiom,
% 173.13/173.31 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))
% 173.13/173.31 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))))
% 173.13/173.31 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__Un,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.31 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.31 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_f__the__inv__into__f,axiom,
% 173.13/173.31 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.31 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__def,axiom,
% 173.13/173.31 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__double__eq__0__iff,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Int_Oring__char__0(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_add__eq__if,axiom,
% 173.13/173.31 ! [V_n,V_m] :
% 173.13/173.31 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 173.13/173.31 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => 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)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf1E,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 173.13/173.31 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 173.13/173.31 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf1I,axiom,
% 173.13/173.31 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 173.13/173.31 ( hBOOL(hAPP(V_A_2,V_x_2))
% 173.13/173.31 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_IntE,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_IntI,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_one__reorient,axiom,
% 173.13/173.31 ! [V_x_2,T_a] :
% 173.13/173.31 ( class_Groups_Oone(T_a)
% 173.13/173.31 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 173.13/173.31 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__assoc,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__left__commute,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__left__absorb,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__commute,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__absorb,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf1D2,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 173.13/173.31 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf1D1,axiom,
% 173.13/173.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 173.13/173.31 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__apply,axiom,
% 173.13/173.31 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__assoc,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I2_J,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf_Oassoc,axiom,
% 173.13/173.31 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__left__commute,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I3_J,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf_Oleft__commute,axiom,
% 173.13/173.31 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__left__idem,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I4_J,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf_Oleft__idem,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__commute,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__aci_I1_J,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf_Ocommute,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__idem,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf_Oidem,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__fun__def,axiom,
% 173.13/173.31 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__1,axiom,
% 173.13/173.31 ! [T_a] :
% 173.13/173.31 ( class_Rings_Oring__1(T_a)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__bot__left,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__bot__right,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__inf__distrib2,axiom,
% 173.13/173.31 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.31 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__distrib2,axiom,
% 173.13/173.31 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.31 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__inf__distrib1,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__distrib1,axiom,
% 173.13/173.31 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_sup__inf__absorb,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__sup__absorb,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Olattice(T_a)
% 173.13/173.31 => 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 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_IntD2,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_IntD1,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__iff,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__empty__left,axiom,
% 173.13/173.31 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__empty__right,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_disjoint__iff__not__equal,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 <=> ! [B_x] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.31 => ! [B_xa] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 173.13/173.31 => B_x != B_xa ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_insert__inter__insert,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Int__crazy,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Int__distrib2,axiom,
% 173.13/173.31 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__Un__distrib2,axiom,
% 173.13/173.31 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Int__distrib,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__Un__distrib,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Int2,axiom,
% 173.13/173.31 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Int__distrib2,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__Diff,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Int__distrib,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__Int,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.31 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_restrict__restrict,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__Int__eq,axiom,
% 173.13/173.31 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__odd__nonzero,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Int_Oring__char__0(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => 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)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_compl__inf__bot,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inf__compl__bot,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__eq,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_compl__sup,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_compl__inf,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__right,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__left,axiom,
% 173.13/173.31 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 173.13/173.31 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 173.13/173.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__right__if0,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__left__if0,axiom,
% 173.13/173.31 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 173.13/173.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__right__if1,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Int__insert__left__if1,axiom,
% 173.13/173.31 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 173.13/173.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__disjoint,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__triv,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Un__Diff__Int,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Un,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Int,axiom,
% 173.13/173.31 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_One__nat__def,axiom,
% 173.13/173.31 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__disjoint,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__disjoint2,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__eq__plus1,axiom,
% 173.13/173.31 ! [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)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__eq__plus1__left,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 173.13/173.31 ! [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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_diff__Suc__1,axiom,
% 173.13/173.31 ! [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 ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__Un,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Compl__Int,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__Compl,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Diff__eq,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_dom__restrict,axiom,
% 173.13/173.31 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__0,axiom,
% 173.13/173.31 ! [T_a] :
% 173.13/173.31 ( class_Rings_Oring__1(T_a)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__add,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Rings_Oring__1(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__diff,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Rings_Oring__1(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__minus,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Rings_Oring__1(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_map__add__comm,axiom,
% 173.13/173.31 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 173.13/173.31 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.31 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__f__eq,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__f__f,axiom,
% 173.13/173.31 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__onto,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_inj__on__the__inv__into,axiom,
% 173.13/173.31 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_one__neq__zero,axiom,
% 173.13/173.31 ! [T_a] :
% 173.13/173.31 ( class_Rings_Ozero__neq__one(T_a)
% 173.13/173.31 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_zero__neq__one,axiom,
% 173.13/173.31 ! [T_a] :
% 173.13/173.31 ( class_Rings_Ozero__neq__one(T_a)
% 173.13/173.31 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_compl__unique,axiom,
% 173.13/173.31 ! [V_y,V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 173.13/173.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 173.13/173.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Ints__odd__less__0,axiom,
% 173.13/173.31 ! [V_a_2,T_a] :
% 173.13/173.31 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 173.13/173.31 ! [V_n_2,T_a] :
% 173.13/173.31 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.31 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_the__inv__into__into,axiom,
% 173.13/173.31 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__diff__1,axiom,
% 173.13/173.31 ! [V_n] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.31 => 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 ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__pred_H,axiom,
% 173.13/173.31 ! [V_n] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.31 => 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))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__eq__if,axiom,
% 173.13/173.31 ! [V_n,V_m] :
% 173.13/173.31 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.31 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.31 => 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)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_order__refl,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Orderings_Opreorder(T_a)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_UNIV__I,axiom,
% 173.13/173.31 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_negative__zless,axiom,
% 173.13/173.31 ! [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))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_equalityI,axiom,
% 173.13/173.31 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.31 => V_A_2 = V_B_2 ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_subsetD,axiom,
% 173.13/173.31 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_empty__subsetI,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_less__zeroE,axiom,
% 173.13/173.31 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__mono,axiom,
% 173.13/173.31 ! [V_n,V_m] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_lessI,axiom,
% 173.13/173.31 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_zero__less__Suc,axiom,
% 173.13/173.31 ! [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))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_negative__zless__0,axiom,
% 173.13/173.31 ! [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))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_int__Suc,axiom,
% 173.13/173.31 ! [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)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_int__1,axiom,
% 173.13/173.31 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) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_less__1__mult,axiom,
% 173.13/173.31 ! [V_n,V_m,T_a] :
% 173.13/173.31 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 173.13/173.31 => 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))) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_comm__semiring__class_Odistrib,axiom,
% 173.13/173.31 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Ocomm__semiring(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_combine__common__factor,axiom,
% 173.13/173.31 ! [V_c,V_b,V_e,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Osemiring(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_of__nat__0__less__iff,axiom,
% 173.13/173.31 ! [V_n_2,T_a] :
% 173.13/173.31 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__mult__right,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Oring(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__mult__left,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Oring(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__mult__commute,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Oring(T_a)
% 173.13/173.31 => 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)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_minus__mult__minus,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Rings_Oring(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_square__eq__iff,axiom,
% 173.13/173.31 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.31 ( class_Rings_Oidom(T_a)
% 173.13/173.31 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 173.13/173.31 <=> ( V_a_2 = V_b_2
% 173.13/173.31 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_times_Oidem,axiom,
% 173.13/173.31 ! [V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__idem,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__left__idem,axiom,
% 173.13/173.31 ! [V_b,V_a,T_a] :
% 173.13/173.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.31 => 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) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_rev__predicate1D,axiom,
% 173.13/173.31 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 173.13/173.31 ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 173.13/173.31 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_predicate1D,axiom,
% 173.13/173.31 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 173.13/173.31 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.31 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__less__mono2,axiom,
% 173.13/173.31 ! [V_k,V_j,V_i] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 173.13/173.31 => 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))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__less__mono1,axiom,
% 173.13/173.31 ! [V_k,V_j,V_i] :
% 173.13/173.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 173.13/173.31 => 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))) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__less__cancel2,axiom,
% 173.13/173.31 ! [V_n_2,V_k_2,V_m_2] :
% 173.13/173.31 ( 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)))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_mult__less__cancel1,axiom,
% 173.13/173.31 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.31 ( 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)))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_nat__0__less__mult__iff,axiom,
% 173.13/173.31 ! [V_n_2,V_m_2] :
% 173.13/173.31 ( 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)))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 173.13/173.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_Suc__mult__less__cancel1,axiom,
% 173.13/173.31 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.31 ( 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)))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_order__less__irrefl,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Orderings_Opreorder(T_a)
% 173.13/173.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_subset__UNIV,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_top__greatest,axiom,
% 173.13/173.31 ! [V_x,T_a] :
% 173.13/173.31 ( class_Orderings_Otop(T_a)
% 173.13/173.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_subset__refl,axiom,
% 173.13/173.31 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_top__apply,axiom,
% 173.13/173.31 ! [V_x_2,T_b,T_a] :
% 173.13/173.31 ( class_Orderings_Otop(T_a)
% 173.13/173.31 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_linorder__not__less,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Orderings_Olinorder(T_a)
% 173.13/173.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_linorder__not__le,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Orderings_Olinorder(T_a)
% 173.13/173.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_linorder__neq__iff,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Orderings_Olinorder(T_a)
% 173.13/173.31 => ( V_x_2 != V_y_2
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_not__less__iff__gr__or__eq,axiom,
% 173.13/173.31 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.31 ( class_Orderings_Olinorder(T_a)
% 173.13/173.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 173.13/173.31 | V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.31
% 173.13/173.31 fof(fact_le__fun__def,axiom,
% 173.13/173.31 ! [V_g_2,V_f_2,T_a,T_b] :
% 173.13/173.31 ( class_Orderings_Oord(T_b)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.13/173.32 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__le__less__linear,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__linear,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_psubset__eq,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 & V_A_2 != V_B_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__fun__def,axiom,
% 173.13/173.32 ! [V_g_2,V_f_2,T_a,T_b] :
% 173.13/173.32 ( class_Orderings_Oord(T_b)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.13/173.32 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__le,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 & V_x_2 != V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__le__not__le,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_set__eq__subset,axiom,
% 173.13/173.32 ! [T_a,V_B_2,V_A_2] :
% 173.13/173.32 ( V_A_2 = V_B_2
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__eq__iff,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( V_x_2 = V_y_2
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__iff__psubset__eq,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 | V_A_2 = V_B_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__le__less,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 | V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__less__linear,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 | V_x = V_y
% 173.13/173.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_leI,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__leE,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__antisym__conv3,axiom,
% 173.13/173.32 ! [V_x_2,V_y_2,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__antisym__conv1,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__neq__le__trans,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( V_a != V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I12_J,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( V_a != V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__neqE,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( V_x != V_y
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__imp__neq,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => V_x != V_y ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__not__sym,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_leD,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_equalityD1,axiom,
% 173.13/173.32 ! [T_a,V_B_2,V_A_2] :
% 173.13/173.32 ( V_A_2 = V_B_2
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_equalityD2,axiom,
% 173.13/173.32 ! [T_a,V_B_2,V_A_2] :
% 173.13/173.32 ( V_A_2 = V_B_2
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__eq__refl,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( V_x = V_y
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_psubset__imp__subset,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__imp__le,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__imp__not__less,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__antisym__conv2,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__funD,axiom,
% 173.13/173.32 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 173.13/173.32 ( class_Orderings_Oord(T_b)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__imp__not__eq,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => V_x != V_y ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__imp__not__eq2,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => V_y != V_x ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__le__imp__less__or__eq,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 | V_x = V_y ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__antisym__conv,axiom,
% 173.13/173.32 ! [V_x_2,V_y_2,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__le__neq__trans,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( V_a != V_b
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I11_J,axiom,
% 173.13/173.32 ! [V_a,V_b,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.32 => ( V_a != V_b
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__asym_H,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I9_J,axiom,
% 173.13/173.32 ! [V_a,V_b,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_ord__eq__less__trans,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oord(T_a)
% 173.13/173.32 => ( V_a = V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I1_J,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( V_a = V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_ord__eq__le__trans,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oord(T_a)
% 173.13/173.32 => ( V_a = V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I3_J,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( V_a = V_b
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_psubset__subset__trans,axiom,
% 173.13/173.32 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_ord__less__eq__trans,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oord(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( V_b = V_c
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I2_J,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.32 => ( V_b = V_c
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__trans,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__le__trans,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I10_J,axiom,
% 173.13/173.32 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I7_J,axiom,
% 173.13/173.32 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__psubset__trans,axiom,
% 173.13/173.32 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__trans,axiom,
% 173.13/173.32 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_ord__le__eq__trans,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Orderings_Oord(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( V_b = V_c
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I4_J,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.32 => ( V_b = V_c
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__le__less__trans,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__antisym,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => V_x = V_y ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__trans,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I8_J,axiom,
% 173.13/173.32 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I5_J,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => V_x = V_y ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_xt1_I6_J,axiom,
% 173.13/173.32 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.32 ( class_Orderings_Oorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_order__less__asym,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Opreorder(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_equalityE,axiom,
% 173.13/173.32 ! [T_a,V_B_2,V_A_2] :
% 173.13/173.32 ( V_A_2 = V_B_2
% 173.13/173.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__funE,axiom,
% 173.13/173.32 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 173.13/173.32 ( class_Orderings_Oord(T_b)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__le__cases,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__cases,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Olinorder(T_a)
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => ( V_x != V_y
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__neqE__linordered__idom,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.32 => ( V_x != V_y
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__not__refl,axiom,
% 173.13/173.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__mult,axiom,
% 173.13/173.32 ! [V_n,V_m,T_a] :
% 173.13/173.32 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_nat__neq__iff,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( V_m_2 != V_n_2
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_nat__mult__commute,axiom,
% 173.13/173.32 ! [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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__eq__iff,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,T_a] :
% 173.13/173.32 ( class_Nat_Osemiring__char__0(T_a)
% 173.13/173.32 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
% 173.13/173.32 <=> V_m_2 = V_n_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__less__iff,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__le__iff,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_nat__mult__assoc,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_linorder__neqE__nat,axiom,
% 173.13/173.32 ! [V_y,V_x] :
% 173.13/173.32 ( V_x != V_y
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__irrefl__nat,axiom,
% 173.13/173.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__not__refl2,axiom,
% 173.13/173.32 ! [V_m,V_n] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 173.13/173.32 => V_m != V_n ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__not__refl3,axiom,
% 173.13/173.32 ! [V_t,V_s] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 173.13/173.32 => V_s != V_t ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__imp__of__nat__less,axiom,
% 173.13/173.32 ! [V_n,V_m,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__less__imp__less,axiom,
% 173.13/173.32 ! [V_n,V_m,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_nat__less__cases,axiom,
% 173.13/173.32 ! [V_P_2,V_n_2,V_m_2] :
% 173.13/173.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 173.13/173.32 => ( ( V_m_2 = V_n_2
% 173.13/173.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 173.13/173.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 173.13/173.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__0__le__iff,axiom,
% 173.13/173.32 ! [V_n,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__le__imp__of__nat,axiom,
% 173.13/173.32 ! [V_m,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_of__nat__less__0__iff,axiom,
% 173.13/173.32 ! [V_m,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.32 => ~ 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_split__mult__neg__le,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__cancel__semiring(T_a)
% 173.13/173.32 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_split__mult__pos__le,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__left__le__imp__le,axiom,
% 173.13/173.32 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__right__le__imp__le,axiom,
% 173.13/173.32 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__imp__less__left,axiom,
% 173.13/173.32 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__left__less__imp__less,axiom,
% 173.13/173.32 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__imp__less__right,axiom,
% 173.13/173.32 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__right__less__imp__less,axiom,
% 173.13/173.32 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__mono_H,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__le__less__imp__less,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__le__imp__less,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__mono_H,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__left__mono__neg,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__right__mono__neg,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__left__mono__neg,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__right__mono__neg,axiom,
% 173.13/173.32 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__mult__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__comm__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__right__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__mult__strict__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__strict__right__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__nonpos__nonpos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__neg__neg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__nonpos__nonneg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__cancel__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__neg__pos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__le__cancel__left__neg,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__cancel__left__neg,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__less__mult__pos2,axiom,
% 173.13/173.32 ! [V_a,V_b,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__less__mult__pos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__nonneg__nonpos2,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__cancel__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__nonneg__nonpos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__cancel__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__pos__neg2,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__pos__neg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__nonneg__nonneg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__cancel__semiring(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__pos__pos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__le__cancel__left__pos,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__cancel__left__pos,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__cancel__left__disj,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__less__cancel__right__disj,axiom,
% 173.13/173.32 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)))
% 173.13/173.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__le__0__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__le__mult__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( 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_2),V_b_2)))
% 173.13/173.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 173.13/173.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__less__int__conv,axiom,
% 173.13/173.32 ! [V_n_2] :
% 173.13/173.32 ( 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)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zero__le__square,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__square__less__zero,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring(T_a)
% 173.13/173.32 => ~ 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 173.13/173.32 ! [V_ry,V_rx,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 173.13/173.32 ! [V_ry,V_rx,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zless__int,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( 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)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 173.13/173.32 ! [V_rx,V_ly,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 173.13/173.32 ! [V_rx,V_ly,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 173.13/173.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 173.13/173.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 173.13/173.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__le__less__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__le__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zless__iff__Suc__zadd,axiom,
% 173.13/173.32 ! [V_z_2,V_w_2] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 173.13/173.32 <=> ? [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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__zero__left,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Omult__zero(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__zero__right,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Omult__zero(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__eq__0__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Oring__no__zero__divisors(T_a)
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_no__zero__divisors,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ono__zero__divisors(T_a)
% 173.13/173.32 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_divisors__zero,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ono__zero__divisors(T_a)
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__left__le__one__le,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.32 => 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)) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__right__le__one__le,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.32 => 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)) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__add__iff1,axiom,
% 173.13/173.32 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( 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_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 173.13/173.32 <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__add__iff2,axiom,
% 173.13/173.32 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( 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_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__add__iff1,axiom,
% 173.13/173.32 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( 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_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 173.13/173.32 <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__add__iff2,axiom,
% 173.13/173.32 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Rings_Oordered__ring(T_a)
% 173.13/173.32 => ( 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_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_convex__bound__lt,axiom,
% 173.13/173.32 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.32 => 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)) ) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inj__of__nat,axiom,
% 173.13/173.32 ! [T_a] :
% 173.13/173.32 ( class_Nat_Osemiring__char__0(T_a)
% 173.13/173.32 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Powp__mono,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sum__squares__gt__zero__iff,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
% 173.13/173.32 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__sum__squares__lt__zero,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring(T_a)
% 173.13/173.32 => ~ 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sum__squares__le__zero__iff,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.32 => ( 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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.32 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sum__squares__ge__zero,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__ring(T_a)
% 173.13/173.32 => 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)))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__pos__nonneg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__nonneg__pos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__strict__increasing,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__strict__increasing2,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__neg__nonpos,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__nonpos__neg,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_int__Suc0__eq__1,axiom,
% 173.13/173.32 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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_one__less__mult,axiom,
% 173.13/173.32 ! [V_m,V_n] :
% 173.13/173.32 ( 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))
% 173.13/173.32 => ( 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))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_n__less__n__mult__m,axiom,
% 173.13/173.32 ! [V_m,V_n] :
% 173.13/173.32 ( 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))
% 173.13/173.32 => ( 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))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_n__less__m__mult__n,axiom,
% 173.13/173.32 ! [V_m,V_n] :
% 173.13/173.32 ( 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))
% 173.13/173.32 => ( 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))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inj__image__subset__iff,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.32 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_surj__Compl__image__subset,axiom,
% 173.13/173.32 ! [V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.32 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_convex__bound__le,axiom,
% 173.13/173.32 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Olinordered__semiring__1(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.32 => 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)) ) ) ) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_int__0,axiom,
% 173.13/173.32 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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_int__eq__0__conv,axiom,
% 173.13/173.32 ! [V_n_2] :
% 173.13/173.32 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.32 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_negative__eq__positive,axiom,
% 173.13/173.32 ! [V_m_2,V_n_2] :
% 173.13/173.32 ( 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)
% 173.13/173.32 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.32 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zadd__int,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_zadd__int__left,axiom,
% 173.13/173.32 ! [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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_psubsetD,axiom,
% 173.13/173.32 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_crossproduct__eq,axiom,
% 173.13/173.32 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 173.13/173.32 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> ( V_w_2 = V_x_2
% 173.13/173.32 | V_y_2 = V_z_2 ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 173.13/173.32 ! [V_b,V_m,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_crossproduct__noteq,axiom,
% 173.13/173.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 173.13/173.32 => ( ( V_a_2 != V_b_2
% 173.13/173.32 & V_ca_2 != V_d_2 )
% 173.13/173.32 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__imp__less__left,axiom,
% 173.13/173.32 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__imp__less__right,axiom,
% 173.13/173.32 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__strict__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__strict__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__strict__right__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__cancel__left,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__cancel__right,axiom,
% 173.13/173.32 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_in__mono,axiom,
% 173.13/173.32 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_set__rev__mp,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_set__mp,axiom,
% 173.13/173.32 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_iso__tuple__UNIV__I,axiom,
% 173.13/173.32 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__psubset__empty,axiom,
% 173.13/173.32 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__le__imp__le__left,axiom,
% 173.13/173.32 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__le__imp__le__right,axiom,
% 173.13/173.32 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__mono,axiom,
% 173.13/173.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__left__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__right__mono,axiom,
% 173.13/173.32 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__le__cancel__left,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__le__cancel__right,axiom,
% 173.13/173.32 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_diff__eq__diff__less,axiom,
% 173.13/173.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__1__left,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__1,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__1__right,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult_Ocomm__neutral,axiom,
% 173.13/173.32 ! [V_a,T_a] :
% 173.13/173.32 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_bot__least,axiom,
% 173.13/173.32 ! [V_x,T_a] :
% 173.13/173.32 ( class_Orderings_Obot(T_a)
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_diff__eq__diff__less__eq,axiom,
% 173.13/173.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__supI1,axiom,
% 173.13/173.32 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__supI2,axiom,
% 173.13/173.32 ! [V_a,V_b,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__0,axiom,
% 173.13/173.32 ! [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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__0__right,axiom,
% 173.13/173.32 ! [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) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__is__0,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.32 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__cancel1,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.32 ( 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)
% 173.13/173.32 <=> ( V_m_2 = V_n_2
% 173.13/173.32 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_mult__cancel2,axiom,
% 173.13/173.32 ! [V_n_2,V_k_2,V_m_2] :
% 173.13/173.32 ( 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)
% 173.13/173.32 <=> ( V_m_2 = V_n_2
% 173.13/173.32 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__infI1,axiom,
% 173.13/173.32 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 173.13/173.32 => 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)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__infI2,axiom,
% 173.13/173.32 ! [V_a,V_x,V_b,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 173.13/173.32 => 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)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Suc__mult__cancel1,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.32 ( 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)
% 173.13/173.32 <=> V_m_2 = V_n_2 ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__empty,axiom,
% 173.13/173.32 ! [V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__sup__ord_I3_J,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Olattice(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__ge1,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__sup__ord_I4_J,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Lattices_Olattice(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__ge2,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__iff__sup,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__sup__iff,axiom,
% 173.13/173.32 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__supI1,axiom,
% 173.13/173.32 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__supI2,axiom,
% 173.13/173.32 ! [V_a,V_b,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__absorb2,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__absorb1,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__supI,axiom,
% 173.13/173.32 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 173.13/173.32 => 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)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__least,axiom,
% 173.13/173.32 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 173.13/173.32 => 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)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_sup__mono,axiom,
% 173.13/173.32 ! [V_d,V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__supE,axiom,
% 173.13/173.32 ! [V_x,V_b,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.32 => ( 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))
% 173.13/173.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__minus__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_minus__less__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_neg__less__iff__less,axiom,
% 173.13/173.32 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__sup__ord_I1_J,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Olattice(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__le1,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__sup__ord_I2_J,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Olattice(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__le2,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => 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)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__iff__inf,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__inf__iff,axiom,
% 173.13/173.32 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2)))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__infI1,axiom,
% 173.13/173.32 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.32 => 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)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__infI2,axiom,
% 173.13/173.32 ! [V_a,V_x,V_b,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 173.13/173.32 => 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)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__absorb1,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__absorb2,axiom,
% 173.13/173.32 ! [V_x,V_y,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__infI,axiom,
% 173.13/173.32 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__greatest,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_inf__mono,axiom,
% 173.13/173.32 ! [V_d,V_b,V_c,V_a,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 173.13/173.32 => 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))) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__infE,axiom,
% 173.13/173.32 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.32 => ( 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)))
% 173.13/173.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_UNIV__not__empty,axiom,
% 173.13/173.32 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__less0,axiom,
% 173.13/173.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_neq0__conv,axiom,
% 173.13/173.32 ! [V_n_2] :
% 173.13/173.32 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__nat__zero__code,axiom,
% 173.13/173.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_gr__implies__not0,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.32 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_gr0I,axiom,
% 173.13/173.32 ! [V_n] :
% 173.13/173.32 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_insert__mono,axiom,
% 173.13/173.32 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__insertI2,axiom,
% 173.13/173.32 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__insertI,axiom,
% 173.13/173.32 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_compl__le__compl__iff,axiom,
% 173.13/173.32 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.32 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_compl__mono,axiom,
% 173.13/173.32 ! [V_y,V_x,T_a] :
% 173.13/173.32 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__minus__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_minus__le__iff,axiom,
% 173.13/173.32 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_neg__le__iff__le,axiom,
% 173.13/173.32 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_le__imp__neg__le,axiom,
% 173.13/173.32 ! [V_b,V_a,T_a] :
% 173.13/173.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__mult__distrib2,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__mult__distrib,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Suc__less__SucD,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Suc__lessD,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__SucE,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 173.13/173.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.32 => V_m = V_n ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__trans__Suc,axiom,
% 173.13/173.32 ! [V_k,V_j,V_i] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Suc__lessI,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.32 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__SucI,axiom,
% 173.13/173.32 ! [V_n,V_m] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__antisym,axiom,
% 173.13/173.32 ! [V_m,V_n] :
% 173.13/173.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 173.13/173.32 => V_m = V_n ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__less__less__Suc__eq,axiom,
% 173.13/173.32 ! [V_m_2,V_n_2] :
% 173.13/173.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 173.13/173.32 <=> V_n_2 = V_m_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Suc__less__eq,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( 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)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__Suc__eq,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 173.13/173.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.32 | V_m_2 = V_n_2 ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__less__eq,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2] :
% 173.13/173.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__image__iff,axiom,
% 173.13/173.32 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 173.13/173.32 <=> ? [B_AA] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 173.13/173.32 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_image__mono,axiom,
% 173.13/173.32 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_termination__basic__simps_I2_J,axiom,
% 173.13/173.32 ! [V_y,V_z,V_x] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_termination__basic__simps_I1_J,axiom,
% 173.13/173.32 ! [V_z,V_y,V_x] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__add__less1,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_not__add__less2,axiom,
% 173.13/173.32 ! [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)) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_nat__add__left__cancel__less,axiom,
% 173.13/173.32 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.32 ( 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)))
% 173.13/173.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_trans__less__add1,axiom,
% 173.13/173.32 ! [V_m,V_j,V_i] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_trans__less__add2,axiom,
% 173.13/173.32 ! [V_m,V_j,V_i] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__mono1,axiom,
% 173.13/173.32 ! [V_k,V_j,V_i] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.32 => 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))) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__less__mono,axiom,
% 173.13/173.32 ! [V_l,V_k,V_j,V_i] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 173.13/173.32 => 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))) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_less__add__eq__less,axiom,
% 173.13/173.32 ! [V_n,V_m,V_l,V_k] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 173.13/173.32 => ( 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)
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_add__lessD1,axiom,
% 173.13/173.32 ! [V_k,V_j,V_i] :
% 173.13/173.32 ( 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))
% 173.13/173.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Un__upper1,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Un__upper2,axiom,
% 173.13/173.32 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_subset__Un__eq,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Un__absorb1,axiom,
% 173.13/173.32 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Un__absorb2,axiom,
% 173.13/173.32 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 173.13/173.32
% 173.13/173.32 fof(fact_Un__least,axiom,
% 173.13/173.32 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 173.13/173.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Un__mono,axiom,
% 173.13/173.33 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__lower1,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__lower2,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__absorb2,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__absorb1,axiom,
% 173.13/173.33 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__greatest,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__mono,axiom,
% 173.13/173.33 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__mult__distrib2,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__mult__distrib,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Un__UNIV__left,axiom,
% 173.13/173.33 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Un__UNIV__right,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__UNIV__left,axiom,
% 173.13/173.33 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Int__UNIV__right,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Diff__subset,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Diff__mono,axiom,
% 173.13/173.33 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_double__diff,axiom,
% 173.13/173.33 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__imp__diff__less,axiom,
% 173.13/173.33 ! [V_n,V_k,V_j] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__less__mono2,axiom,
% 173.13/173.33 ! [V_l,V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_subset__inj__on,axiom,
% 173.13/173.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__eq,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 173.13/173.33 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_injD,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 173.13/173.33 => V_x_2 = V_y_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__1,axiom,
% 173.13/173.33 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__1__eq__mult__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 173.13/173.33 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.33 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__1__right,axiom,
% 173.13/173.33 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__eq__1__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.33 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.33 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_pos__add__strict,axiom,
% 173.13/173.33 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__subset__Compl__iff,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__anti__mono,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_thin,axiom,
% 173.13/173.33 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 173.13/173.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
% 173.13/173.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_weaken,axiom,
% 173.13/173.33 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] :
% 173.13/173.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 173.13/173.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_asm,axiom,
% 173.13/173.33 ! [V_Ga_2,V_ts_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 173.13/173.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_eq__add__iff1,axiom,
% 173.13/173.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Oring(T_a)
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 173.13/173.33 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_eq__add__iff2,axiom,
% 173.13/173.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Oring(T_a)
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 173.13/173.33 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__less__one,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__one__less__zero,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__le__one,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__one__le__zero,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => ~ 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__minus__self__iff,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__add__one,axiom,
% 173.13/173.33 ! [V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => 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)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_square__eq__1__iff,axiom,
% 173.13/173.33 ! [V_x_2,T_a] :
% 173.13/173.33 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.33 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.33 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_pred__subset__eq,axiom,
% 173.13/173.33 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_range__composition,axiom,
% 173.13/173.33 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__image__Compl__subset,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__fun,axiom,
% 173.13/173.33 ! [T_c,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sup__top__left,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Obounded__lattice__top(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sup__top__right,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Obounded__lattice__top(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inf__top__left,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Obounded__lattice__top(T_a)
% 173.13/173.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inf__top__right,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Obounded__lattice__top(T_a)
% 173.13/173.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inf__eq__top__iff,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.33 ( class_Lattices_Obounded__lattice__top(T_a)
% 173.13/173.33 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 173.13/173.33 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 173.13/173.33 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_UNIV__option__conv,axiom,
% 173.13/173.33 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__less__Least,axiom,
% 173.13/173.33 ! [V_P_2,V_k_2,T_a] :
% 173.13/173.33 ( class_Orderings_Owellorder(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),c_Orderings_Oord__class_OLeast(T_a,V_P_2)))
% 173.13/173.33 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Least__le,axiom,
% 173.13/173.33 ! [V_k_2,V_P_2,T_a] :
% 173.13/173.33 ( class_Orderings_Owellorder(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Oord__class_OLeast(T_a,V_P_2)),V_k_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_psubset__insert__iff,axiom,
% 173.13/173.33 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 173.13/173.33 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__scale__eq__noteq,axiom,
% 173.13/173.33 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 173.13/173.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 173.13/173.33 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 => ( ( V_a = V_b
% 173.13/173.33 & V_c != V_d )
% 173.13/173.33 => 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)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sum__squares__eq__zero__iff,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__ring__strict(T_a)
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__less__two,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.33 => 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)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( 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_2),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_even__less__0__iff,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__pos__pos,axiom,
% 173.13/173.33 ! [V_b,V_a,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__neg__neg,axiom,
% 173.13/173.33 ! [V_b,V_a,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__iff__diff__less__0,axiom,
% 173.13/173.33 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( 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_2),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__nonneg__nonneg,axiom,
% 173.13/173.33 ! [V_b,V_a,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__nonneg__eq__0__iff,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__increasing,axiom,
% 173.13/173.33 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__increasing2,axiom,
% 173.13/173.33 ! [V_a,V_b,V_c,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__nonpos__nonpos,axiom,
% 173.13/173.33 ! [V_b,V_a,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 173.13/173.33 ! [V_m,V_a,T_a] :
% 173.13/173.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 173.13/173.33 ! [V_a,V_m,T_a] :
% 173.13/173.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 173.13/173.33 ! [V_m,T_a] :
% 173.13/173.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__iff__diff__le__0,axiom,
% 173.13/173.33 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_neg__less__nonneg,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_neg__less__0__iff__less,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_neg__0__less__iff__less,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_minus__le__self__iff,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_neg__le__0__iff__le,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__minus__self__iff,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_neg__0__le__iff__le,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_of__nat__0,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Rings_Ocomm__ring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_subset__insert,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 173.13/173.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_insert__subset,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 173.13/173.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__eq__1__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( 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))
% 173.13/173.33 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.33 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_range__eqI,axiom,
% 173.13/173.33 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 173.13/173.33 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_rangeI,axiom,
% 173.13/173.33 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_distrib__inf__le,axiom,
% 173.13/173.33 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Olattice(T_a)
% 173.13/173.33 => 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)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_distrib__sup__le,axiom,
% 173.13/173.33 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Olattice(T_a)
% 173.13/173.33 => 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)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_subset__singletonD,axiom,
% 173.13/173.33 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.33 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__Suc__right,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__Suc,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_of__nat__add,axiom,
% 173.13/173.33 ! [V_n,V_m,T_a] :
% 173.13/173.33 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_gr0__conv__Suc,axiom,
% 173.13/173.33 ! [V_n_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 173.13/173.33 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__Suc0,axiom,
% 173.13/173.33 ! [V_n_2] :
% 173.13/173.33 ( 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))))
% 173.13/173.33 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__Suc__eq__0__disj,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 173.13/173.33 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.33 | ? [B_j] :
% 173.13/173.33 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 173.13/173.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__gr__0,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 173.13/173.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__add__Suc1,axiom,
% 173.13/173.33 ! [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)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__add__Suc2,axiom,
% 173.13/173.33 ! [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)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__iff__Suc__add,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__on__strict__subset,axiom,
% 173.13/173.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Diff__UNIV,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__Int__subset,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,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_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_ball__UNIV,axiom,
% 173.13/173.33 ! [V_P_2,T_a] :
% 173.13/173.33 ( ! [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.33 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.33 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__less__diff,axiom,
% 173.13/173.33 ! [V_m_2,V_n_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__less,axiom,
% 173.13/173.33 ! [V_m,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 173.13/173.33 => 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Un__Int__assoc__eq,axiom,
% 173.13/173.33 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__less__Suc,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_comp__surj,axiom,
% 173.13/173.33 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 173.13/173.33 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,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_c,tc_HOL_Obool)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__eq__self__implies__10,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 173.13/173.33 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.33 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__diff__subset,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__diff__conv,axiom,
% 173.13/173.33 ! [V_k_2,V_j_2,V_i_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__diff__inverse,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => 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 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Diff__partition,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Diff__subset__conv,axiom,
% 173.13/173.33 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__image__eq__iff,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
% 173.13/173.33 <=> V_A_2 = V_B_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__comp,axiom,
% 173.13/173.33 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 173.13/173.33 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_of__nat__1,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_subset__Compl__self__eq,axiom,
% 173.13/173.33 ! [V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 173.13/173.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__UNIV__eq,axiom,
% 173.13/173.33 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__empty__eq,axiom,
% 173.13/173.33 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Ints__mult,axiom,
% 173.13/173.33 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Oring__1(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__partition,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__partition2,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 173.13/173.33 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Ints__of__nat,axiom,
% 173.13/173.33 ! [V_n_2,T_a] :
% 173.13/173.33 ( class_Rings_Oring__1(T_a)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__singleton,axiom,
% 173.13/173.33 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_map__le__implies__dom__le,axiom,
% 173.13/173.33 ! [V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),c_Map_Odom(T_a,T_b,V_g_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_the__inv__f__f,axiom,
% 173.13/173.33 ! [V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_dom__const,axiom,
% 173.13/173.33 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_compl__top__eq,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.33 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_compl__bot__eq,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.33 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sup__compl__top,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_compl__sup__top,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Lattices_Oboolean__algebra(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_of__nat__Suc,axiom,
% 173.13/173.33 ! [V_m,T_a] :
% 173.13/173.33 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__image__mem__iff,axiom,
% 173.13/173.33 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_range__ex1__eq,axiom,
% 173.13/173.33 ! [V_b_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.33 <=> ? [B_x] :
% 173.13/173.33 ( V_b_2 = hAPP(V_f_2,B_x)
% 173.13/173.33 & ! [B_y] :
% 173.13/173.33 ( V_b_2 = hAPP(V_f_2,B_y)
% 173.13/173.33 => B_y = B_x ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__Suc__less,axiom,
% 173.13/173.33 ! [V_i,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__pred,axiom,
% 173.13/173.33 ! [V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.33 => 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 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__diff__split,axiom,
% 173.13/173.33 ! [V_b_2,V_a_2,V_P_2] :
% 173.13/173.33 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 173.13/173.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.33 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 173.13/173.33 & ! [B_d] :
% 173.13/173.33 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 173.13/173.33 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__diff__split__asm,axiom,
% 173.13/173.33 ! [V_b_2,V_a_2,V_P_2] :
% 173.13/173.33 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 173.13/173.33 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.33 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 173.13/173.33 | ? [B_d] :
% 173.13/173.33 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 173.13/173.33 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__on__image__Int,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__Int,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__on__image__set__diff,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__set__diff,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_disjoint__eq__subset__Compl,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_subset__insert__iff,axiom,
% 173.13/173.33 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 173.13/173.33 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__single__insert,axiom,
% 173.13/173.33 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__on__iff__surj,axiom,
% 173.13/173.33 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 173.13/173.33 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 => ( ? [B_f] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 173.13/173.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) )
% 173.13/173.33 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__less__cancel1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__eq__cancel1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.33 => ( 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)
% 173.13/173.33 <=> V_m_2 = V_n_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_flat__lub__def,axiom,
% 173.13/173.33 ! [V_b_2,V_A_2,T_a] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.33 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 173.13/173.33 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_left__add__mult__distrib,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( 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)
% 173.13/173.33 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.33 | V_m_2 = V_n_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Least__mono,axiom,
% 173.13/173.33 ! [V_S_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( ( class_Orderings_Oorder(T_b)
% 173.13/173.33 & class_Orderings_Oorder(T_a) )
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.33 => ( ? [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.13/173.33 & ! [B_xa] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_S_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) )
% 173.13/173.33 => c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__1__neg,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_top1I,axiom,
% 173.13/173.33 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le0,axiom,
% 173.13/173.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_negative__zle,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__diff1__eq,axiom,
% 173.13/173.33 ! [V_z_2,V_w_2] :
% 173.13/173.33 ( 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))))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_negative__zle__0,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zsgn__def,axiom,
% 173.13/173.33 ! [V_i] :
% 173.13/173.33 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.33 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 173.13/173.33 => 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)) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__int__zless__negative,axiom,
% 173.13/173.33 ! [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)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__int,axiom,
% 173.13/173.33 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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__zminus,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__imp__0__less,axiom,
% 173.13/173.33 ! [V_z] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_odd__less__0,axiom,
% 173.13/173.33 ! [V_z_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_odd__nonzero,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__add1__eq__le,axiom,
% 173.13/173.33 ! [V_z_2,V_w_2] :
% 173.13/173.33 ( 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))))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zless__add1__eq,axiom,
% 173.13/173.33 ! [V_z_2,V_w_2] :
% 173.13/173.33 ( 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))))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 173.13/173.33 | V_w_2 = V_z_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add1__zle__eq,axiom,
% 173.13/173.33 ! [V_z_2,V_w_2] :
% 173.13/173.33 ( 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))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zless__imp__add1__zle,axiom,
% 173.13/173.33 ! [V_z,V_w] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__1__right,axiom,
% 173.13/173.33 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__1,axiom,
% 173.13/173.33 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__0__neq__1,axiom,
% 173.13/173.33 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__0__less__1,axiom,
% 173.13/173.33 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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__one__le__iff__zero__less,axiom,
% 173.13/173.33 ! [V_z_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_pos__zmult__eq__1__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.33 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.33 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_psubset__trans,axiom,
% 173.13/173.33 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__sgn,axiom,
% 173.13/173.33 ! [V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__refl,axiom,
% 173.13/173.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__le__linear,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_eq__imp__le,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( V_m = V_n
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__trans,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__antisym,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => V_m = V_n ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__zless__mono2,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zero__zle__int,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__less__0__conv,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zless__le,axiom,
% 173.13/173.33 ! [V_w_2,V_z_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 173.13/173.33 & V_z_2 != V_w_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zless__linear,axiom,
% 173.13/173.33 ! [V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 173.13/173.33 | V_x = V_y
% 173.13/173.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__int__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( 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)
% 173.13/173.33 <=> V_m_2 = V_n_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__int,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__zless__mono,axiom,
% 173.13/173.33 ! [V_z,V_z_H,V_w,V_w_H] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__left__mono,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__strict__right__mono,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__zmult__distrib,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__zmult__distrib2,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__iff__zadd,axiom,
% 173.13/173.33 ! [V_z_2,V_w_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 173.13/173.33 <=> ? [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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__bin__lemma,axiom,
% 173.13/173.33 ! [V_l_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 173.13/173.33 <=> 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__0__right,axiom,
% 173.13/173.33 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__0,axiom,
% 173.13/173.33 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__commute,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__left__commute,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__assoc,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zadd__zminus__inverse2,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zminus__zadd__distrib,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zminus__zminus,axiom,
% 173.13/173.33 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zminus__0,axiom,
% 173.13/173.33 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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__int__def,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__int__def__symmetric,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__0__eq,axiom,
% 173.13/173.33 ! [V_n_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 173.13/173.33 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 173.13/173.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__le__0__conv,axiom,
% 173.13/173.33 ! [V_n_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__zle__neg,axiom,
% 173.13/173.33 ! [V_m_2,V_n_2] :
% 173.13/173.33 ( 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))))
% 173.13/173.33 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.33 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__n__not__le__n,axiom,
% 173.13/173.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__less__eq__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__Suc__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__le__mono,axiom,
% 173.13/173.33 ! [V_m_2,V_n_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__SucI,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__SucE,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 173.13/173.33 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__leD,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_not__zle__0__negative,axiom,
% 173.13/173.33 ! [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))))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_termination__basic__simps_I5_J,axiom,
% 173.13/173.33 ! [V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__or__eq__imp__le,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 | V_m = V_n )
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__neq__implies__less,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => ( V_m != V_n
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__imp__le__nat,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__eq__less__or__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 | V_m_2 = V_n_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__less__le,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 & V_m_2 != V_n_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__leE,axiom,
% 173.13/173.33 ! [V_n,V_k,V_m] :
% 173.13/173.33 ( 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))
% 173.13/173.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__leD1,axiom,
% 173.13/173.33 ! [V_n,V_k,V_m] :
% 173.13/173.33 ( 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))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__leD2,axiom,
% 173.13/173.33 ! [V_n,V_k,V_m] :
% 173.13/173.33 ( 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))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__le__mono,axiom,
% 173.13/173.33 ! [V_l,V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__le__mono1,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_trans__le__add2,axiom,
% 173.13/173.33 ! [V_m,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_trans__le__add1,axiom,
% 173.13/173.33 ! [V_m,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__add__left__cancel__le,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__iff__add,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__add1,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__add2,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_termination__basic__simps_I3_J,axiom,
% 173.13/173.33 ! [V_z,V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_termination__basic__simps_I4_J,axiom,
% 173.13/173.33 ! [V_y,V_z,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__int,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_int__mult,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__diff__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat_Odiff__diff__eq,axiom,
% 173.13/173.33 ! [V_n,V_m,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 173.13/173.33 => 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) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_eq__diff__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 173.13/173.33 => ( 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)
% 173.13/173.33 <=> V_m_2 = V_n_2 ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__diff__cancel,axiom,
% 173.13/173.33 ! [V_n,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 173.13/173.33 => 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 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__le__mono,axiom,
% 173.13/173.33 ! [V_l,V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__le__mono2,axiom,
% 173.13/173.33 ! [V_l,V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__le__self,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiff__int,axiom,
% 173.13/173.33 ! [V_m,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__le__mono,axiom,
% 173.13/173.33 ! [V_l,V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__le__mono2,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__le__mono1,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__cube,axiom,
% 173.13/173.33 ! [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)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__square,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_evaln__nonstrict,axiom,
% 173.13/173.33 ! [V_m,V_t,V_n,V_s,V_c] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_monoD,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( ( class_Orderings_Oorder(T_b)
% 173.13/173.33 & class_Orderings_Oorder(T_a) )
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.33 => 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))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__Suc,axiom,
% 173.13/173.33 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 173.13/173.33 <=> 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn0,axiom,
% 173.13/173.33 ! [T_a] :
% 173.13/173.33 ( class_Groups_Osgn__if(T_a)
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__0__0,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__times,axiom,
% 173.13/173.33 ! [V_b,V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__zless__mono2__lemma,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__mult__le__cancel1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__eq__Suc__le,axiom,
% 173.13/173.33 ! [V_m_2,V_n_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__Suc__eq__le,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__le__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__imp__less__Suc,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__leI,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__less__Suc__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 173.13/173.33 <=> V_n_2 = V_m_2 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__le__lessD,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__is__0__eq_H,axiom,
% 173.13/173.33 ! [V_n,V_m] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__is__0__eq,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__diff__le,axiom,
% 173.13/173.33 ! [V_m,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Suc__mult__le__cancel1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__eq__add__iff2,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.33 => ( 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)
% 173.13/173.33 <=> 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) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__diff__add__eq2,axiom,
% 173.13/173.33 ! [V_n,V_m,V_u,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__le__add__iff2,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__eq__add__iff1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 173.13/173.33 => ( 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)
% 173.13/173.33 <=> 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 ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__diff__add__eq1,axiom,
% 173.13/173.33 ! [V_n,V_m,V_u,V_i,V_j] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__le__add__iff1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__less__mono,axiom,
% 173.13/173.33 ! [V_c,V_b,V_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__diff__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__add__assoc2,axiom,
% 173.13/173.33 ! [V_i,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__diff__assoc2,axiom,
% 173.13/173.33 ! [V_i,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__add__assoc,axiom,
% 173.13/173.33 ! [V_i,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__imp__diff__is__add,axiom,
% 173.13/173.33 ! [V_k_2,V_j_2,V_i_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.33 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 173.13/173.33 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__add__diff__inverse2,axiom,
% 173.13/173.33 ! [V_m,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => 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 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__diff__conv2,axiom,
% 173.13/173.33 ! [V_i_2,V_j_2,V_k_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_add__diff__assoc,axiom,
% 173.13/173.33 ! [V_i,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__add__diff__inverse,axiom,
% 173.13/173.33 ! [V_m,V_n] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => 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 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__add__diff,axiom,
% 173.13/173.33 ! [V_m,V_n,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 173.13/173.33 => 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_le__diff__conv,axiom,
% 173.13/173.33 ! [V_i_2,V_k_2,V_j_2] :
% 173.13/173.33 ( 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))
% 173.13/173.33 <=> 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__diff__right,axiom,
% 173.13/173.33 ! [V_i,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__Un,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 173.13/173.33 => 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)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__Int,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_less__eq__Suc__le__raw,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__iff__le__Suc,axiom,
% 173.13/173.33 ! [V_f_2,T_a] :
% 173.13/173.33 ( class_Orderings_Oorder(T_a)
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_a,V_f_2)
% 173.13/173.33 <=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__sup,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( ( class_Lattices_Osemilattice__sup(T_b)
% 173.13/173.33 & class_Lattices_Osemilattice__sup(T_a) )
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_A_2),V_B_2)))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mono__inf,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( ( class_Lattices_Osemilattice__inf(T_b)
% 173.13/173.33 & class_Lattices_Osemilattice__inf(T_a) )
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__less__add__iff1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_nat__less__add__iff2,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.33 => ( 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)))
% 173.13/173.33 <=> 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__greater,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__less,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_one__le__mult__iff,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> ( 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))
% 173.13/173.33 & 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__le__cancel2,axiom,
% 173.13/173.33 ! [V_n_2,V_k_2,V_m_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_mult__le__cancel1,axiom,
% 173.13/173.33 ! [V_n_2,V_m_2,V_k_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__Suc__diff__eq1,axiom,
% 173.13/173.33 ! [V_m,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_diff__Suc__diff__eq2,axiom,
% 173.13/173.33 ! [V_m,V_j,V_k] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 173.13/173.33 => 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)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_of__nat__diff,axiom,
% 173.13/173.33 ! [V_m,V_n,T_a] :
% 173.13/173.33 ( class_Rings_Oring__1(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.33 => 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)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__1__pos,axiom,
% 173.13/173.33 ! [V_a_2,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__pos,axiom,
% 173.13/173.33 ! [V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__if,axiom,
% 173.13/173.33 ! [V_x,T_a] :
% 173.13/173.33 ( class_Groups_Osgn__if(T_a)
% 173.13/173.33 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 173.13/173.33 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_sgn__neg,axiom,
% 173.13/173.33 ! [V_a,T_a] :
% 173.13/173.33 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.33 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiff__int__split,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2,V_P_2] :
% 173.13/173.33 ( hBOOL(hAPP(V_P_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))))
% 173.13/173.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 173.13/173.33 => hBOOL(hAPP(V_P_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)))) )
% 173.13/173.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 173.13/173.33 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_self__quotient__aux1,axiom,
% 173.13/173.33 ! [V_q,V_r,V_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.33 => ( 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))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_self__quotient__aux2,axiom,
% 173.13/173.33 ! [V_q,V_r,V_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.33 => ( 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))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 173.13/173.33 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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_q__pos__lemma,axiom,
% 173.13/173.33 ! [V_r_H,V_q_H,V_b_H] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__refl,axiom,
% 173.13/173.33 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__commute,axiom,
% 173.13/173.33 ! [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) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__linear,axiom,
% 173.13/173.33 ! [V_w,V_z] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 173.13/173.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zmult__assoc,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__trans,axiom,
% 173.13/173.33 ! [V_k,V_j,V_i] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zle__antisym,axiom,
% 173.13/173.33 ! [V_w,V_z] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 173.13/173.33 => V_z = V_w ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiff__zmult__distrib,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiff__zmult__distrib2,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 173.13/173.33 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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 173.13/173.33 ! [V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 173.13/173.33 ! [V_A_2,V_x_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 173.13/173.33 <=> 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2] :
% 173.13/173.33 ( V_A_2 = V_B_2
% 173.13/173.33 <=> 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) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 <=> 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 <=> 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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 173.13/173.33 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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2] :
% 173.13/173.33 ( 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)
% 173.13/173.33 <=> V_x_2 = V_y_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 173.13/173.33 ! [V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.33 => 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))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 173.13/173.33 ! [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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 173.13/173.33 ! [V_P_2] :
% 173.13/173.33 ( ? [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.33 & hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.33 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 173.13/173.33 ! [V_P_2] :
% 173.13/173.33 ( ! [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.33 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.33 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 173.13/173.33 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))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 173.13/173.33 ! [V_y_2,V_x_2] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 173.13/173.33 ! [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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 173.13/173.33 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)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 173.13/173.33 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 173.13/173.33 ( 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)
% 173.13/173.33 => ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_unique__quotient__lemma__neg,axiom,
% 173.13/173.33 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_zdiv__mono2__lemma,axiom,
% 173.13/173.33 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 173.13/173.33 ( 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)
% 173.13/173.33 => ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_unique__quotient__lemma,axiom,
% 173.13/173.33 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_q__neg__lemma,axiom,
% 173.13/173.33 ! [V_r_H,V_q_H,V_b_H] :
% 173.13/173.33 ( 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)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_coinduct3__mono__lemma,axiom,
% 173.13/173.33 ! [V_B_2,V_X_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( class_Orderings_Oorder(T_a)
% 173.13/173.33 => ( c_Orderings_Oorder__class_Omono(T_a,tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 173.13/173.33 => c_Orderings_Oorder__class_Omono(T_a,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_small_H_Osimps,axiom,
% 173.13/173.33 ! [V_f_2,V_i_2,V_d_2] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 173.13/173.33 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 173.13/173.33 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_tsub__def,axiom,
% 173.13/173.33 ! [V_x,V_y] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 173.13/173.33 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 173.13/173.33 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__vimage__singleton,axiom,
% 173.13/173.33 ! [V_a_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_decr__mult__lemma,axiom,
% 173.13/173.33 ! [V_k_2,V_P_2,V_d_2] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 173.13/173.33 => ( ! [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.33 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.33 => ! [B_x] :
% 173.13/173.33 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.33 => hBOOL(hAPP(V_P_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)))) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_negD,axiom,
% 173.13/173.33 ! [V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.33 => ? [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))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimageI,axiom,
% 173.13/173.33 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 173.13/173.33 ( hAPP(V_f_2,V_a_2) = V_b_2
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__ident,axiom,
% 173.13/173.33 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__code,axiom,
% 173.13/173.33 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 173.13/173.33 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimageI2,axiom,
% 173.13/173.33 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimageD,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__eq,axiom,
% 173.13/173.33 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 173.13/173.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__empty,axiom,
% 173.13/173.33 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__mono,axiom,
% 173.13/173.33 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__UNIV,axiom,
% 173.13/173.33 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,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_a,tc_HOL_Obool)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__Un,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__Int,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__compose,axiom,
% 173.13/173.33 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__Diff,axiom,
% 173.13/173.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__Compl,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__vimage__subset,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_surj__image__vimage__eq,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__singleton__eq,axiom,
% 173.13/173.33 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 173.13/173.33 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__insert,axiom,
% 173.13/173.33 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__subsetD,axiom,
% 173.13/173.33 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 173.13/173.33 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_image__vimage__eq,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_inj__vimage__image__eq,axiom,
% 173.13/173.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__const,axiom,
% 173.13/173.33 ! [T_b,V_A_2,V_ca_2,T_a] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__subsetI,axiom,
% 173.13/173.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 173.13/173.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_vimage__if,axiom,
% 173.13/173.33 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] :
% 173.13/173.33 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 173.13/173.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) )
% 173.13/173.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 173.13/173.33 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 173.13/173.33
% 173.13/173.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 173.13/173.33 ! [V_y,V_x] :
% 173.13/173.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.34 => 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))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_tsub__eq,axiom,
% 173.13/173.34 ! [V_x,V_y] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 173.13/173.34 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_incr__mult__lemma,axiom,
% 173.13/173.34 ! [V_k_2,V_P_2,V_d_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 173.13/173.34 => ( ! [B_x] :
% 173.13/173.34 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.34 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.34 => ! [B_x] :
% 173.13/173.34 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.34 => hBOOL(hAPP(V_P_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)))) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_ex__least__nat__less,axiom,
% 173.13/173.34 ! [V_n_2,V_P_2] :
% 173.13/173.34 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 173.13/173.34 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 173.13/173.34 => ? [B_k] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 173.13/173.34 & ! [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 173.13/173.34 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 173.13/173.34 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__less__imp__eq__int,axiom,
% 173.13/173.34 ! [V_k] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 173.13/173.34 => ? [B_n] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 173.13/173.34 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_incr__lemma,axiom,
% 173.13/173.34 ! [V_x,V_z,V_d] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_decr__lemma,axiom,
% 173.13/173.34 ! [V_z,V_x,V_d] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_inj__on__diff__nat,axiom,
% 173.13/173.34 ! [V_k_2,V_N_2] :
% 173.13/173.34 ( ! [B_x] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__idempotent,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__ge__self,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__le__D1,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__eq__0,axiom,
% 173.13/173.34 ! [V_a_2,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__zero,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__add__abs,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__mult__self,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__mult,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__minus__commute,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__one,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__minus__cancel,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__of__nat,axiom,
% 173.13/173.34 ! [V_n,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__int__eq,axiom,
% 173.13/173.34 ! [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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__of__nonneg,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__le__zero__iff,axiom,
% 173.13/173.34 ! [V_a_2,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__ge__zero,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__of__pos,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__less__abs__iff,axiom,
% 173.13/173.34 ! [V_a_2,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)))
% 173.13/173.34 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__not__less__zero,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ~ 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__triangle__ineq,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__mult__less,axiom,
% 173.13/173.34 ! [V_d,V_b,V_c,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__triangle__ineq2__sym,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__triangle__ineq2,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__triangle__ineq3,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__ge__minus__self,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__le__iff,axiom,
% 173.13/173.34 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 173.13/173.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 173.13/173.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__leI,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__le__D2,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__less__iff,axiom,
% 173.13/173.34 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 173.13/173.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__zmult__eq__1,axiom,
% 173.13/173.34 ! [V_n,V_m] :
% 173.13/173.34 ( 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)
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__sgn,axiom,
% 173.13/173.34 ! [V_k,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__sgn__abs,axiom,
% 173.13/173.34 ! [V_x,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__eq__mult,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Oordered__ring__abs(T_a)
% 173.13/173.34 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 173.13/173.34 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__mult__pos,axiom,
% 173.13/173.34 ! [V_y,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__diff__triangle__ineq,axiom,
% 173.13/173.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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))))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__triangle__ineq4,axiom,
% 173.13/173.34 ! [V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__of__nonpos,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__minus__le__zero,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__of__neg,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__if,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Oabs__if(T_a)
% 173.13/173.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zabs__less__one__iff,axiom,
% 173.13/173.34 ! [V_z_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zabs__def,axiom,
% 173.13/173.34 ! [V_i] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.34 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_int__val__lemma,axiom,
% 173.13/173.34 ! [V_k_2,V_f_2,V_n_2] :
% 173.13/173.34 ( ! [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 173.13/173.34 => 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))) )
% 173.13/173.34 => ( 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))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 173.13/173.34 => ? [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 173.13/173.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat0__intermed__int__val,axiom,
% 173.13/173.34 ! [V_k_2,V_f_2,V_n_2] :
% 173.13/173.34 ( ! [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 173.13/173.34 => 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))) )
% 173.13/173.34 => ( 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))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 173.13/173.34 => ? [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 173.13/173.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_coinduct__set,axiom,
% 173.13/173.34 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 173.13/173.34 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__coinduct__set,axiom,
% 173.13/173.34 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] :
% 173.13/173.34 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_A_2))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_expand__Suc,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__intermed__int__val,axiom,
% 173.13/173.34 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 173.13/173.34 ( ! [B_i] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 173.13/173.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 173.13/173.34 => 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))) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 173.13/173.34 => ? [B_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 173.13/173.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 173.13/173.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__number__of,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Int_Oring__char__0(T_a) )
% 173.13/173.34 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 173.13/173.34 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__reorient,axiom,
% 173.13/173.34 ! [V_x_2,V_w_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber(T_a)
% 173.13/173.34 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 173.13/173.34 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_of__nat__number__of__lemma,axiom,
% 173.13/173.34 ! [V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( ( 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)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ 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)))
% 173.13/173.34 => 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) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_gfp__upperbound,axiom,
% 173.13/173.34 ! [V_f_2,V_X_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,V_X_2)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_gfp__unfold,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__gfp__unfold,axiom,
% 173.13/173.34 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__number__of__eq__not__less,axiom,
% 173.13/173.34 ! [V_w_2,V_v_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber(T_a)
% 173.13/173.34 & class_Orderings_Olinorder(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_right__distrib__number__of,axiom,
% 173.13/173.34 ! [V_c,V_b,V_v,T_b] :
% 173.13/173.34 ( ( class_Int_Onumber(T_b)
% 173.13/173.34 & class_Rings_Osemiring(T_b) )
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_left__distrib__number__of,axiom,
% 173.13/173.34 ! [V_v,V_b,V_a,T_b] :
% 173.13/173.34 ( ( class_Int_Onumber(T_b)
% 173.13/173.34 & class_Rings_Osemiring(T_b) )
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_right__diff__distrib__number__of,axiom,
% 173.13/173.34 ! [V_c,V_b,V_v,T_b] :
% 173.13/173.34 ( ( class_Int_Onumber(T_b)
% 173.13/173.34 & class_Rings_Oring(T_b) )
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_left__diff__distrib__number__of,axiom,
% 173.13/173.34 ! [V_v,V_b,V_a,T_b] :
% 173.13/173.34 ( ( class_Int_Onumber(T_b)
% 173.13/173.34 & class_Rings_Oring(T_b) )
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__number__of,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__number__of,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__add,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__number__of__eq,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__number__of__left,axiom,
% 173.13/173.34 ! [V_z,V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__number__of__left,axiom,
% 173.13/173.34 ! [V_z,V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_arith__simps_I32_J,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__mult,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__diff,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__minus,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_arith__simps_I30_J,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Ints__number__of,axiom,
% 173.13/173.34 ! [V_w_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_weak__coinduct,axiom,
% 173.13/173.34 ! [V_f_2,V_X_2,V_a_2,T_a] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__number__of__diff1,axiom,
% 173.13/173.34 ! [V_c,V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__number__of__mult,axiom,
% 173.13/173.34 ! [V_z,V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__number__of__eq,axiom,
% 173.13/173.34 ! [V_w,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_gfp__lemma3,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_gfp__lemma2,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_weak__coinduct__image,axiom,
% 173.13/173.34 ! [V_f_2,V_g_2,T_b,V_X_2,V_a_2,T_a] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_a,T_b,V_g_2),V_X_2))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__number__of,axiom,
% 173.13/173.34 ! [V_x,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( ( 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)))
% 173.13/173.34 => 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)) )
% 173.13/173.34 & ( ~ 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)))
% 173.13/173.34 => 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) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__number__of__diff2,axiom,
% 173.13/173.34 ! [V_w,V_c,V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_gfp__fun__UnI2,axiom,
% 173.13/173.34 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 173.13/173.34 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_coinduct,axiom,
% 173.13/173.34 ! [V_X_2,V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_coinduct__lemma,axiom,
% 173.13/173.34 ! [V_f_2,V_X_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)))))
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__coinduct,axiom,
% 173.13/173.34 ! [V_X_2,V_f_2,V_A_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),V_A_2))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),V_A_2)) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__coinduct3,axiom,
% 173.13/173.34 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] :
% 173.13/173.34 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_coinduct3,axiom,
% 173.13/173.34 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 173.13/173.34 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))))))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_coinduct3__lemma,axiom,
% 173.13/173.34 ! [V_f_2,V_X_2,T_a] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))))))
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__number__of__eq,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 173.13/173.34 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_H,V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__mult__left,axiom,
% 173.13/173.34 ! [V_k,V_v_H,V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__is__id,axiom,
% 173.13/173.34 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 173.13/173.34
% 173.13/173.34 fof(fact_iszero__Numeral0,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__is__num__zero,axiom,
% 173.13/173.34 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__const,axiom,
% 173.13/173.34 ! [V_t_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => c_Inductive_Ocomplete__lattice__class_Olfp(T_a,hAPP(c_COMBK(T_a,T_a),V_t_2)) = V_t_2 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of2,axiom,
% 173.13/173.34 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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__eq__number__of__int__code,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__number__of__int__code,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_plus__numeral__code_I9_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Pls__def,axiom,
% 173.13/173.34 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_times__numeral__code_I5_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I19_J,axiom,
% 173.13/173.34 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I2_J,axiom,
% 173.13/173.34 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__Pls__right,axiom,
% 173.13/173.34 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__Pls,axiom,
% 173.13/173.34 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__numeral__code_I5_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__Pls,axiom,
% 173.13/173.34 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__bin__simps_I1_J,axiom,
% 173.13/173.34 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__Pls,axiom,
% 173.13/173.34 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__lowerbound,axiom,
% 173.13/173.34 ! [V_A_2,V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_A_2)),V_A_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_A_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__lfp__unfold,axiom,
% 173.13/173.34 ! [V_f_2,V_h_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__unfold,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_iszero__def,axiom,
% 173.13/173.34 ! [V_z_2,T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => ( c_Int_Oiszero(T_a,V_z_2)
% 173.13/173.34 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_iszero__0,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__iszero__1,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__Pls,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_semiring__norm_I112_J,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__numeral__0__right,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__numeral__0,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_bin__less__0__simps_I1_J,axiom,
% 173.13/173.34 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_semiring__norm_I113_J,axiom,
% 173.13/173.34 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__Pls,axiom,
% 173.13/173.34 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__special_I1_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 173.13/173.34 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__special_I3_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.34 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__0__number__of,axiom,
% 173.13/173.34 ! [V_v_2] :
% 173.13/173.34 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__number__of__0,axiom,
% 173.13/173.34 ! [V_v_2] :
% 173.13/173.34 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_H_2,V_v_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 173.13/173.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_H_2,V_v_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__numeral__code_I6_J,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__lemma3,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__lemma2,axiom,
% 173.13/173.34 ! [V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__special_I3_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__special_I1_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__special_I3_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__special_I1_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__0__number__of,axiom,
% 173.13/173.34 ! [V_v_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_H,V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_lfp__induct,axiom,
% 173.13/173.34 ! [V_P_2,V_f_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_P_2))),V_P_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_P_2)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_def__lfp__induct,axiom,
% 173.13/173.34 ! [V_P_2,V_f_2,V_A_2,T_a] :
% 173.13/173.34 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.34 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)
% 173.13/173.34 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_A_2),V_P_2))),V_P_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_A_2),V_P_2)) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__add__1,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__1__add__number__of,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__diff__1,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nats__number__of,axiom,
% 173.13/173.34 ! [V_w_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Suc__diff__number__of,axiom,
% 173.13/173.34 ! [V_m,V_v] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__special_I4_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.34 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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))))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_succ__Pls,axiom,
% 173.13/173.34 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I51_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 173.13/173.34 <=> V_k_2 = V_l_2 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_succ__pred,axiom,
% 173.13/173.34 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__Bit1,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__eq__int__code_I16_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I34_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I17_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__int__code_I16_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I46_J,axiom,
% 173.13/173.34 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I39_J,axiom,
% 173.13/173.34 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_bin__less__0__simps_I4_J,axiom,
% 173.13/173.34 ! [V_w_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I22_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I12_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Bit1__def,axiom,
% 173.13/173.34 ! [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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_iszero__number__of__Bit1,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Int_Oring__char__0(T_a) )
% 173.13/173.34 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__iff__pred__less,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_pred__def,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__Bit1,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__numeral__1,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__numeral__1__right,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_numeral__1__eq__1,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_semiring__norm_I110_J,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I29_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I5_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_one__is__num__one,axiom,
% 173.13/173.34 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Numeral1__eq1__nat,axiom,
% 173.13/173.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__numeral__1__eq__1,axiom,
% 173.13/173.34 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__iszero__Numeral1,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_succ__def,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nats__0,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nats__add,axiom,
% 173.13/173.34 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nats__mult,axiom,
% 173.13/173.34 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nats__1,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_of__nat__in__Nats,axiom,
% 173.13/173.34 ! [V_n_2,T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_numeral__1__eq__Suc__0,axiom,
% 173.13/173.34 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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_numeral__3__eq__3,axiom,
% 173.13/173.34 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)))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 173.13/173.34 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))))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Suc3__eq__add__3,axiom,
% 173.13/173.34 ! [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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 173.13/173.34 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)))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__special_I2_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_le__special_I4_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__special_I4_J,axiom,
% 173.13/173.34 ! [V_x_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__special_I2_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__succ,axiom,
% 173.13/173.34 ! [V_k,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__special_I3_J,axiom,
% 173.13/173.34 ! [V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__special_I2_J,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 173.13/173.34 ! [V_m,V_n] :
% 173.13/173.34 ( 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))
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__pred,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__special_I2_J,axiom,
% 173.13/173.34 ! [V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__special_I1_J,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__special_I2_J,axiom,
% 173.13/173.34 ! [V_y_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 173.13/173.34 <=> c_Int_Oiszero(T_a,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_y_2)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__number__of__odd__number__of,axiom,
% 173.13/173.34 ! [V_v_2,V_w_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( ( 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)))
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) )
% 173.13/173.34 & ( ~ 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)))
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__Bit1,axiom,
% 173.13/173.34 ! [V_w_2] :
% 173.13/173.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 173.13/173.34 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 173.13/173.34 => 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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Suc__nat__number__of__add,axiom,
% 173.13/173.34 ! [V_n,V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zpower__number__of__odd,axiom,
% 173.13/173.34 ! [V_z_2,V_w_2] :
% 173.13/173.34 ( ( 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)))
% 173.13/173.34 => 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))) )
% 173.13/173.34 & ( ~ 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)))
% 173.13/173.34 => 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) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_one__code__numeral__code,axiom,
% 173.13/173.34 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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__number__of__odd,axiom,
% 173.13/173.34 ! [V_z_2,V_w_2,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( ( 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)))
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) )
% 173.13/173.34 & ( ~ 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)))
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_int__power,axiom,
% 173.13/173.34 ! [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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zpower__int,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_code__numeral__zero__minus__one,axiom,
% 173.13/173.34 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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 173.13/173.34 ! [V_q,V_y,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 173.13/173.34 ! [V_q,V_p,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zpower__zpower,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 173.13/173.34 ! [V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__0,axiom,
% 173.13/173.34 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__int,axiom,
% 173.13/173.34 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__1,axiom,
% 173.13/173.34 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 173.13/173.34 ! [V_q,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 173.13/173.34 ! [V_q,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 173.13/173.34 ! [V_q,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 173.13/173.34 ! [V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 173.13/173.34 ! [V_q,V_p,V_x,T_a] :
% 173.13/173.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 173.13/173.34 ! [V_n,V_x] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zpower__zadd__distrib,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Ints__power,axiom,
% 173.13/173.34 ! [V_n_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Rings_Oring__1(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__eq__ge__0,axiom,
% 173.13/173.34 ! [V_x_2] :
% 173.13/173.34 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__def,axiom,
% 173.13/173.34 ! [V_Z_2] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__number__of__Pls,axiom,
% 173.13/173.34 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__number__of__Bit1,axiom,
% 173.13/173.34 ! [V_w_2] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 173.13/173.34 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__le__zpower__abs,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__code__numeral__code,axiom,
% 173.13/173.34 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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__imp__number__of__eq__0,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__zminus__int,axiom,
% 173.13/173.34 ! [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))))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power3__eq__cube,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__eq__if,axiom,
% 173.13/173.34 ! [V_p,V_m] :
% 173.13/173.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 173.13/173.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 => 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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__less__zpower__abs__iff,axiom,
% 173.13/173.34 ! [V_n_2,V_x_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.34 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_H_2,V_v_2] :
% 173.13/173.34 ( 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)
% 173.13/173.34 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 173.13/173.34 => 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))) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 173.13/173.34 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 173.13/173.34 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 173.13/173.34 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__add__left,axiom,
% 173.13/173.34 ! [V_k,V_v_H,V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.34 => 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) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_int__nat__number__of,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__number__of__pred__iff__0,axiom,
% 173.13/173.34 ! [V_v_2] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 173.13/173.34 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_of__nat__number__of__eq,axiom,
% 173.13/173.34 ! [V_v,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Suc__nat__number__of,axiom,
% 173.13/173.34 ! [V_v] :
% 173.13/173.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__strict__mono,axiom,
% 173.13/173.34 ! [V_n,V_b,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.34 => 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))) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_one__less__power,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__increasing__iff,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__le__imp__le__exp,axiom,
% 173.13/173.34 ! [V_n,V_m,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => ( 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)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__decreasing,axiom,
% 173.13/173.34 ! [V_a,V_N,V_n,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 => 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))) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__strict__decreasing,axiom,
% 173.13/173.34 ! [V_a,V_N,V_n,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 => 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))) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_field__power__not__zero,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 173.13/173.34 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 173.13/173.34 ! [V_m_2,V_x_2] :
% 173.13/173.34 ( 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))
% 173.13/173.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__Suc__0,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__zero__less__power__iff,axiom,
% 173.13/173.34 ! [V_n_2,V_x_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 173.13/173.34 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__power__less__imp__less,axiom,
% 173.13/173.34 ! [V_n,V_m,V_i] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 173.13/173.34 => ( 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)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__mult__distrib,axiom,
% 173.13/173.34 ! [V_n,V_b,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__commutes,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__one,axiom,
% 173.13/173.34 ! [V_n,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_of__nat__power,axiom,
% 173.13/173.34 ! [V_n,V_m,T_a] :
% 173.13/173.34 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__mult,axiom,
% 173.13/173.34 ! [V_n,V_m,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__abs,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__one__right,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__le__power,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__mono,axiom,
% 173.13/173.34 ! [V_n,V_b,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__less__power,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__eq__0__iff,axiom,
% 173.13/173.34 ! [V_n_2,V_a_2,T_a] :
% 173.13/173.34 ( ( class_Power_Opower(T_a)
% 173.13/173.34 & class_Rings_Omult__zero(T_a)
% 173.13/173.34 & class_Rings_Ono__zero__divisors(T_a)
% 173.13/173.34 & class_Rings_Ozero__neq__one(T_a) )
% 173.13/173.34 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.34 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.34 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_one__le__power,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__0__Suc,axiom,
% 173.13/173.34 ! [V_n,T_a] :
% 173.13/173.34 ( ( class_Power_Opower(T_a)
% 173.13/173.34 & class_Rings_Osemiring__0(T_a) )
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__inject__exp,axiom,
% 173.13/173.34 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 173.13/173.34 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 173.13/173.34 <=> V_m_2 = V_n_2 ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__Suc2,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__Suc,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Power_Opower(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__one__le__power,axiom,
% 173.13/173.34 ! [V_n,V_i] :
% 173.13/173.34 ( 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))
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__0,axiom,
% 173.13/173.34 ! [V_a,T_a] :
% 173.13/173.34 ( class_Power_Opower(T_a)
% 173.13/173.34 => 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) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__add,axiom,
% 173.13/173.34 ! [V_n,V_m,V_a,T_a] :
% 173.13/173.34 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_abs__power__minus,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__less__imp__less__base,axiom,
% 173.13/173.34 ! [V_b,V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( 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)))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__inject__base,axiom,
% 173.13/173.34 ! [V_b,V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( 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))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.34 => V_a = V_b ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__le__imp__le__base,axiom,
% 173.13/173.34 ! [V_b,V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( 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))))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__less__power__Suc,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__gt1__lemma,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__0__left,axiom,
% 173.13/173.34 ! [V_n,T_a] :
% 173.13/173.34 ( ( class_Power_Opower(T_a)
% 173.13/173.34 & class_Rings_Osemiring__0(T_a) )
% 173.13/173.34 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 => 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) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__gt1,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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)))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__strict__increasing,axiom,
% 173.13/173.34 ! [V_a,V_N,V_n,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__less__imp__less__exp,axiom,
% 173.13/173.34 ! [V_n,V_m,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => ( 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)))
% 173.13/173.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__strict__increasing__iff,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_zero__le__power__abs,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => 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))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__increasing,axiom,
% 173.13/173.34 ! [V_a,V_N,V_n,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__minus,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Oring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__Suc__less,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__eq__imp__eq__base,axiom,
% 173.13/173.34 ! [V_b,V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( 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)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.34 => V_a = V_b ) ) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__Suc__less__one,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.34 => 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))) ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__of__aux__code,axiom,
% 173.13/173.34 ! [V_n,V_i] :
% 173.13/173.34 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.34 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 173.13/173.34 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__nat__number__of,axiom,
% 173.13/173.34 ! [V_v_2,V_v_H_2] :
% 173.13/173.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 173.13/173.34 => 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) )
% 173.13/173.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 173.13/173.34 => 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)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__power__power,axiom,
% 173.13/173.34 ! [T_a] :
% 173.13/173.34 ( class_Power_Opower(T_a)
% 173.13/173.34 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_power__minus1__odd,axiom,
% 173.13/173.34 ! [V_n,T_a] :
% 173.13/173.34 ( class_Rings_Oring__1(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_odd__power__less__zero,axiom,
% 173.13/173.34 ! [V_n,V_a,T_a] :
% 173.13/173.34 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.34 => 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))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I48_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 173.13/173.34 <=> V_k_2 = V_l_2 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I31_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__eq__int__code_I13_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__int__code_I13_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I14_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Bit0__Pls,axiom,
% 173.13/173.34 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I38_J,axiom,
% 173.13/173.34 ! [V_l_2] :
% 173.13/173.34 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 173.13/173.34 <=> c_Int_OPls = V_l_2 ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I44_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 173.13/173.34 <=> V_k_2 = c_Int_OPls ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I49_J,axiom,
% 173.13/173.34 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I50_J,axiom,
% 173.13/173.34 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__Bit0__Bit0,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Bit0__def,axiom,
% 173.13/173.34 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__int,axiom,
% 173.13/173.34 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 173.13/173.34
% 173.13/173.34 fof(fact_mult__Bit0,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__bin__simps_I7_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_minus__Bit0,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 173.13/173.34 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)))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 173.13/173.34 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__0,axiom,
% 173.13/173.34 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 173.13/173.34 ! [V_y_2,V_x_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 173.13/173.34 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 173.13/173.34 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_all__nat,axiom,
% 173.13/173.34 ! [V_P_2] :
% 173.13/173.34 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.34 <=> ! [B_x] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.34 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_ex__nat,axiom,
% 173.13/173.34 ! [V_P_2] :
% 173.13/173.34 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.34 <=> ? [B_x] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.34 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_eq__nat__nat__iff,axiom,
% 173.13/173.34 ! [V_z_H_2,V_z_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 173.13/173.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 173.13/173.34 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 173.13/173.34 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_bin__less__0__simps_I3_J,axiom,
% 173.13/173.34 ! [V_w_2] :
% 173.13/173.34 ( 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)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I21_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I27_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I32_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__eq__int__code_I14_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I10_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I4_J,axiom,
% 173.13/173.34 ! [V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_less__int__code_I15_J,axiom,
% 173.13/173.34 ! [V_k2_2,V_k1_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_rel__simps_I16_J,axiom,
% 173.13/173.34 ! [V_l_2,V_k_2] :
% 173.13/173.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of,axiom,
% 173.13/173.34 ! [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) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__def,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__Bit0__Bit1,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_add__Bit1__Bit0,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__bin__simps_I3_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__bin__simps_I9_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_diff__bin__simps_I10_J,axiom,
% 173.13/173.34 ! [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)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 173.13/173.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__nat,axiom,
% 173.13/173.34 ! [V_z] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 173.13/173.34 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_not__neg__nat,axiom,
% 173.13/173.34 ! [V_z] :
% 173.13/173.34 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 173.13/173.34 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_neg__number__of__Bit0,axiom,
% 173.13/173.34 ! [V_w_2] :
% 173.13/173.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 173.13/173.34 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_pred__Bit1,axiom,
% 173.13/173.34 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_pred__Bit0,axiom,
% 173.13/173.34 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 173.13/173.34 ! [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 ).
% 173.13/173.34
% 173.13/173.34 fof(fact_iszero__number__of__Bit0,axiom,
% 173.13/173.34 ! [V_w_2,T_a] :
% 173.13/173.34 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 & class_Int_Oring__char__0(T_a) )
% 173.13/173.34 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 173.13/173.34 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__2,axiom,
% 173.13/173.34 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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_succ__Bit0,axiom,
% 173.13/173.34 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_succ__Bit1,axiom,
% 173.13/173.34 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__number__of__Bit0,axiom,
% 173.13/173.34 ! [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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 173.13/173.34 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))) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_number__of__Bit0,axiom,
% 173.13/173.34 ! [V_w,T_a] :
% 173.13/173.34 ( class_Int_Onumber__ring(T_a)
% 173.13/173.34 => 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)) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__0__iff,axiom,
% 173.13/173.34 ! [V_i_2] :
% 173.13/173.34 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 173.13/173.34
% 173.13/173.34 fof(fact_nat__le__0,axiom,
% 173.13/173.35 ! [V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mono__iff,axiom,
% 173.13/173.35 ! [V_w_2,V_z_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zless__nat__conj,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__1,axiom,
% 173.13/173.35 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__nat__eq,axiom,
% 173.13/173.35 ! [V_z] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__eq__iff,axiom,
% 173.13/173.35 ! [V_z_2,V_m_2] :
% 173.13/173.35 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 173.13/173.35 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__0__le,axiom,
% 173.13/173.35 ! [V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zless__nat__eq__int__zless,axiom,
% 173.13/173.35 ! [V_z_2,V_m_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 173.13/173.35 <=> 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_less__eq__int__code_I15_J,axiom,
% 173.13/173.35 ! [V_k2_2,V_k1_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I33_J,axiom,
% 173.13/173.35 ! [V_l_2,V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_less__int__code_I14_J,axiom,
% 173.13/173.35 ! [V_k2_2,V_k1_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I15_J,axiom,
% 173.13/173.35 ! [V_l_2,V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__zminus__int,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__Bit1,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power_Opower_Opower__0,axiom,
% 173.13/173.35 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__abs__mult__distrib,axiom,
% 173.13/173.35 ! [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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power_Opower_Opower__Suc,axiom,
% 173.13/173.35 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__bin__simps_I8_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__Bit1__Bit1,axiom,
% 173.13/173.35 ! [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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__number__of__even,axiom,
% 173.13/173.35 ! [V_w_2,V_z_2,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zpower__number__of__even,axiom,
% 173.13/173.35 ! [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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__nat__double,axiom,
% 173.13/173.35 ! [V_x,T_a] :
% 173.13/173.35 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_double__number__of__Bit0,axiom,
% 173.13/173.35 ! [V_w,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__less__nat__eq,axiom,
% 173.13/173.35 ! [V_z_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__less__eq__zless,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__eq__iff2,axiom,
% 173.13/173.35 ! [V_w_2,V_m_2] :
% 173.13/173.35 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 173.13/173.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__eq__iff,axiom,
% 173.13/173.35 ! [V_m_2,V_w_2] :
% 173.13/173.35 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 173.13/173.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__le__eq__zle,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 173.13/173.35 => ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__nat,axiom,
% 173.13/173.35 ! [V_i_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 173.13/173.35 <=> ( ! [B_n] :
% 173.13/173.35 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_n)) )
% 173.13/173.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__add__distrib,axiom,
% 173.13/173.35 ! [V_z_H,V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__eq__iff__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_m_2] :
% 173.13/173.35 ( 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)
% 173.13/173.35 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 173.13/173.35 & 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__distrib,axiom,
% 173.13/173.35 ! [V_z_H,V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_number__of1,axiom,
% 173.13/173.35 ! [V_n] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 => ( 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))))
% 173.13/173.35 & 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)))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__diff__distrib,axiom,
% 173.13/173.35 ! [V_z,V_z_H] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 173.13/173.35 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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__number__of__even__number__of,axiom,
% 173.13/173.35 ! [V_w_2,V_v_2,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 173.13/173.35 ! [V_n,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__power__eq,axiom,
% 173.13/173.35 ! [V_n,V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__nat__eq__if,axiom,
% 173.13/173.35 ! [V_z_2,V_z_H_2] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__2,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__2__right,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_one__less__nat__eq,axiom,
% 173.13/173.35 ! [V_z_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_one__add__one__is__two,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__less__iff,axiom,
% 173.13/173.35 ! [V_m_2,V_w_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 173.13/173.35 <=> 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 173.13/173.35 ! [V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__eq__power2,axiom,
% 173.13/173.35 ! [V_a_2,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 173.13/173.35 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
% 173.13/173.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__power2,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_numeral__2__eq__2,axiom,
% 173.13/173.35 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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_semiring__norm_I115_J,axiom,
% 173.13/173.35 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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 173.13/173.35 ! [V_x,T_a] :
% 173.13/173.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__eq__square,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 173.13/173.35 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))))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__2__eq__Suc,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__2__eq__Suc_H,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_one__power2,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__distrib__neg,axiom,
% 173.13/173.35 ! [V_z_H,V_z] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__minus,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__2__right,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__2,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__even__eq,axiom,
% 173.13/173.35 ! [V_n,V_a,T_a] :
% 173.13/173.35 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.35 => 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 173.13/173.35 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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__abs,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_abs__power2,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__1__add__1,axiom,
% 173.13/173.35 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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__eq__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_n_2] :
% 173.13/173.35 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 173.13/173.35 <=> 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))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_eq__number__of__Suc,axiom,
% 173.13/173.35 ! [V_n_2,V_v_2] :
% 173.13/173.35 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 173.13/173.35 <=> 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))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__case__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__eq__imp__eq,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.35 => ( 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))))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.35 => V_x = V_y ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__le__imp__le,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.35 => ( 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))))))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__le__power2,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => 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)))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__less__0,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ~ 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__less__power2,axiom,
% 173.13/173.35 ! [V_a_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( 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_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 173.13/173.35 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_sum__power2__eq__zero__iff,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
% 173.13/173.35 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__eq__square__number__of,axiom,
% 173.13/173.35 ! [V_w,T_b] :
% 173.13/173.35 ( ( class_Groups_Omonoid__mult(T_b)
% 173.13/173.35 & class_Int_Onumber(T_b) )
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_less__2__cases,axiom,
% 173.13/173.35 ! [V_n] :
% 173.13/173.35 ( 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)))))
% 173.13/173.35 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__rec__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__eq__1__iff,axiom,
% 173.13/173.35 ! [V_a_2,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 173.13/173.35 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
% 173.13/173.35 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.35 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 173.13/173.35 ! [V_n,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__minus__even,axiom,
% 173.13/173.35 ! [V_n,V_a,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__nat__number__of__number__of,axiom,
% 173.13/173.35 ! [V_w,V_v] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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)) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__nat__number__of,axiom,
% 173.13/173.35 ! [V_n,V_v] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_less__number__of__Suc,axiom,
% 173.13/173.35 ! [V_n_2,V_v_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_less__Suc__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_n_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> 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))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_le__Suc__number__of,axiom,
% 173.13/173.35 ! [V_v_2,V_n_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> 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))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_le__number__of__Suc,axiom,
% 173.13/173.35 ! [V_n_2,V_v_2] :
% 173.13/173.35 ( 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)))
% 173.13/173.35 <=> 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__less__imp__less,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__semidom(T_a)
% 173.13/173.35 => ( 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))))))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_sum__power2__ge__zero,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => 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))))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_sum__power2__le__zero__iff,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)))
% 173.13/173.35 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__case__add__eq__if,axiom,
% 173.13/173.35 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_sum__power2__gt__zero__iff,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 173.13/173.35 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_not__sum__power2__lt__zero,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ~ 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__sum,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zero__le__even__power_H,axiom,
% 173.13/173.35 ! [V_n,V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => 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)))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__rec__add__eq__if,axiom,
% 173.13/173.35 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),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_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,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))))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__odd__eq,axiom,
% 173.13/173.35 ! [V_n,V_a,T_a] :
% 173.13/173.35 ( class_Groups_Omonoid__mult(T_a)
% 173.13/173.35 => 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))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 173.13/173.35 ! [V_n,V_x,T_a] :
% 173.13/173.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__minus1__even,axiom,
% 173.13/173.35 ! [V_n,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power2__diff,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 173.13/173.35 ! [V_n,V_a,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( 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)))))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__aux__def,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__number__of__Bit1,axiom,
% 173.13/173.35 ! [V_v,V_w] :
% 173.13/173.35 ( ( 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)))
% 173.13/173.35 => 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)) )
% 173.13/173.35 & ( ~ 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)))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__zmod__mult__2,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__morphism__nat__int,axiom,
% 173.13/173.35 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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__zmod__mult__2,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__cong,axiom,
% 173.13/173.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 173.13/173.35 => 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) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__simps_I1_J,axiom,
% 173.13/173.35 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__simps_I2_J,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__left__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__right__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__self1,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__add__self2,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__cong,axiom,
% 173.13/173.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 173.13/173.35 => 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) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__simps_I4_J,axiom,
% 173.13/173.35 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__mult2,axiom,
% 173.13/173.35 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__mult1,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__left__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__right__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mod__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__minus__eq,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__minus__cong,axiom,
% 173.13/173.35 ! [V_a_H,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__0,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__by__0,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__self,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__diff__right__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__diff__left__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__diff__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__diff__cong,axiom,
% 173.13/173.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Oring__div(T_a)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 173.13/173.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 173.13/173.35 => 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) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__self,axiom,
% 173.13/173.35 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zero,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zmult1__eq,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__simps_I3_J,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiff__zmod__left,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiff__zmod__right,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zminus__zmod,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus__zminus,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus2,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zpower__zmod,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self2__is__0,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self1__is__0,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self2,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self1,axiom,
% 173.13/173.35 ! [V_b,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__by__1,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__le__nonneg__dividend,axiom,
% 173.13/173.35 ! [V_k,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__mod__bound,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__mod__bound,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__eq__0__iff,axiom,
% 173.13/173.35 ! [V_d_2,V_m_2] :
% 173.13/173.35 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus2__not__zero,axiom,
% 173.13/173.35 ! [V_l,V_k] :
% 173.13/173.35 ( 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)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus1__not__zero,axiom,
% 173.13/173.35 ! [V_l,V_k] :
% 173.13/173.35 ( 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)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__neg__neg__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__mod__conj,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 & 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__mod__sign,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__pos__pos__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__mod__conj,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 & 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__mod__sign,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => 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))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus2__eq__if,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zminus1__eq__if,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__pos__neg__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__zmod,axiom,
% 173.13/173.35 ! [V_k_2,V_n_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 173.13/173.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 173.13/173.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.35 => ! [B_i,B_j] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 173.13/173.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ! [B_i,B_j] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult2__lemma__aux3,axiom,
% 173.13/173.35 ! [V_q,V_b,V_r,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult2__lemma__aux4,axiom,
% 173.13/173.35 ! [V_q,V_b,V_r,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult2__lemma__aux1,axiom,
% 173.13/173.35 ! [V_q,V_r,V_b,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult2__lemma__aux2,axiom,
% 173.13/173.35 ! [V_q,V_r,V_b,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_divmod__int__rel__mod__eq,axiom,
% 173.13/173.35 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 173.13/173.35 ( 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)
% 173.13/173.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 173.13/173.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__number__of__Bit0,axiom,
% 173.13/173.35 ! [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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_z3mod__def,axiom,
% 173.13/173.35 ! [V_k,V_l] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.35 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__zdiv__mult__2,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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(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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__zdiv__mult__2,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__less,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__less__eq__dividend,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__distrib2,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__distrib,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zminus__zminus,axiom,
% 173.13/173.35 ! [V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zminus2,axiom,
% 173.13/173.35 ! [V_b,V_a] : hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zero,axiom,
% 173.13/173.35 ! [V_b] : 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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__by__0,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__0,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__by__1,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__1,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__Suc,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.35 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__less__divisor,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 173.13/173.35 ! [V_a_2,V_b_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 173.13/173.35 ! [V_a_2,V_b_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__neg__pos__less0,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__self,axiom,
% 173.13/173.35 ! [V_a] :
% 173.13/173.35 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__eq__0__iff,axiom,
% 173.13/173.35 ! [V_d_2,V_m_2] :
% 173.13/173.35 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__if,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__geq,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__number__of__Bit0,axiom,
% 173.13/173.35 ! [V_w,V_v] : 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(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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_DIVISION__BY__ZERO,axiom,
% 173.13/173.35 ! [V_a] :
% 173.13/173.35 ( 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)
% 173.13/173.35 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zdiv__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] : 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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self3,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_le__mod__geq,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zadd1__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_c)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_c))),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__int,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__mult1,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__mult2,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self1__is__id,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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 ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self2__is__id,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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 ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__mult1__if,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__self,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__div__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 173.13/173.35 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__set__def,axiom,
% 173.13/173.35 ! [V_S_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_S_2)
% 173.13/173.35 <=> ! [B_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__eq__0__iff,axiom,
% 173.13/173.35 ! [V_k_2,V_i_2] :
% 173.13/173.35 ( hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 173.13/173.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 173.13/173.35 ! [V_a_2,V_b_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 173.13/173.35 ! [V_i_2,V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2),V_k_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 173.13/173.35 ! [V_b_2,V_a_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__mono2,axiom,
% 173.13/173.35 ! [V_b,V_b_H,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b_H))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__nonneg__neg__le0,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__pos__pos__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 173.13/173.35 ! [V_a_2,V_b_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__nonpos__pos__le0,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__mono2__neg,axiom,
% 173.13/173.35 ! [V_b,V_b_H,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b_H)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__neg__neg__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__mono1,axiom,
% 173.13/173.35 ! [V_b,V_a_H,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H),V_b))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__mono1__neg,axiom,
% 173.13/173.35 ! [V_b,V_a_H,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__le__divisor,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__div__less__self,axiom,
% 173.13/173.35 ! [V_k,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_k)),V_x)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zmult2__eq,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),V_c) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult__self4,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => ( V_A_2 = V_B_2
% 173.13/173.35 <=> 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) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zdiv__equality,axiom,
% 173.13/173.35 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zmult1__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_c))),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zmod__equality,axiom,
% 173.13/173.35 ! [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(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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zmod__equality2,axiom,
% 173.13/173.35 ! [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(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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zdiv__equality_H,axiom,
% 173.13/173.35 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m),V_n)),V_n)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult__div__cancel,axiom,
% 173.13/173.35 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self2,axiom,
% 173.13/173.35 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self1,axiom,
% 173.13/173.35 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__add__self2,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__add__self1,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mod__equality,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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(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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mod__equality2,axiom,
% 173.13/173.35 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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(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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__div__equality,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__div__equality2,axiom,
% 173.13/173.35 ! [V_a,V_b,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),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 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Divides_Osemiring__div(T_a)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),V_b)) = V_a ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__mod,axiom,
% 173.13/173.35 ! [V_k_2,V_n_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 173.13/173.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 173.13/173.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => ! [B_i,B_j] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 173.13/173.35 => ( 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)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__lemma,axiom,
% 173.13/173.35 ! [V_q,V_b,V_r,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__times__mod__eq,axiom,
% 173.13/173.35 ! [V_m,V_k] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mod__distrib,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 173.13/173.35 ! [V_x_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_divmod__int__rel__div__eq,axiom,
% 173.13/173.35 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 173.13/173.35 ( 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)
% 173.13/173.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 173.13/173.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1),V_b_1) = V_y ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__zdiv,axiom,
% 173.13/173.35 ! [V_k_2,V_n_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2),V_k_2)))
% 173.13/173.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.35 => ! [B_i] :
% 173.13/173.35 ( ? [B_j] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 173.13/173.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ! [B_i] :
% 173.13/173.35 ( ? [B_j] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__zmult2__eq,axiom,
% 173.13/173.35 ! [V_b,V_a,V_c] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.35 => 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(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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod2__Suc__Suc,axiom,
% 173.13/173.35 ! [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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zminus2__eq__if,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)) )
% 173.13/173.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__zminus1__eq__if,axiom,
% 173.13/173.35 ! [V_a,V_b] :
% 173.13/173.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)) )
% 173.13/173.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 173.13/173.35 ! [V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => 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 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__neg__lemma,axiom,
% 173.13/173.35 ! [V_n_2,V_P_2,V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(V_P_2,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)))
% 173.13/173.35 <=> ! [B_i,B_j] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__pos__lemma,axiom,
% 173.13/173.35 ! [V_n_2,V_P_2,V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(V_P_2,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)))
% 173.13/173.35 <=> ! [B_i,B_j] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 173.13/173.35 & 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) )
% 173.13/173.35 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__nat__number__of,axiom,
% 173.13/173.35 ! [V_v_H,V_v] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.35 => 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))) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__number__of__Bit1,axiom,
% 173.13/173.35 ! [V_v,V_w] :
% 173.13/173.35 ( ( 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)))
% 173.13/173.35 => 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(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)) )
% 173.13/173.35 & ( ~ 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)))
% 173.13/173.35 => 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(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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__power__div__base,axiom,
% 173.13/173.35 ! [V_k,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 173.13/173.35 => 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)))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod2__gr__0,axiom,
% 173.13/173.35 ! [V_m_2] :
% 173.13/173.35 ( 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))))))
% 173.13/173.35 <=> 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.35 <=> 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.35 <=> 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_one__mod__nat__number__of,axiom,
% 173.13/173.35 ! [V_v_H] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.35 => 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)) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 173.13/173.35 => 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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_z3div__def,axiom,
% 173.13/173.35 ! [V_k,V_l] :
% 173.13/173.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.35 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k),V_l) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.35 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__m1__odd,axiom,
% 173.13/173.35 ! [V_n,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_power__m1__even,axiom,
% 173.13/173.35 ! [V_n,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 173.13/173.35 ! [V_A_2,V_x_2] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 173.13/173.35 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 173.13/173.35 <=> 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 173.13/173.35 ! [V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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)))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__add1__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_c)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b),V_c))),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult2__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_b)),V_c) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__le__dividend,axiom,
% 173.13/173.35 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_m)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__le__mono,axiom,
% 173.13/173.35 ! [V_k,V_n,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_k)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n),V_k))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I42_J,axiom,
% 173.13/173.35 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I45_J,axiom,
% 173.13/173.35 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Bit1__Min,axiom,
% 173.13/173.35 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I43_J,axiom,
% 173.13/173.35 ! [V_l_2] :
% 173.13/173.35 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 173.13/173.35 <=> c_Int_OMin = V_l_2 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I47_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 173.13/173.35 <=> V_k_2 = c_Int_OMin ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I40_J,axiom,
% 173.13/173.35 c_Int_OMin != c_Int_OPls ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I37_J,axiom,
% 173.13/173.35 c_Int_OPls != c_Int_OMin ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I7_J,axiom,
% 173.13/173.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I24_J,axiom,
% 173.13/173.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 173.13/173.35 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 173.13/173.35 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 173.13/173.35 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 173.13/173.35 ! [V_n,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__1,axiom,
% 173.13/173.35 ! [V_m] : 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 ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__less,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__div__cancel__disj,axiom,
% 173.13/173.35 ! [V_n,V_m,V_k] :
% 173.13/173.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult1__eq,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b),V_c))),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mod__mult2__eq,axiom,
% 173.13/173.35 ! [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(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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mod__equality_H,axiom,
% 173.13/173.35 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__div__cancel,axiom,
% 173.13/173.35 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Omod__div__equality_H,axiom,
% 173.13/173.35 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_n)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x),V_y)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__int,axiom,
% 173.13/173.35 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_b)) = 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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_bin__less__0__simps_I2_J,axiom,
% 173.13/173.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I20_J,axiom,
% 173.13/173.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I23_J,axiom,
% 173.13/173.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I30_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I26_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I6_J,axiom,
% 173.13/173.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I3_J,axiom,
% 173.13/173.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I9_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I13_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I28_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I8_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_eq__number__of__Pls__Min,axiom,
% 173.13/173.35 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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Int_OMin__def,axiom,
% 173.13/173.35 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__Min,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 173.13/173.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_neg__number__of__Min,axiom,
% 173.13/173.35 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pred__Pls,axiom,
% 173.13/173.35 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__Min__right,axiom,
% 173.13/173.35 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__Min,axiom,
% 173.13/173.35 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pred__Min,axiom,
% 173.13/173.35 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nonzero__number__of__Min,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_succ__Min,axiom,
% 173.13/173.35 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__bin__simps_I2_J,axiom,
% 173.13/173.35 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_is__nat__def,axiom,
% 173.13/173.35 ! [V_x_2] :
% 173.13/173.35 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__le__mono2,axiom,
% 173.13/173.35 ! [V_k,V_n,V_m] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k),V_n)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k),V_m))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__mult__div__cancel1,axiom,
% 173.13/173.35 ! [V_n,V_m,V_k] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self__is__m,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => 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 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__mult__self1__is__m,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => 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 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__less__dividend,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_m)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__minus1__right,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_mult__minus1,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_number__of__Min,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_arith__simps_I31_J,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_abs__minus__one,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I25_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_rel__simps_I11_J,axiom,
% 173.13/173.35 ! [V_k_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__minus1__right,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__bin__simps_I4_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_minus__Min,axiom,
% 173.13/173.35 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmult__eq__1__iff,axiom,
% 173.13/173.35 ! [V_n_2,V_m_2] :
% 173.13/173.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.35 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.35 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 173.13/173.35 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 173.13/173.35 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 173.13/173.35 ! [V_n,V_m] :
% 173.13/173.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.35 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 173.13/173.35 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__bin__simps_I6_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_diff__bin__simps_I5_J,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zdiv__minus1__right,axiom,
% 173.13/173.35 ! [V_a] : 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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 173.13/173.35 ! [V_x_2,V_A_2] :
% 173.13/173.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 173.13/173.35 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__if,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__geq,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__div,axiom,
% 173.13/173.35 ! [V_k_2,V_n_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2),V_k_2)))
% 173.13/173.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 173.13/173.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 => ! [B_i,B_j] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 173.13/173.35 => ( 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)
% 173.13/173.35 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 173.13/173.35 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_nat__div__distrib,axiom,
% 173.13/173.35 ! [V_y,V_x] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 173.13/173.35 => hAPP(c_Int_Onat,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_abs__power__minus__one,axiom,
% 173.13/173.35 ! [V_n,T_a] :
% 173.13/173.35 ( ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 & class_Rings_Olinordered__idom(T_a) )
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__eq__minus1,axiom,
% 173.13/173.35 ! [V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 173.13/173.35 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_le__div__geq,axiom,
% 173.13/173.35 ! [V_m,V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.35 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__div__lemma,axiom,
% 173.13/173.35 ! [V_m_2,V_q_2,V_n_2] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 173.13/173.35 => ( ( 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))
% 173.13/173.35 & 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)))) )
% 173.13/173.35 <=> V_q_2 = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_split__div_H,axiom,
% 173.13/173.35 ! [V_n_2,V_m_2,V_P_2] :
% 173.13/173.35 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2)))
% 173.13/173.35 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.35 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 173.13/173.35 | ? [B_q] :
% 173.13/173.35 ( 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))
% 173.13/173.35 & 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))))
% 173.13/173.35 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__Suc__eq__div__add3,axiom,
% 173.13/173.35 ! [V_n,V_m] : 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(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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__div__eq__add3__div,axiom,
% 173.13/173.35 ! [V_n,V_m] : 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(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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 173.13/173.35 ! [V_v,V_m] : 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(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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div2__Suc__Suc,axiom,
% 173.13/173.35 ! [V_m] : 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(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))))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_add__self__div__2,axiom,
% 173.13/173.35 ! [V_m] : 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 ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 173.13/173.35 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__nat__number__of,axiom,
% 173.13/173.35 ! [V_v_H,V_v] :
% 173.13/173.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 173.13/173.35 => 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(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))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__pos__neg__trivial,axiom,
% 173.13/173.35 ! [V_b,V_a] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.35 => ( 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)))
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_zmod__minus1,axiom,
% 173.13/173.35 ! [V_b] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_div__2__gt__zero,axiom,
% 173.13/173.35 ! [V_n] :
% 173.13/173.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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)))))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_one__div__nat__number__of,axiom,
% 173.13/173.35 ! [V_v_H] : 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(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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__of__code,axiom,
% 173.13/173.35 ! [V_k] :
% 173.13/173.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.35 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.35 => ( ( 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)
% 173.13/173.35 => 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(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)))))) )
% 173.13/173.35 & ( 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)
% 173.13/173.35 => 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(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)) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__Suc__number__of,axiom,
% 173.13/173.35 ! [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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__number__of__Suc,axiom,
% 173.13/173.35 ! [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)))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_code__numeral_Osize_I1_J,axiom,
% 173.13/173.35 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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__of__nat,axiom,
% 173.13/173.35 ! [V_k,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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)))) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => 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)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__of__mono,axiom,
% 173.13/173.35 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] :
% 173.13/173.35 ( ( class_Orderings_Olinorder(T_b)
% 173.13/173.35 & class_Orderings_Olinorder(T_a) )
% 173.13/173.35 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.35 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_m_2),V_n_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_inf__nat__def,axiom,
% 173.13/173.35 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_inf__min,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.35 & class_Orderings_Olinorder(T_a) )
% 173.13/173.35 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__0R,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__0L,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__Suc__Suc,axiom,
% 173.13/173.35 ! [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)) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__diff,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__le__iff__disj,axiom,
% 173.13/173.35 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 173.13/173.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__infE,axiom,
% 173.13/173.35 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( 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)))
% 173.13/173.35 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__mono,axiom,
% 173.13/173.35 ! [V_d,V_b,V_c,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__greatest,axiom,
% 173.13/173.35 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__infI,axiom,
% 173.13/173.35 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 173.13/173.35 => 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))) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__absorb2,axiom,
% 173.13/173.35 ! [V_x,V_y,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.35 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__absorb1,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.35 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__infI2,axiom,
% 173.13/173.35 ! [V_a,V_x,V_b,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__infI1,axiom,
% 173.13/173.35 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__inf__iff,axiom,
% 173.13/173.35 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2)))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Ole__iff__inf,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.35 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__le2,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__le1,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__less__iff__disj,axiom,
% 173.13/173.35 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 173.13/173.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__less__iff__conj,axiom,
% 173.13/173.35 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)))
% 173.13/173.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 173.13/173.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oless__infI2,axiom,
% 173.13/173.35 ! [V_a,V_x,V_b,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oless__infI1,axiom,
% 173.13/173.35 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 173.13/173.35 => 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)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf_Oidem,axiom,
% 173.13/173.35 ! [V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf_Ocommute,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__commute,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 173.13/173.35 ! [V_b,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__left__idem,axiom,
% 173.13/173.35 ! [V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 173.13/173.35 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__left__commute,axiom,
% 173.13/173.35 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf_Oassoc,axiom,
% 173.13/173.35 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Oinf__assoc,axiom,
% 173.13/173.35 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.35 ( class_Orderings_Olinorder(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__eq__iff,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2,T_a] :
% 173.13/173.35 ( class_Int_Oring__char__0(T_a)
% 173.13/173.35 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 173.13/173.35 <=> V_w_2 = V_z_2 ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__diff__distrib__left,axiom,
% 173.13/173.35 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.35 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__add__distrib__left,axiom,
% 173.13/173.35 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.35 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_number__of__eq,axiom,
% 173.13/173.35 ! [V_k,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_int__number__of__def,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__int__eq,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__number__of,axiom,
% 173.13/173.35 ! [V_v,V_u,T_b] :
% 173.13/173.35 ( ( class_Int_Onumber(T_b)
% 173.13/173.35 & class_Orderings_Oord(T_b) )
% 173.13/173.35 => ( ( 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)))
% 173.13/173.35 => 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) )
% 173.13/173.35 & ( ~ 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)))
% 173.13/173.35 => 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) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__eq__0__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Int_Oring__char__0(T_a)
% 173.13/173.35 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__0__eq__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Int_Oring__char__0(T_a)
% 173.13/173.35 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 173.13/173.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__0,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__le__iff,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__less__iff,axiom,
% 173.13/173.35 ! [V_z_2,V_w_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__add,axiom,
% 173.13/173.35 ! [V_z,V_w,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__number__of__eq,axiom,
% 173.13/173.35 ! [V_v,T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__mult,axiom,
% 173.13/173.35 ! [V_z,V_w,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__1,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__diff,axiom,
% 173.13/173.35 ! [V_z,V_w,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__of__nat__eq,axiom,
% 173.13/173.35 ! [V_n,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__minus,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_Ints__of__int,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__power,axiom,
% 173.13/173.35 ! [V_n,V_z,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__max_Omono__inf,axiom,
% 173.13/173.35 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.35 ( ( class_Lattices_Osemilattice__inf(T_b)
% 173.13/173.35 & class_Orderings_Olinorder(T_a) )
% 173.13/173.35 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__m1,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Int_Onumber__ring(T_a)
% 173.13/173.35 => 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) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__Suc2,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__Suc1,axiom,
% 173.13/173.35 ! [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) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__le__0__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__0__le__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__less__0__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__0__less__iff,axiom,
% 173.13/173.35 ! [V_z_2,T_a] :
% 173.13/173.35 ( class_Rings_Olinordered__idom(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 173.13/173.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__nat__nat,axiom,
% 173.13/173.35 ! [V_z,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 173.13/173.35 => 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) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_small__int__def,axiom,
% 173.13/173.35 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_of__int__num,axiom,
% 173.13/173.35 ! [V_k_2,T_a] :
% 173.13/173.35 ( class_Rings_Oring__1(T_a)
% 173.13/173.35 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 173.13/173.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 173.13/173.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),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_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),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))))) ) ) ) ) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_min__ord__min,axiom,
% 173.13/173.35 ! [T_a] :
% 173.13/173.35 ( class_Orderings_Oord(T_a)
% 173.13/173.35 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_code__numeral_Osize_I2_J,axiom,
% 173.13/173.35 ! [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))) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_code__numeral_Oinject,axiom,
% 173.13/173.35 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 173.13/173.35 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 173.13/173.35 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 173.13/173.35 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 173.13/173.35
% 173.13/173.35 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Suc__code__numeral__minus__one,axiom,
% 173.13/173.36 ! [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 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_code__numeral_Osize_I4_J,axiom,
% 173.13/173.36 ! [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))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_full__small__int__def,axiom,
% 173.13/173.36 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__def,axiom,
% 173.13/173.36 ! [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))))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Nitpick_OFrac__def,axiom,
% 173.13/173.36 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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__correct,axiom,
% 173.13/173.36 ! [V_a,V_b] :
% 173.13/173.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_code__numeral_Osize_I3_J,axiom,
% 173.13/173.36 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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 173.13/173.36 ! [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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_zmult2__lemma,axiom,
% 173.13/173.36 ! [V_c,V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 173.13/173.36 => 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(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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 173.13/173.36 ! [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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_adjust__eq,axiom,
% 173.13/173.36 ! [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))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_bot__empty__eq2,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pred__equals__eq2,axiom,
% 173.13/173.36 ! [V_S_2,V_R_2,T_b,T_a] :
% 173.13/173.36 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
% 173.13/173.36 <=> V_R_2 = V_S_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pred__subset__eq2,axiom,
% 173.13/173.36 ! [V_S_2,V_R_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup__Un__eq2,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf__Int__eq2,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_small__prod__def,axiom,
% 173.13/173.36 ! [V_d_2,V_f_2,T_a,T_b] :
% 173.13/173.36 ( ( class_Smallcheck_Osmall(T_b)
% 173.13/173.36 & class_Smallcheck_Osmall(T_a) )
% 173.13/173.36 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_unique__remainder,axiom,
% 173.13/173.36 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => V_r = V_r_H ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_unique__quotient,axiom,
% 173.13/173.36 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => V_q = V_q_H ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_self__remainder,axiom,
% 173.13/173.36 ! [V_r,V_q,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__0,axiom,
% 173.13/173.36 ! [V_b] :
% 173.13/173.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 173.13/173.36 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = 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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_self__quotient,axiom,
% 173.13/173.36 ! [V_r,V_q,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__mod,axiom,
% 173.13/173.36 ! [V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__div,axiom,
% 173.13/173.36 ! [V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = V_q ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__mod__div,axiom,
% 173.13/173.36 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__div__mod,axiom,
% 173.13/173.36 ! [V_a,V_b] :
% 173.13/173.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_nat__gcd_Osimps,axiom,
% 173.13/173.36 ! [V_x,V_y] :
% 173.13/173.36 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 173.13/173.36 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_zadd1__lemma,axiom,
% 173.13/173.36 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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(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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_zminus1__lemma,axiom,
% 173.13/173.36 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => 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))))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__relI,axiom,
% 173.13/173.36 ! [V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)
% 173.13/173.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_zmult1__lemma,axiom,
% 173.13/173.36 ! [V_a,V_r,V_q,V_c,V_b] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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(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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_adjust__def,axiom,
% 173.13/173.36 ! [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))))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__imageI,axiom,
% 173.13/173.36 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_norm__frac_Osimps,axiom,
% 173.13/173.36 ! [V_a_2,V_b_2] :
% 173.13/173.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.36 => 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)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b_2))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( 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))))
% 173.13/173.36 => 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))) )
% 173.13/173.36 & ( ~ 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))))
% 173.13/173.36 => 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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_splitI,axiom,
% 173.13/173.36 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup2CI,axiom,
% 173.13/173.36 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 173.13/173.36 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup2E,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf2I,axiom,
% 173.13/173.36 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf2E,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 173.13/173.36 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 173.13/173.36 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mem__splitI,axiom,
% 173.13/173.36 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod__caseI,axiom,
% 173.13/173.36 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_bot2E,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_swap__inj__on,axiom,
% 173.13/173.36 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_splitD_H,axiom,
% 173.13/173.36 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_ca_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf2D1,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf2D2,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup2I2,axiom,
% 173.13/173.36 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup2I1,axiom,
% 173.13/173.36 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_predicate2D,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_rev__predicate2D,axiom,
% 173.13/173.36 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_less__by__empty,axiom,
% 173.13/173.36 ! [V_B_2,T_a,V_A_2] :
% 173.13/173.36 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Pair__inject,axiom,
% 173.13/173.36 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 173.13/173.36 ( 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)
% 173.13/173.36 => ~ ( V_a = V_a_H
% 173.13/173.36 => V_b != V_b_H ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Pair__eq,axiom,
% 173.13/173.36 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.36 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2)
% 173.13/173.36 <=> ( V_a_2 = V_a_H_2
% 173.13/173.36 & V_b_2 = V_b_H_2 ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__paired__All,axiom,
% 173.13/173.36 ! [T_b,T_a,V_P_2] :
% 173.13/173.36 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.36 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__weak__cong,axiom,
% 173.13/173.36 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 173.13/173.36 ( V_p_2 = V_q_2
% 173.13/173.36 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__correct,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__twice,axiom,
% 173.13/173.36 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod_Osimps_I2_J,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__conv,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_splitD,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__div__mod,axiom,
% 173.13/173.36 ! [V_l,V_k] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.36 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__minus1,axiom,
% 173.13/173.36 ! [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))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__eta,axiom,
% 173.13/173.36 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__paired__The,axiom,
% 173.13/173.36 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_The__split__eq,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg_Osimps,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( ( ( 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)))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ ( 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)))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__eqn__number__of,axiom,
% 173.13/173.36 ! [V_w,V_v] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( 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))))
% 173.13/173.36 => 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))) )
% 173.13/173.36 & ( ~ 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))))
% 173.13/173.36 => 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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg__eqn,axiom,
% 173.13/173.36 ! [V_a,V_b] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => ( ( 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)))
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ 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)))
% 173.13/173.36 => 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))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_in__rel__def,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__mod__code__numeral__def,axiom,
% 173.13/173.36 ! [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(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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Nitpick_Orefl_H__def,axiom,
% 173.13/173.36 ! [V_r_2,T_a] :
% 173.13/173.36 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 173.13/173.36 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( 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)))
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ 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)))
% 173.13/173.36 => 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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__0,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__correct,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__div__mod,axiom,
% 173.13/173.36 ! [V_l,V_k] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 173.13/173.36 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__eqn__number__of,axiom,
% 173.13/173.36 ! [V_w,V_v] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( 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)))
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ 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)))
% 173.13/173.36 => 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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg__eqn,axiom,
% 173.13/173.36 ! [V_a,V_b] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.36 => 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))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg_Osimps,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__def,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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))) ) ) ) ) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => 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))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__step,axiom,
% 173.13/173.36 ! [V_m,V_n] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.36 => 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(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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__pdivmod,axiom,
% 173.13/173.36 ! [V_l_2,V_k_2] :
% 173.13/173.36 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__code,axiom,
% 173.13/173.36 ! [V_l_2,V_k_2] :
% 173.13/173.36 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negateSnd__def,axiom,
% 173.13/173.36 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apsnd__conv,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apsnd__compose,axiom,
% 173.13/173.36 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__zero,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__base,axiom,
% 173.13/173.36 ! [V_n,V_m] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 173.13/173.36 => 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negateSnd__eq,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__div__mod,axiom,
% 173.13/173.36 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__int__rel__neg,axiom,
% 173.13/173.36 ! [V_qr,V_b,V_a] :
% 173.13/173.36 ( 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))
% 173.13/173.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__if,axiom,
% 173.13/173.36 ! [V_m_2,V_n_2] :
% 173.13/173.36 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pdivmod__def,axiom,
% 173.13/173.36 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pdivmod__posDivAlg,axiom,
% 173.13/173.36 ! [V_k,V_l] :
% 173.13/173.36 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 173.13/173.36 ! [V_a,V_r,V_q,V_c,V_b] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 173.13/173.36 => 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(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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 173.13/173.36 ! [V_c,V_r,V_q,V_b,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 173.13/173.36 => 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(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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg_Opsimps,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( ( 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)))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ ( 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)))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_small_H_Opsimps,axiom,
% 173.13/173.36 ! [V_i_2,V_d_2,V_f_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 173.13/173.36 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 173.13/173.36 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__unique,axiom,
% 173.13/173.36 ! [V_qr_H,V_qr,V_n,V_m] :
% 173.13/173.36 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 173.13/173.36 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 173.13/173.36 => V_qr = V_qr_H ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_accp__downward,axiom,
% 173.13/173.36 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 173.13/173.36 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_accp_Oequations,axiom,
% 173.13/173.36 ! [V_a_2,V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 173.13/173.36 <=> ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 173.13/173.36 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_accp_Osimps,axiom,
% 173.13/173.36 ! [V_a_2,V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 173.13/173.36 <=> ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 173.13/173.36 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__eq,axiom,
% 173.13/173.36 ! [V_qr,V_n,V_m] :
% 173.13/173.36 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 173.13/173.36 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 173.13/173.36 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__def,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_accp__subset,axiom,
% 173.13/173.36 ! [V_R2_2,V_R1_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__eq,axiom,
% 173.13/173.36 ! [V_r,V_q,V_n,V_m] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__eq,axiom,
% 173.13/173.36 ! [V_r,V_q,V_n,V_m] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = V_q ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel,axiom,
% 173.13/173.36 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 173.13/173.36 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 173.13/173.36 => 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(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)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg_Opsimps,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => 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))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_norm__frac_Opsimps,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.36 => 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)) )
% 173.13/173.36 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 173.13/173.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 173.13/173.36 => 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)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b_2))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_negDivAlg_Opinduct,axiom,
% 173.13/173.36 ! [V_P_2,V_a1_2,V_a0_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ! [B_a,B_b] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( ~ ( 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)))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_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))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_small_H_Opinduct,axiom,
% 173.13/173.36 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
% 173.13/173.36 => ( ! [B_f,B_d,B_i] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
% 173.13/173.36 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 173.13/173.36 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_posDivAlg_Opinduct,axiom,
% 173.13/173.36 ! [V_P_2,V_a1_2,V_a0_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ! [B_a,B_b] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_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))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_nat__gcd_Opsimps,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 173.13/173.36 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__pos__neg__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => 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))))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_in__measure,axiom,
% 173.13/173.36 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)))
% 173.13/173.36 <=> 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_snd__eqD,axiom,
% 173.13/173.36 ! [V_a,V_y,V_x,T_a,T_b] :
% 173.13/173.36 ( 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
% 173.13/173.36 => V_y = V_a ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_snd__conv,axiom,
% 173.13/173.36 ! [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 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apsnd__eq__conv,axiom,
% 173.13/173.36 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 173.13/173.36 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2)
% 173.13/173.36 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_snd__apsnd,axiom,
% 173.13/173.36 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_snd__def,axiom,
% 173.13/173.36 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__int__def,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__neg__pos,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__pos__pos,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__pos__pos__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__pos__neg,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__neg__neg,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_norm__frac_Opinduct,axiom,
% 173.13/173.36 ! [V_P_2,V_a1_2,V_a0_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ! [B_a,B_b] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__pos__neg__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => 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))))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_nat__gcd_Opinduct,axiom,
% 173.13/173.36 ! [V_P_2,V_a1_2,V_a0_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ! [B_x,B_y] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mlex__leq,axiom,
% 173.13/173.36 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod__eqI,axiom,
% 173.13/173.36 ! [V_q,V_p,T_b,T_a] :
% 173.13/173.36 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 173.13/173.36 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 173.13/173.36 => V_p = V_q ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Pair__fst__snd__eq,axiom,
% 173.13/173.36 ! [T_b,T_a,V_t_2,V_s_2] :
% 173.13/173.36 ( V_s_2 = V_t_2
% 173.13/173.36 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 173.13/173.36 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_fst__conv,axiom,
% 173.13/173.36 ! [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 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_fst__eqD,axiom,
% 173.13/173.36 ! [V_a,V_y,V_x,T_b,T_a] :
% 173.13/173.36 ( 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
% 173.13/173.36 => V_x = V_a ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_fst__apsnd,axiom,
% 173.13/173.36 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_fst__def,axiom,
% 173.13/173.36 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_surjective__pairing,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__collapse,axiom,
% 173.13/173.36 ! [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 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod__case__beta,axiom,
% 173.13/173.36 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__comp,axiom,
% 173.13/173.36 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__int__def,axiom,
% 173.13/173.36 ! [V_b,V_a] : 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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mod__nat__def,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__comp__eq,axiom,
% 173.13/173.36 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__beta,axiom,
% 173.13/173.36 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_split__def,axiom,
% 173.13/173.36 ! [V_p_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_The__split,axiom,
% 173.13/173.36 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__neg__pos,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__pos__pos,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__pos__pos__1__number__of,axiom,
% 173.13/173.36 ! [V_w] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__pos__neg,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__neg__neg,axiom,
% 173.13/173.36 ! [V_b,V_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 173.13/173.36 => 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)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mlex__less,axiom,
% 173.13/173.36 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 173.13/173.36 ( 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)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod__size__simp,axiom,
% 173.13/173.36 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,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_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_conjI__realizer,axiom,
% 173.13/173.36 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 173.13/173.36 ( hBOOL(hAPP(V_P_2,V_p_2))
% 173.13/173.36 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 173.13/173.36 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2))))
% 173.13/173.36 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_exI__realizer,axiom,
% 173.13/173.36 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_prod_Orecs,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_div__nat__def,axiom,
% 173.13/173.36 ! [V_n,V_m] : 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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_divmod__nat__rel__def,axiom,
% 173.13/173.36 ! [V_qr_2,V_n_2,V_m_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 173.13/173.36 <=> ( 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))
% 173.13/173.36 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.36 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 & 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)) ) )
% 173.13/173.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 173.13/173.36 => ( 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)))
% 173.13/173.36 & 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))) ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_in__lex__prod,axiom,
% 173.13/173.36 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2))
% 173.13/173.36 | ( V_a_2 = V_a_H_2
% 173.13/173.36 & 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_b_H_2)),V_s_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__number__of__Suc,axiom,
% 173.13/173.36 ! [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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__Suc__number__of,axiom,
% 173.13/173.36 ! [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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apsnd__apfst,axiom,
% 173.13/173.36 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__inf__absorb,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 173.13/173.36 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 173.13/173.36 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__of__mono,axiom,
% 173.13/173.36 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] :
% 173.13/173.36 ( ( class_Orderings_Olinorder(T_b)
% 173.13/173.36 & class_Orderings_Olinorder(T_a) )
% 173.13/173.36 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_m_2),V_n_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__0R,axiom,
% 173.13/173.36 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__0L,axiom,
% 173.13/173.36 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__Suc__Suc,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__less__iff__conj,axiom,
% 173.13/173.36 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_less__max__iff__disj,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Oless__supI2,axiom,
% 173.13/173.36 ! [V_a,V_b,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Oless__supI1,axiom,
% 173.13/173.36 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup_Oidem,axiom,
% 173.13/173.36 ! [V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup_Ocommute,axiom,
% 173.13/173.36 ! [V_b,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__commute,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 173.13/173.36 ! [V_b,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__left__idem,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 173.13/173.36 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__left__commute,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup_Oassoc,axiom,
% 173.13/173.36 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__assoc,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__diff__distrib__left,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__add__distrib__left,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_le__maxI1,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_le__maxI2,axiom,
% 173.13/173.36 ! [V_x,V_y,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__iff__sup,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.36 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__sup__iff,axiom,
% 173.13/173.36 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__supI1,axiom,
% 173.13/173.36 ! [V_b,V_a,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__supI2,axiom,
% 173.13/173.36 ! [V_a,V_b,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 173.13/173.36 => 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__absorb2,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__absorb1,axiom,
% 173.13/173.36 ! [V_x,V_y,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__supI,axiom,
% 173.13/173.36 ! [V_b,V_x,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__least,axiom,
% 173.13/173.36 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Osup__mono,axiom,
% 173.13/173.36 ! [V_d,V_b,V_c,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 173.13/173.36 => 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))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Ole__supE,axiom,
% 173.13/173.36 ! [V_x,V_b,V_a,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( 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))
% 173.13/173.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 173.13/173.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_le__max__iff__disj,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 173.13/173.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup__max,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.36 & class_Orderings_Olinorder(T_a) )
% 173.13/173.36 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup__nat__def,axiom,
% 173.13/173.36 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apfst__conv,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apfst__compose,axiom,
% 173.13/173.36 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_fst__apfst,axiom,
% 173.13/173.36 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apfst__eq__conv,axiom,
% 173.13/173.36 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.36 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2)
% 173.13/173.36 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_snd__apfst,axiom,
% 173.13/173.36 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__number__of,axiom,
% 173.13/173.36 ! [V_v,V_u,T_b] :
% 173.13/173.36 ( ( class_Int_Onumber(T_b)
% 173.13/173.36 & class_Orderings_Oord(T_b) )
% 173.13/173.36 => ( ( 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)))
% 173.13/173.36 => 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) )
% 173.13/173.36 & ( ~ 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)))
% 173.13/173.36 => 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) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Odistrib__sup__le,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Odistrib__inf__le,axiom,
% 173.13/173.36 ! [V_z,V_y,V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => 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)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_minus__min__eq__max,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_minus__max__eq__min,axiom,
% 173.13/173.36 ! [V_y,V_x,T_a] :
% 173.13/173.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_nat__minus__add__max,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apsnd__apfst__commute,axiom,
% 173.13/173.36 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__Suc2,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__Suc1,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__max_Omono__sup,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.36 ( ( class_Lattices_Osemilattice__sup(T_b)
% 173.13/173.36 & class_Orderings_Olinorder(T_a) )
% 173.13/173.36 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_A_2),V_B_2)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_apfst__apsnd,axiom,
% 173.13/173.36 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_dual__min,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_same__fstI,axiom,
% 173.13/173.36 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 173.13/173.36 ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__ord__max,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( class_Orderings_Oord(T_a)
% 173.13/173.36 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__lessI2,axiom,
% 173.13/173.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oidem,axiom,
% 173.13/173.36 ! [V_x,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oidem,axiom,
% 173.13/173.36 ! [V_x,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Oidem,axiom,
% 173.13/173.36 ! [V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Oidem,axiom,
% 173.13/173.36 ! [V_x,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_dual__max,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__lessI1,axiom,
% 173.13/173.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__leqI2,axiom,
% 173.13/173.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_smax__insertI,axiom,
% 173.13/173.36 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_smin__insertI,axiom,
% 173.13/173.36 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__leqI1,axiom,
% 173.13/173.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_smin__emptyI,axiom,
% 173.13/173.36 ! [V_X_2] :
% 173.13/173.36 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_wmin__insertI,axiom,
% 173.13/173.36 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_wmax__insertI,axiom,
% 173.13/173.36 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_wmin__emptyI,axiom,
% 173.13/173.36 ! [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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__strict__def,axiom,
% 173.13/173.36 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__weak__def,axiom,
% 173.13/173.36 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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__weak__def,axiom,
% 173.13/173.36 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)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__rpair__set,axiom,
% 173.13/173.36 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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_min__rpair__set,axiom,
% 173.13/173.36 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)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_less__than__iff,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2] :
% 173.13/173.36 ( 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))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_pair__less__def,axiom,
% 173.13/173.36 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__strict__def,axiom,
% 173.13/173.36 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__ext__additive,axiom,
% 173.13/173.36 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_max__extp__max__ext__eq,axiom,
% 173.13/173.36 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 173.13/173.36 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mlex__prod__def,axiom,
% 173.13/173.36 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_intrel__iff,axiom,
% 173.13/173.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 173.13/173.36 ( 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))
% 173.13/173.36 <=> 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) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_rp__inv__image__rp,axiom,
% 173.13/173.36 ! [V_f_2,T_b,V_P_2,T_a] :
% 173.13/173.36 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 173.13/173.36 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_rp__inv__image__def,axiom,
% 173.13/173.36 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_in__inv__image,axiom,
% 173.13/173.36 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2)))
% 173.13/173.36 <=> 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,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__intrel__iff,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2] :
% 173.13/173.36 ( 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))))
% 173.13/173.36 <=> 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 173.13/173.36 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_accp__acc__eq,axiom,
% 173.13/173.36 ! [V_x_2,V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__mono,axiom,
% 173.13/173.36 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__Int__subset,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Un__Image,axiom,
% 173.13/173.36 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__Un,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__empty,axiom,
% 173.13/173.36 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_rev__ImageI,axiom,
% 173.13/173.36 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__iff,axiom,
% 173.13/173.36 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 173.13/173.36 <=> ? [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_acc__subset,axiom,
% 173.13/173.36 ! [V_R2_2,V_R1_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Image__singleton__iff,axiom,
% 173.13/173.36 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,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))))))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_acc_Osimps,axiom,
% 173.13/173.36 ! [V_r_2,V_a_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 173.13/173.36 <=> ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_acc__downward,axiom,
% 173.13/173.36 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 173.13/173.36 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 173.13/173.36
% 173.13/173.36 fof(fact_measure__def,axiom,
% 173.13/173.36 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_of__int,axiom,
% 173.13/173.36 ! [V_j_2,V_i_2,T_a] :
% 173.13/173.36 ( class_Rings_Oring__1(T_a)
% 173.13/173.36 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_One__int__def,axiom,
% 173.13/173.36 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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mult,axiom,
% 173.13/173.36 ! [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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_le,axiom,
% 173.13/173.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 173.13/173.36 ( 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)))))))
% 173.13/173.36 <=> 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_minus,axiom,
% 173.13/173.36 ! [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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Zero__int__def,axiom,
% 173.13/173.36 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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_int__def,axiom,
% 173.13/173.36 ! [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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_add,axiom,
% 173.13/173.36 ! [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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_nat,axiom,
% 173.13/173.36 ! [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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_less,axiom,
% 173.13/173.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 173.13/173.36 ( 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)))))))
% 173.13/173.36 <=> 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_irrefl__def,axiom,
% 173.13/173.36 ! [V_r_2,T_a] :
% 173.13/173.36 ( c_Relation_Oirrefl(T_a,V_r_2)
% 173.13/173.36 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_eq__Abs__Integ,axiom,
% 173.13/173.36 ! [V_z_2] :
% 173.13/173.36 ~ ! [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))))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Field__insert,axiom,
% 173.13/173.36 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ImageE,axiom,
% 173.13/173.36 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 173.13/173.36 => ~ ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
% 173.13/173.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Field__empty,axiom,
% 173.13/173.36 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_mono__Field,axiom,
% 173.13/173.36 ! [V_s_2,V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Field__Un,axiom,
% 173.13/173.36 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__class__nondisjoint,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_subset__equiv__class,axiom,
% 173.13/173.36 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_smax__emptyI,axiom,
% 173.13/173.36 ! [V_Y_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 173.13/173.36 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 173.13/173.36 => 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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_wmax__emptyI,axiom,
% 173.13/173.36 ! [V_X_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 173.13/173.36 => 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)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Field,axiom,
% 173.13/173.36 ! [V_r_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__intrel,axiom,
% 173.13/173.36 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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__class__self,axiom,
% 173.13/173.36 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__class__eq,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.13/173.36 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__class__eq__iff,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.36 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_eq__equiv__class__iff,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.36 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_eq__equiv__class,axiom,
% 173.13/173.36 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 173.13/173.36 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_equiv__class__subset,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Diff,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Int,axiom,
% 173.13/173.36 ! [V_Ga_2,V_F_2,T_a] :
% 173.13/173.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.36 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) )
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__imageI,axiom,
% 173.13/173.36 ! [V_h_2,T_b,V_F_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite_OinsertI,axiom,
% 173.13/173.36 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite_OemptyI,axiom,
% 173.13/173.36 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 173.13/173.36 ! [V_A_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 173.13/173.36 <=> 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))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_infinite__UNIV__nat,axiom,
% 173.13/173.36 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__dom__body,axiom,
% 173.13/173.36 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 173.13/173.36 ! [V_A_2] :
% 173.13/173.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 173.13/173.36 <=> 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))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__code,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Finite__Set_Ofinite(T_a)
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Finite__Set_Ofinite(T_a)
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__range__updI,axiom,
% 173.13/173.36 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite_Oequations_I1_J,axiom,
% 173.13/173.36 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__insert,axiom,
% 173.13/173.36 ! [V_A_2,V_a_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 173.13/173.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_rev__finite__subset,axiom,
% 173.13/173.36 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__subset,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__fun__UNIVD2,axiom,
% 173.13/173.36 ! [T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Plus__UNIV__iff,axiom,
% 173.13/173.36 ! [T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))))
% 173.13/173.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__UNIV,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( class_Finite__Set_Ofinite(T_a)
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Un,axiom,
% 173.13/173.36 ! [V_Ga_2,V_F_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__UnI,axiom,
% 173.13/173.36 ! [V_Ga_2,V_F_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Diff2,axiom,
% 173.13/173.36 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__surj,axiom,
% 173.13/173.36 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Diff__insert,axiom,
% 173.13/173.36 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))))
% 173.13/173.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__imageD,axiom,
% 173.13/173.36 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 173.13/173.36 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__compl,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 173.13/173.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__Prod__UNIV,axiom,
% 173.13/173.36 ! [T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__range__imageI,axiom,
% 173.13/173.36 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__surj__inj,axiom,
% 173.13/173.36 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)))
% 173.13/173.36 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_endo__inj__surj,axiom,
% 173.13/173.36 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2))
% 173.13/173.36 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 173.13/173.36 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__UNIV__inj__surj,axiom,
% 173.13/173.36 ! [V_f_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.36 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__UNIV__surj__inj,axiom,
% 173.13/173.36 ! [V_f_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__option__UNIV,axiom,
% 173.13/173.36 ! [T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))))
% 173.13/173.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__vimageD,axiom,
% 173.13/173.36 ! [V_F_2,V_h_2,T_b,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
% 173.13/173.36 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__vimageI,axiom,
% 173.13/173.36 ! [V_h_2,T_b,V_F_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.36 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 173.13/173.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_in__finite__psubset,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__pointwise,axiom,
% 173.13/173.36 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 173.13/173.36 => ( ! [B_p] :
% 173.13/173.36 ( 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(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_b),tc_HOL_Obool))))
% 173.13/173.36 => 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(V_P_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_b),tc_HOL_Obool)))) )
% 173.13/173.36 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
% 173.13/173.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 173.13/173.36 => 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_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)))))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_infinite__UNIV__int,axiom,
% 173.13/173.36 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 173.13/173.36 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__comp,axiom,
% 173.13/173.36 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__left__comp,axiom,
% 173.13/173.36 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Oempty,axiom,
% 173.13/173.36 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 173.13/173.36 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 173.13/173.36 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ocommute__comp_H,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.36 => 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)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ounion__inter,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_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)))))) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.36 => ( 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))
% 173.13/173.36 => 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)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding_Ounion,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => 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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 173.13/173.36 ! [V_N_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 173.13/173.36 <=> ? [B_m] :
% 173.13/173.36 ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_finite__nat__set__iff__bounded,axiom,
% 173.13/173.36 ! [V_N_2] :
% 173.13/173.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 173.13/173.36 <=> ? [B_m] :
% 173.13/173.36 ! [B_x] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image_Oreindex,axiom,
% 173.13/173.36 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 173.13/173.36 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__image_Odistrib,axiom,
% 173.13/173.36 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.36 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),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)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Osingleton,axiom,
% 173.13/173.36 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Ounion__inter,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_folding__one_Ounion__disjoint,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.36 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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)) ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_eq__equiv__class__iff2,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.36 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 173.13/173.36 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 173.13/173.36 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 173.13/173.36 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__empty,axiom,
% 173.13/173.36 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__is__empty2,axiom,
% 173.13/173.36 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)
% 173.13/173.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__is__empty,axiom,
% 173.13/173.36 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 173.13/173.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_singleton__quotient,axiom,
% 173.13/173.36 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__disj,axiom,
% 173.13/173.36 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( V_X_2 = V_Y_2
% 173.13/173.36 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotientI,axiom,
% 173.13/173.36 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__eq__iff,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 173.13/173.36 => ( V_X_2 = V_Y_2
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__eqI,axiom,
% 173.13/173.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 173.13/173.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.36 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotient__diff1,axiom,
% 173.13/173.36 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 173.13/173.36 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Integ__def,axiom,
% 173.13/173.36 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) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OatMost__iff,axiom,
% 173.13/173.36 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OatLeast__iff,axiom,
% 173.13/173.36 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OlessThan__iff,axiom,
% 173.13/173.36 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_quotientE,axiom,
% 173.13/173.36 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.36 => ~ ! [B_x] :
% 173.13/173.36 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 173.13/173.36 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)))
% 173.13/173.36 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 173.13/173.36 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_ord_OgreaterThan__iff,axiom,
% 173.13/173.36 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 173.13/173.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 173.13/173.36 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Osingleton,axiom,
% 173.13/173.36 ! [V_x_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_sup__Inf__absorb,axiom,
% 173.13/173.36 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oin__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Osubset__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Ounion__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Ounion__inter,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__fin_Oclosed,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Oremove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_minus__Min__eq__Max,axiom,
% 173.13/173.36 ! [V_S_2,T_a] :
% 173.13/173.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.36 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_minus__Max__eq__Min,axiom,
% 173.13/173.36 ! [V_S_2,T_a] :
% 173.13/173.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.36 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Osingleton,axiom,
% 173.13/173.36 ! [V_x_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Osingleton,axiom,
% 173.13/173.36 ! [V_x_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Osingleton,axiom,
% 173.13/173.36 ! [V_x_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min__le,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max__ge,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max__in,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min__in,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oin__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_inf__Sup__absorb,axiom,
% 173.13/173.36 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Oin__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Oin__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min__antimono,axiom,
% 173.13/173.36 ! [V_N_2,V_M_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 173.13/173.36 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max__mono,axiom,
% 173.13/173.36 ! [V_N_2,V_M_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 173.13/173.36 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min__insert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max__insert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Osubset__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Osubset__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Ounion__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Osubset__idem,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min__Un,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max__Un,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Inf__le__Sup,axiom,
% 173.13/173.36 ! [V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Oinsert,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Sup__fin_Ounion__inter,axiom,
% 173.13/173.36 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Lattices_Olattice(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Max_Oinsert__remove,axiom,
% 173.13/173.36 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.36 ( class_Orderings_Olinorder(T_a)
% 173.13/173.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.36 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.36
% 173.13/173.36 fof(fact_Min_Ounion__disjoint,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Min_Ounion__inter,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Max_Ounion__disjoint,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Max_Ounion__inter,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Max_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Min_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Sup__fin_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Lattices_Olattice(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Ounion__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Oidem__comp,axiom,
% 173.13/173.37 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 173.13/173.37 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Oinsert__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.37 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_equivp__equiv,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 173.13/173.37 <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 173.13/173.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 173.13/173.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__one_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_identity__equivp,axiom,
% 173.13/173.37 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_equivp__def,axiom,
% 173.13/173.37 ! [V_R_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 173.13/173.37 <=> ! [B_x,B_y] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 173.13/173.37 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_equivp__reflp,axiom,
% 173.13/173.37 ! [V_x_2,V_R_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 173.13/173.37 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_equivp__symp,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_equivp__transp,axiom,
% 173.13/173.37 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__le__Sup,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 173.13/173.37 ! [V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 173.13/173.37 ! [V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 173.13/173.37 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 173.13/173.37 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 173.13/173.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff__singleton,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff__singleton__if,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__UNIV__unit,axiom,
% 173.13/173.37 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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 173.13/173.37 ! [V_A_2] :
% 173.13/173.37 ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Oempty,axiom,
% 173.13/173.37 ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__infinite,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.37 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.37 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__image,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__eq__0__iff,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__ge__0__finite,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( 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_a),V_A_2)))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__insert__le,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__seteq,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
% 173.13/173.37 => V_A_2 = V_B_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__mono,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__image__le,axiom,
% 173.13/173.37 ! [V_f_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_eq__card__imp__inj__on,axiom,
% 173.13/173.37 ! [V_f_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
% 173.13/173.37 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_inj__on__iff__eq__card,axiom,
% 173.13/173.37 ! [V_f_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_pigeonhole,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 173.13/173.37 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__quotient__disjoint,axiom,
% 173.13/173.37 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_psubset__card__mono,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__insert__if,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__insert__disjoint,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__gt__0__iff,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( 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_a),V_A_2)))
% 173.13/173.37 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__UNIV__card__ge__0,axiom,
% 173.13/173.37 ! [T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.37 => 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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Un__Int,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Ounion__inter,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__bij__eq,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2))
% 173.13/173.37 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff__subset,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff__subset__Int,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_diff__card__le__card__Diff,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => 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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__UNIV__bool,axiom,
% 173.13/173.37 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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__psubset,axiom,
% 173.13/173.37 ! [V_A_2,V_B_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__insert,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Un__disjoint,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff1__le,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Oinsert,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__inj__on__le,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_inj__on__iff__card__le,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.37 => ( ? [B_f] :
% 173.13/173.37 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) )
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Suc__Diff1,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff1__less,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff2__less,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Diff__insert,axiom,
% 173.13/173.37 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Oinsert__remove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__fun__UNIVD1,axiom,
% 173.13/173.37 ! [T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))))
% 173.13/173.37 => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Oremove,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Ounion__inter__neutral,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Suc__eq,axiom,
% 173.13/173.37 ! [V_k_2,V_A_2,T_a] :
% 173.13/173.37 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 173.13/173.37 <=> ? [B_b,B_B] :
% 173.13/173.37 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 173.13/173.37 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 173.13/173.37 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 173.13/173.37 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.37 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Plus__conv__if,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) )
% 173.13/173.37 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Plus__eq__empty__conv,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))
% 173.13/173.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__Plus__iff,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 173.13/173.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__Plus,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__PlusD_I1_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__PlusD_I2_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UNIV__Plus__UNIV,axiom,
% 173.13/173.37 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Plus,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__Pow,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),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_a),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__greaterThanLessThan__int,axiom,
% 173.13/173.37 ! [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)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__gen__delta,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),V_ca_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__greaterThanLessThan__int,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_PowI,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__UNIV,axiom,
% 173.13/173.37 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__insert,axiom,
% 173.13/173.37 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__top,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_int__setprod,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_of__nat__setprod,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 & class_Rings_Osemiring__1(T_a) )
% 173.13/173.37 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_of__int__setprod,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 & class_Rings_Oring__1(T_a) )
% 173.13/173.37 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__Int__eq,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_abs__setprod,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__timesf,axiom,
% 173.13/173.37 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__1,axiom,
% 173.13/173.37 ! [V_A_2,T_b,T_a] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_a] :
% 173.13/173.37 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.37 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__Pow__surj,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.37 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 173.13/173.37 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Cantors__paradox,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__Pow__iff,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 173.13/173.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__not__empty,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__zero,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Rings_Ocomm__semiring__1(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__zero__iff,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 173.13/173.37 & class_Rings_Ono__zero__divisors(T_b) )
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__empty,axiom,
% 173.13/173.37 ! [V_f_2,T_b,T_a] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oempty,axiom,
% 173.13/173.37 ! [V_g_2,T_b,T_a] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oinfinite,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__infinite,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__eq__1__iff,axiom,
% 173.13/173.37 ! [V_f_2,V_F_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 173.13/173.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.37 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.37 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.37 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Odistrib,axiom,
% 173.13/173.37 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__bottom,axiom,
% 173.13/173.37 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__iff,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_PowD,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__pos__nat__iff,axiom,
% 173.13/173.37 ! [V_f_2,V_S_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( 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_a,tc_Nat_Onat),V_f_2),V_S_2)))
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__reindex,axiom,
% 173.13/173.37 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__reindex__cong,axiom,
% 173.13/173.37 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 173.13/173.37 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThanLessThan__empty,axiom,
% 173.13/173.37 ! [V_k_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 173.13/173.37 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__mono,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Un__Pow__subset,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__delta_H,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__delta,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__constant,axiom,
% 173.13/173.37 ! [V_y_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oinsert,axiom,
% 173.13/173.37 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__insert,axiom,
% 173.13/173.37 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__Un__Int,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Ounion__inter,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oreindex,axiom,
% 173.13/173.37 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__Pow__mono,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Pow__empty,axiom,
% 173.13/173.37 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__greaterThanLessThan,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oinsert__remove,axiom,
% 173.13/173.37 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Ounion__disjoint,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__Un__disjoint,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Powp__Pow__eq,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oremove,axiom,
% 173.13/173.37 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__Un__one,axiom,
% 173.13/173.37 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 173.13/173.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I4_J,axiom,
% 173.13/173.37 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__greaterThanAtMost,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__greaterThanLessThan,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__greaterThanAtMost__int,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThanAtMost__empty,axiom,
% 173.13/173.37 ! [V_k_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 173.13/173.37 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 173.13/173.37 ! [V_l_2,V_k_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 173.13/173.37 ! [V_l_2,V_k_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I20_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I14_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__greaterThanAtMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__greaterThanAtMost,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I10_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__greaterThanLessThan,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__greaterThanAtMost__int,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I16_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.37 ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__diff1,axiom,
% 173.13/173.37 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Fields_Ofield(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_quotient__def,axiom,
% 173.13/173.37 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP1__I,axiom,
% 173.13/173.37 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__UN,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__o,axiom,
% 173.13/173.37 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_diff__divide__distrib,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__1,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP1__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_times__divide__eq__right,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_add__divide__distrib,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__zero,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__zero__left,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_power__divide,axiom,
% 173.13/173.37 ! [V_n,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_minus__divide__left,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Image__UN,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__eq__divide__eq,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 173.13/173.37 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__divide__eq__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 173.13/173.37 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__eq__imp,axiom,
% 173.13/173.37 ! [V_a,V_b,V_c,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 173.13/173.37 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_eq__divide__imp,axiom,
% 173.13/173.37 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 173.13/173.37 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__self__if,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 173.13/173.37 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 173.13/173.37 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__self,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_right__inverse__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 173.13/173.37 <=> V_a_2 = V_b_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__minus__divide__right,axiom,
% 173.13/173.37 ! [V_a,V_b,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__minus__divide__divide,axiom,
% 173.13/173.37 ! [V_a,V_b,T_a] :
% 173.13/173.37 ( class_Rings_Odivision__ring(T_a)
% 173.13/173.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__power__divide,axiom,
% 173.13/173.37 ! [V_n,V_a,V_b,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_power__one__over,axiom,
% 173.13/173.37 ! [V_n,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__UN__eq,axiom,
% 173.13/173.37 ! [V_x_2,V_r_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__dividef,axiom,
% 173.13/173.37 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__eq__eq__number__of1,axiom,
% 173.13/173.37 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2
% 173.13/173.37 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) )
% 173.13/173.37 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__eq__eq__number__of,axiom,
% 173.13/173.37 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
% 173.13/173.37 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) )
% 173.13/173.37 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_eq__divide__eq__number__of,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 173.13/173.37 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) = V_b_2 )
% 173.13/173.37 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_eq__divide__eq__number__of1,axiom,
% 173.13/173.37 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
% 173.13/173.37 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 )
% 173.13/173.37 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__Numeral0,axiom,
% 173.13/173.37 ! [V_x,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__Numeral1,axiom,
% 173.13/173.37 ! [V_x,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => 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 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__numeral__1,axiom,
% 173.13/173.37 ! [V_a,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => 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 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__minus1,axiom,
% 173.13/173.37 ! [V_x,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Image__eq__UN,axiom,
% 173.13/173.37 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,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))))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_less__divide__eq__number__of1,axiom,
% 173.13/173.37 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_less__divide__eq__number__of,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__less__eq__number__of,axiom,
% 173.13/173.37 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__less__eq__number__of1,axiom,
% 173.13/173.37 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_power__diff,axiom,
% 173.13/173.37 ! [V_m,V_n,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_minus1__divide,axiom,
% 173.13/173.37 ! [V_x,T_a] :
% 173.13/173.37 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_le__divide__eq__number__of1,axiom,
% 173.13/173.37 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_le__divide__eq__number__of,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__le__eq__number__of,axiom,
% 173.13/173.37 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__le__eq__number__of1,axiom,
% 173.13/173.37 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_half__gt__zero__iff,axiom,
% 173.13/173.37 ! [V_r_2,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => ( 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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_half__gt__zero,axiom,
% 173.13/173.37 ! [V_r,T_a] :
% 173.13/173.37 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 & class_Int_Onumber__ring(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 173.13/173.37 => 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)))))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__I,axiom,
% 173.13/173.37 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__Pow__subset,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_le__divide__eq,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ball__UN,axiom,
% 173.13/173.37 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 => ! [B_xa] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__commute,axiom,
% 173.13/173.37 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__UN__flatten,axiom,
% 173.13/173.37 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I9_J,axiom,
% 173.13/173.37 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I9_J,axiom,
% 173.13/173.37 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_times__divide__times__eq,axiom,
% 173.13/173.37 ! [V_w,V_z,V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_minus__divide__divide,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => 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) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_minus__divide__right,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_abs__divide,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__le__iff,axiom,
% 173.13/173.37 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2))
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_less__SUP__iff,axiom,
% 173.13/173.37 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 173.13/173.37 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.37 & class_Orderings_Olinorder(T_a) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2)))
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__iff,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__const,axiom,
% 173.13/173.37 ! [V_M_2,T_a,V_A_2,T_b] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UNION__empty__conv_I1_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.37 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__empty2,axiom,
% 173.13/173.37 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__constant,axiom,
% 173.13/173.37 ! [V_ca_2,T_b,T_a,V_A_2] :
% 173.13/173.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UNION__empty__conv_I2_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.37 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__subset__iff,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I10_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__UN,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I10_J,axiom,
% 173.13/173.37 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__Un,axiom,
% 173.13/173.37 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__Un__distrib,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I5_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I4_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I5_J,axiom,
% 173.13/173.37 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__UN__distrib,axiom,
% 173.13/173.37 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I4_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__UN__distrib2,axiom,
% 173.13/173.37 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUPR__apply,axiom,
% 173.13/173.37 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.37 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I6_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I6_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_vimage__UN,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__right__mono__neg,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__right__mono,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__le__0__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_zero__le__divide__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( 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_a_2),V_b_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_zero__less__divide__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( 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_a_2),V_b_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__less__0__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__pos__pos,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__pos__neg,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__neg__pos,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__neg__neg,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__strict__right__mono,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__strict__right__mono__neg,axiom,
% 173.13/173.37 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_eq__divide__eq,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 173.13/173.37 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 )
% 173.13/173.37 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__eq__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 173.13/173.37 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) )
% 173.13/173.37 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__divide__mult__cancel__right,axiom,
% 173.13/173.37 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__divide__mult__cancel__left,axiom,
% 173.13/173.37 ! [V_b,V_a,V_c,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_frac__eq__eq,axiom,
% 173.13/173.37 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2)
% 173.13/173.37 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__subset,axiom,
% 173.13/173.37 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nonzero__abs__divide,axiom,
% 173.13/173.37 ! [V_a,V_b,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_le__SUPI,axiom,
% 173.13/173.37 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 173.13/173.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__insert__distrib,axiom,
% 173.13/173.37 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__upper,axiom,
% 173.13/173.37 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__absorb,axiom,
% 173.13/173.37 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I1_J,axiom,
% 173.13/173.37 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__singleton,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I1_J,axiom,
% 173.13/173.37 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_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))) )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I2_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => 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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__extend__simps_I3_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I2_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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)) )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__simps_I3_J,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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)) )
% 173.13/173.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__insert,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__nonpos__neg,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__nonpos__pos,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_frac__le,axiom,
% 173.13/173.37 ! [V_z,V_w,V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 173.13/173.37 => 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))) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_frac__less,axiom,
% 173.13/173.37 ! [V_z,V_w,V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 173.13/173.37 => 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))) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_frac__less2,axiom,
% 173.13/173.37 ! [V_z,V_w,V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 173.13/173.37 => 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))) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__nonneg__neg,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__nonneg__pos,axiom,
% 173.13/173.37 ! [V_y,V_x,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__strict__left__mono__neg,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__strict__left__mono,axiom,
% 173.13/173.37 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_neg__divide__less__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_neg__less__divide__eq,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__imp__less__div__pos,axiom,
% 173.13/173.37 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__imp__div__pos__less,axiom,
% 173.13/173.37 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_pos__divide__less__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_pos__less__divide__eq,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__less__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_less__divide__eq,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_add__num__frac,axiom,
% 173.13/173.37 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_add__divide__eq__iff,axiom,
% 173.13/173.37 ! [V_y,V_x,V_z,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_add__frac__num,axiom,
% 173.13/173.37 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Ofield__inverse__zero(T_a)
% 173.13/173.37 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__add__eq__iff,axiom,
% 173.13/173.37 ! [V_y,V_x,V_z,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_add__frac__eq,axiom,
% 173.13/173.37 ! [V_w,V_x,V_z,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_diff__frac__eq,axiom,
% 173.13/173.37 ! [V_w,V_x,V_z,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__diff__eq__iff,axiom,
% 173.13/173.37 ! [V_y,V_x,V_z,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_diff__divide__eq__iff,axiom,
% 173.13/173.37 ! [V_y,V_x,V_z,T_a] :
% 173.13/173.37 ( class_Fields_Ofield(T_a)
% 173.13/173.37 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.37 => 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) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_gt__half__sum,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_less__half__sum,axiom,
% 173.13/173.37 ! [V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 173.13/173.37 => 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))))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_abs__div__pos,axiom,
% 173.13/173.37 ! [V_x,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__eq__UN,axiom,
% 173.13/173.37 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_vimage__eq__UN,axiom,
% 173.13/173.37 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,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))))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__left__mono__neg,axiom,
% 173.13/173.37 ! [V_c,V_b,V_a,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__left__mono,axiom,
% 173.13/173.37 ! [V_c,V_a,V_b,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_neg__divide__le__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_neg__le__divide__eq,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__imp__le__div__pos,axiom,
% 173.13/173.37 ! [V_x,V_z,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_mult__imp__div__pos__le,axiom,
% 173.13/173.37 ! [V_z,V_x,V_y,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 173.13/173.37 => ( 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)))
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_pos__divide__le__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_pos__le__divide__eq,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_divide__le__eq,axiom,
% 173.13/173.37 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2))
% 173.13/173.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_minus__int__def,axiom,
% 173.13/173.37 ! [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))))))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__equiv__class2,axiom,
% 173.13/173.37 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 173.13/173.37 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__equiv__class,axiom,
% 173.13/173.37 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP2__I,axiom,
% 173.13/173.37 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Rep__Integ__inject,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2] :
% 173.13/173.37 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 173.13/173.37 <=> V_x_2 = V_y_2 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Rep__Integ__inverse,axiom,
% 173.13/173.37 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 173.13/173.37
% 173.13/173.37 fof(fact_congruent2__implies__congruent,axiom,
% 173.13/173.37 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Rep__Integ,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP__UN__eq2,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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))
% 173.13/173.37 <=> 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_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_congruent__def,axiom,
% 173.13/173.37 ! [V_f_2,V_r_2,T_b,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_congruent2D,axiom,
% 173.13/173.37 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2))
% 173.13/173.37 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_congruentD,axiom,
% 173.13/173.37 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2))
% 173.13/173.37 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_congruent2__implies__congruent__UN,axiom,
% 173.13/173.37 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 173.13/173.37 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 173.13/173.37 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_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)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_nat__def,axiom,
% 173.13/173.37 ! [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)))))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__equiv__class__inject,axiom,
% 173.13/173.37 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 173.13/173.37 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => ! [B_y] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 173.13/173.37 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) )
% 173.13/173.37 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__equiv__class__type2,axiom,
% 173.13/173.37 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 173.13/173.37 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2)))
% 173.13/173.37 => ( ! [B_x1] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 173.13/173.37 => ! [B_x2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__equiv__class__type,axiom,
% 173.13/173.37 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SUP2__iff,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__Un,axiom,
% 173.13/173.37 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Fields_Ofield(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.37 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__on__def,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__on__def_H,axiom,
% 173.13/173.37 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 <=> ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) )
% 173.13/173.37 & ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__on__Id__on,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__on__def_H,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__on__empty,axiom,
% 173.13/173.37 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__on__Un,axiom,
% 173.13/173.37 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 173.13/173.37 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__on__Int,axiom,
% 173.13/173.37 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 173.13/173.37 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__on__empty,axiom,
% 173.13/173.37 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Image__Id__on,axiom,
% 173.13/173.37 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__onD2,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__onD1,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_refl__onD,axiom,
% 173.13/173.37 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 173.13/173.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__on__eqI,axiom,
% 173.13/173.37 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 173.13/173.37 ( V_a_2 = V_b_2
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__on__iff,axiom,
% 173.13/173.37 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
% 173.13/173.37 <=> ( V_x_2 = V_y_2
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Id__onE,axiom,
% 173.13/173.37 ! [V_A_2,V_ca_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2)))
% 173.13/173.37 => ~ ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition__Integ,axiom,
% 173.13/173.37 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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__Un__disjoint,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__empty,axiom,
% 173.13/173.37 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 173.13/173.37 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.37 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_folding__image_Oeq__fold,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.37 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__distrib,axiom,
% 173.13/173.37 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__insert,axiom,
% 173.13/173.37 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Oab__semigroup__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_OF__eq,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod_Oeq__fold,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__Un__Int,axiom,
% 173.13/173.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__reindex,axiom,
% 173.13/173.37 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 173.13/173.37 ( class_Groups_Oab__semigroup__mult(T_c)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 173.13/173.37 => 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(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__eq__fold__image,axiom,
% 173.13/173.37 ! [V_f_2,T_b,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,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_a),c_Set_Oinsert(T_b)),V_f_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))),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__def,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card_Oeq__fold__g,axiom,
% 173.13/173.37 ! [V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_OAbs__image,axiom,
% 173.13/173.37 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_ORep__range,axiom,
% 173.13/173.37 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_comm__monoid__big_OF__eq,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 173.13/173.37 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.37 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.37 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_ORep__inverse,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_ORep__inject,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 173.13/173.37 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 173.13/173.37 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.37 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 173.13/173.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.37 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_OAbs__inject,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 173.13/173.37 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 173.13/173.37 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_OAbs__inverse,axiom,
% 173.13/173.37 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 173.13/173.37 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_type__definition_ORep,axiom,
% 173.13/173.37 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 173.13/173.37 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 173.13/173.37 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_fold__image__Un__one,axiom,
% 173.13/173.37 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 173.13/173.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.13/173.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Max_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Min_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Inf__fin_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Lattices_Olattice(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Sup__fin_Ohom__commute,axiom,
% 173.13/173.37 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.37 ( class_Lattices_Olattice(T_a)
% 173.13/173.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_strong__setprod__reindex__cong,axiom,
% 173.13/173.37 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 173.13/173.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.37 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.37 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__mono__one__right,axiom,
% 173.13/173.37 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 173.13/173.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_setprod__mono__one__left,axiom,
% 173.13/173.37 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 173.13/173.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 173.13/173.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.13/173.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__empty__induct,axiom,
% 173.13/173.37 ! [V_P_2,V_A_2,T_a] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.37 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 173.13/173.37 => ( ! [B_a,B_A] :
% 173.13/173.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 173.13/173.37 => ( hBOOL(hAPP(V_P_2,B_A))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) )
% 173.13/173.37 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I19_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__atLeastAtMost,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__atLeastAtMost__int,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__add__atLeastAtMost,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__Suc__atLeastAtMost,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 173.13/173.37 ! [V_n_2,V_m_2] :
% 173.13/173.37 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 173.13/173.37 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 173.13/173.37 => 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))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2] :
% 173.13/173.37 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 173.13/173.37 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastatMost__empty__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastatMost__empty__iff2,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastatMost__empty,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 173.13/173.37 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastatMost__subset__iff,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)))
% 173.13/173.37 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastAtMost__singleton,axiom,
% 173.13/173.37 ! [V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 173.13/173.37 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.37 <=> ( V_a_2 = V_b_2
% 173.13/173.37 & V_b_2 = V_ca_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastAtMost__singleton_H,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( V_a_2 = V_b_2
% 173.13/173.37 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__uminus__atLeastAtMost,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 173.13/173.37 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__atLeastAtMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastAtMostSuc__conv,axiom,
% 173.13/173.37 ! [V_n_2,V_m_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 173.13/173.37 => 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)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__atLeastAtMost,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastatMost__psubset__iff,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)))
% 173.13/173.37 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 173.13/173.37 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2))
% 173.13/173.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I22_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I16_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I13_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I12_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_simp__from__to,axiom,
% 173.13/173.37 ! [V_i_2,V_j_2] :
% 173.13/173.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 173.13/173.37 => 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)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__atLeastAtMost__int,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I5_J,axiom,
% 173.13/173.37 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I8_J,axiom,
% 173.13/173.37 ! [V_B_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I6_J,axiom,
% 173.13/173.37 ! [V_A_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 173.13/173.37 => 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)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I4_J,axiom,
% 173.13/173.37 ! [V_A_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( B_x != V_t_2
% 173.13/173.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ex__nat__less,axiom,
% 173.13/173.37 ! [V_P_2,V_n_2] :
% 173.13/173.37 ( ? [B_m] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 173.13/173.37 & hBOOL(hAPP(V_P_2,B_m)) )
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_all__nat__less,axiom,
% 173.13/173.37 ! [V_P_2,V_n_2] :
% 173.13/173.37 ( ! [B_m] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_m)) )
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I3_J,axiom,
% 173.13/173.37 ! [V_B_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xa] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 173.13/173.37 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 173.13/173.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I4_J,axiom,
% 173.13/173.37 ! [V_B_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( B_x != V_t_2
% 173.13/173.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I7_J,axiom,
% 173.13/173.37 ! [V_B_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 173.13/173.37 => 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))) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I5_J,axiom,
% 173.13/173.37 ! [V_A_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 173.13/173.37 => 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)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I3_J,axiom,
% 173.13/173.37 ! [V_A_2,V_t_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ( 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))
% 173.13/173.37 => ( ! [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xa] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 173.13/173.37 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 173.13/173.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I6_J,axiom,
% 173.13/173.37 ! [V_t_2,V_B_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I8_J,axiom,
% 173.13/173.37 ! [V_t_2,V_A_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_periodic__finite__ex,axiom,
% 173.13/173.37 ! [V_P_2,V_d_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 173.13/173.37 => ( ! [B_x,B_k] :
% 173.13/173.37 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.37 <=> hBOOL(hAPP(V_P_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)))) )
% 173.13/173.37 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_aset_I7_J,axiom,
% 173.13/173.37 ! [V_t_2,V_A_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 173.13/173.37 => 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))) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_bset_I5_J,axiom,
% 173.13/173.37 ! [V_t_2,V_B_2,V_D_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 173.13/173.37 => ! [B_x] :
% 173.13/173.37 ( ! [B_xa] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => ! [B_xb] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 173.13/173.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 173.13/173.37 => 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)) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 173.13/173.37 ! [V_x_2,V_y_2,V_ca_2] :
% 173.13/173.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 173.13/173.37 => 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)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 173.13/173.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 173.13/173.37 => 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))) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 173.13/173.37 => 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)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThan__0,axiom,
% 173.13/173.37 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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__atLeastLessThan,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_finite__atMost,axiom,
% 173.13/173.37 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 173.13/173.37 => V_b_2 = V_d_2 ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 173.13/173.37 => V_a_2 = V_ca_2 ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__eq__iff,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)
% 173.13/173.37 <=> ( V_a_2 = V_ca_2
% 173.13/173.37 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Compl__atMost,axiom,
% 173.13/173.37 ! [V_k_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Compl__greaterThan,axiom,
% 173.13/173.37 ! [V_k_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThan__eq__iff,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 173.13/173.37 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atMost__eq__iff,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 173.13/173.37 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_all__nat__less__eq,axiom,
% 173.13/173.37 ! [V_P_2,V_n_2] :
% 173.13/173.37 ( ! [B_m] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_m)) )
% 173.13/173.37 <=> ! [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ex__nat__less__eq,axiom,
% 173.13/173.37 ! [V_P_2,V_n_2] :
% 173.13/173.37 ( ? [B_m] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 173.13/173.37 & hBOOL(hAPP(V_P_2,B_m)) )
% 173.13/173.37 <=> ? [B_x] :
% 173.13/173.37 ( 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)))
% 173.13/173.37 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__atMost__UNIV,axiom,
% 173.13/173.37 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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan0,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__atLeastLessThan,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__Suc__atLeastLessThan,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__empty,axiom,
% 173.13/173.37 ! [V_a_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 173.13/173.37 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__empty__iff,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 173.13/173.37 ! [V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)
% 173.13/173.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__subset__iff,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 173.13/173.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 173.13/173.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I17_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__diff,axiom,
% 173.13/173.37 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 173.13/173.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__UN__finite__eq,axiom,
% 173.13/173.37 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I11_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeast0AtMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__add__atLeastLessThan,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_card__atMost,axiom,
% 173.13/173.37 ! [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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atMost__Suc,axiom,
% 173.13/173.37 ! [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)) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atMost__iff,axiom,
% 173.13/173.37 ! [V_k_2,V_i_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oord(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atMost__subset__iff,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThan__iff,axiom,
% 173.13/173.37 ! [V_k_2,V_i_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oord(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_greaterThan__subset__iff,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)))
% 173.13/173.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_UN__le__add__shift,axiom,
% 173.13/173.37 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__singleton,axiom,
% 173.13/173.37 ! [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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__un_I21_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThan__add__Un,axiom,
% 173.13/173.37 ! [V_k_2,V_j_2,V_i_2] :
% 173.13/173.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.37 => 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))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I15_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__atLeastLessThan,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_subset__card__intvl__is__intvl,axiom,
% 173.13/173.37 ! [V_k_2,V_A_2] :
% 173.13/173.37 ( 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)))))
% 173.13/173.37 => 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))) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_ivl__disj__int_I9_J,axiom,
% 173.13/173.37 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.37 ( class_Orderings_Oorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_image__uminus__atLeastLessThan,axiom,
% 173.13/173.37 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.37 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atLeastLessThanSuc,axiom,
% 173.13/173.37 ! [V_n_2,V_m_2] :
% 173.13/173.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.37 => 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)) )
% 173.13/173.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.37 => 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)) ) ) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_atMost__0,axiom,
% 173.13/173.37 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))) ).
% 173.13/173.37
% 173.13/173.37 fof(fact_Int__atLeastAtMostR1,axiom,
% 173.13/173.37 ! [V_d_2,V_ca_2,V_b_2,T_a] :
% 173.13/173.37 ( class_Orderings_Olinorder(T_a)
% 173.13/173.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.37
% 173.13/173.38 fof(fact_Int__atLeastAtMostL1,axiom,
% 173.13/173.38 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I9_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I3_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I1_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I7_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I15_J,axiom,
% 173.13/173.38 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I11_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I5_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_greaterThan__Suc,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__le__eq__Un0,axiom,
% 173.13/173.38 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I6_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I3_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I18_J,axiom,
% 173.13/173.38 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__finite2__subset,axiom,
% 173.13/173.38 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 173.13/173.38 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I12_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I7_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__lessThan,axiom,
% 173.13/173.38 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__atLeastLessThan__int,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__eq__iff,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 173.13/173.38 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__eq__iff,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 173.13/173.38 <=> V_x_2 = V_y_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Compl__lessThan,axiom,
% 173.13/173.38 ! [V_k_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Compl__atLeast,axiom,
% 173.13/173.38 ! [V_k_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__lessThan,axiom,
% 173.13/173.38 ! [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 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__lessThan__UNIV,axiom,
% 173.13/173.38 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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__atLeast__UNIV,axiom,
% 173.13/173.38 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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast0LessThan,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__0,axiom,
% 173.13/173.38 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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__Suc,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__Suc__atMost,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 173.13/173.38 ! [V_u_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 173.13/173.38 => 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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__iff,axiom,
% 173.13/173.38 ! [V_k_2,V_i_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oord(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__iff,axiom,
% 173.13/173.38 ! [V_k_2,V_i_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oord(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__subset__iff,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__subset__iff,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__0,axiom,
% 173.13/173.38 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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__strict__subset__iff,axiom,
% 173.13/173.38 ! [V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2)))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__Suc__greaterThan,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__add__int__atLeastLessThan,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__atLeastLessThan__int,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_single__Diff__lessThan,axiom,
% 173.13/173.38 ! [V_k_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I14_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I8_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I4_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I2_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I8_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Int__atLeastAtMostR2,axiom,
% 173.13/173.38 ! [V_d_2,V_ca_2,V_a_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_d_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Int__atLeastAtMostL2,axiom,
% 173.13/173.38 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_b_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__int_I6_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__uminus__atLeast,axiom,
% 173.13/173.38 ! [V_x_2,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.38 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__uminus__atMost,axiom,
% 173.13/173.38 ! [V_x_2,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.38 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeast__Suc,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__uminus__greaterThan,axiom,
% 173.13/173.38 ! [V_x_2,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.38 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__uminus__lessThan,axiom,
% 173.13/173.38 ! [V_x_2,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 173.13/173.38 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I2_J,axiom,
% 173.13/173.38 ! [V_u_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atMost__Int__atLeast,axiom,
% 173.13/173.38 ! [V_n_2,T_a] :
% 173.13/173.38 ( class_Orderings_Oorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I10_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I1_J,axiom,
% 173.13/173.38 ! [V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ivl__disj__un_I13_J,axiom,
% 173.13/173.38 ! [V_u_2,V_l_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_arith__series__int,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__finite2__eq,axiom,
% 173.13/173.38 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 173.13/173.38 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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)
% 173.13/173.38 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__finite__subset,axiom,
% 173.13/173.38 ! [V_C_2,V_A_2,T_a] :
% 173.13/173.38 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__abs,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__abs__ge__zero,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__subtractf,axiom,
% 173.13/173.38 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_of__nat__setsum,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.38 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_of__int__setsum,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Oring__1(T_a)
% 173.13/173.38 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__0,axiom,
% 173.13/173.38 ! [V_A_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_abs__setsum__abs,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__addf,axiom,
% 173.13/173.38 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__negf,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__commute,axiom,
% 173.13/173.38 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__product,axiom,
% 173.13/173.38 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__left__distrib,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__right__distrib,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__divide__distrib,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Fields_Ofield(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__infinite,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oinfinite,axiom,
% 173.13/173.38 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oempty,axiom,
% 173.13/173.38 ! [V_g_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__empty,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Odistrib,axiom,
% 173.13/173.38 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__lessThan__Suc,axiom,
% 173.13/173.38 ! [V_n_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 173.13/173.38 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 173.13/173.38 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 173.13/173.38 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 173.13/173.38 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__reindex,axiom,
% 173.13/173.38 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__add__nat__ivl,axiom,
% 173.13/173.38 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff__nat__ivl,axiom,
% 173.13/173.38 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__delta,axiom,
% 173.13/173.38 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__delta_H,axiom,
% 173.13/173.38 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__constant,axiom,
% 173.13/173.38 ! [V_A_2,V_y_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__atMost__Suc,axiom,
% 173.13/173.38 ! [V_n_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oinsert,axiom,
% 173.13/173.38 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__insert,axiom,
% 173.13/173.38 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Un__Int,axiom,
% 173.13/173.38 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff,axiom,
% 173.13/173.38 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oreindex,axiom,
% 173.13/173.38 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_OF__eq,axiom,
% 173.13/173.38 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oeq__fold,axiom,
% 173.13/173.38 ! [V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 173.13/173.38 ! [V_k_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__head__upt__Suc,axiom,
% 173.13/173.38 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__head__Suc,axiom,
% 173.13/173.38 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__restrict__set,axiom,
% 173.13/173.38 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oinsert__remove,axiom,
% 173.13/173.38 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Un__disjoint,axiom,
% 173.13/173.38 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Un,axiom,
% 173.13/173.38 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__op__ivl__Suc,axiom,
% 173.13/173.38 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__cl__ivl__Suc,axiom,
% 173.13/173.38 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__head,axiom,
% 173.13/173.38 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__ub__add__nat,axiom,
% 173.13/173.38 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( 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))))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff1_H,axiom,
% 173.13/173.38 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Oremove,axiom,
% 173.13/173.38 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff1,axiom,
% 173.13/173.38 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff1__ring,axiom,
% 173.13/173.38 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Rings_Oring(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_arith__series__general,axiom,
% 173.13/173.38 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 173.13/173.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.38 => 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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_geometric__sum,axiom,
% 173.13/173.38 ! [V_n_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Fields_Ofield(T_a)
% 173.13/173.38 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_gauss__sum,axiom,
% 173.13/173.38 ! [V_n_2,T_a] :
% 173.13/173.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 173.13/173.38 => 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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__natinterval__difff,axiom,
% 173.13/173.38 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a),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)))) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__mono2,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.38 => ( ! [B_b] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__bounded,axiom,
% 173.13/173.38 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 173.13/173.38 & class_Rings_Osemiring__1(T_b) )
% 173.13/173.38 => ( ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_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_a),V_A_2))),V_K_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 173.13/173.38 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.38 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__eq__0__iff,axiom,
% 173.13/173.38 ! [V_f_2,V_F_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 173.13/173.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__eq__setsum,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_int__setsum,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__eq__Suc0__iff,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.38 <=> ? [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.13/173.38 & ! [B_xa] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 173.13/173.38 => ( B_x != B_xa
% 173.13/173.38 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__eq__1__iff,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.38 <=> ? [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 173.13/173.38 & ! [B_xa] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 173.13/173.38 => ( B_x != B_xa
% 173.13/173.38 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 173.13/173.38 ! [V_k_2,V_f_2] :
% 173.13/173.38 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff__nat,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_a] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__diff1__nat,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Un__nat,axiom,
% 173.13/173.38 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.38 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_arith__series__nat,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a] :
% 173.13/173.38 ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Un__zero,axiom,
% 173.13/173.38 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 173.13/173.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__mono3,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__reindex__nonzero,axiom,
% 173.13/173.38 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.13/173.38 => ! [B_y] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 173.13/173.38 => ( B_x != B_y
% 173.13/173.38 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 173.13/173.38 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__nonneg__0,axiom,
% 173.13/173.38 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 173.13/173.38 => ( ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 173.13/173.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 173.13/173.38 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__nonneg__leq__bound,axiom,
% 173.13/173.38 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 173.13/173.38 => ( ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 173.13/173.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sum__diff__distrib,axiom,
% 173.13/173.38 ! [V_n_2,V_P_2,V_Q_2] :
% 173.13/173.38 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
% 173.13/173.38 => 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_P_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_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__mono__zero__left,axiom,
% 173.13/173.38 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 173.13/173.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__mono__zero__right,axiom,
% 173.13/173.38 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 173.13/173.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.13/173.38 => 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) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__subset__induct,axiom,
% 173.13/173.38 ! [V_P_2,V_A_2,V_F_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 173.13/173.38 => ( ! [B_a,B_F] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 173.13/173.38 => ( hBOOL(hAPP(V_P_2,B_F))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Oidem,axiom,
% 173.13/173.38 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Oin__idem,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__strict__mono,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_field__le__mult__one__interval,axiom,
% 173.13/173.38 ! [V_y,V_x,T_a] :
% 173.13/173.38 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 173.13/173.38 => ( ! [B_z] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 173.13/173.38 => 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)) ) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.38 => ( V_A_2 = V_B_2
% 173.13/173.38 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph__permute__diff,axiom,
% 173.13/173.38 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 & class_Groups_Ocomm__monoid__mult(T_a) )
% 173.13/173.38 => ( V_A_2 = V_B_2
% 173.13/173.38 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 173.13/173.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_max__extp_Oequations,axiom,
% 173.13/173.38 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 173.13/173.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 173.13/173.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 173.13/173.38 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 & ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 173.13/173.38 => ? [B_xa] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_empty__fold__graphE,axiom,
% 173.13/173.38 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2))
% 173.13/173.38 => V_x_2 = V_z_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph_OemptyI,axiom,
% 173.13/173.38 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 173.13/173.38 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph__imp__finite,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph_OinsertI,axiom,
% 173.13/173.38 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__graph__insert__swap,axiom,
% 173.13/173.38 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Diff1__fold__graph,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1Set_Ointros,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_max__ext_Ointros,axiom,
% 173.13/173.38 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 173.13/173.38 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 173.13/173.38 => ? [B_xa] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_empty__fold1SetE,axiom,
% 173.13/173.38 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1Set__nonempty,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 173.13/173.38 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1Set__sing,axiom,
% 173.13/173.38 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2))
% 173.13/173.38 <=> V_a_2 = V_b_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Oone__frac__def,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Ofrac__def,axiom,
% 173.13/173.38 ! [V_b,V_a,T_a] : c_Nitpick_Ofrac(T_a,V_a,V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1Set_Oequations,axiom,
% 173.13/173.38 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2))
% 173.13/173.38 <=> ? [B_a,B_A] :
% 173.13/173.38 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 173.13/173.38 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 173.13/173.38 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__fold1SetE,axiom,
% 173.13/173.38 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2))
% 173.13/173.38 => ~ ! [B_a,B_A] :
% 173.13/173.38 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__split__eq__Sigma,axiom,
% 173.13/173.38 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SigmaI,axiom,
% 173.13/173.38 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Diff__distrib2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__Diff__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Diff__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__empty1,axiom,
% 173.13/173.38 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__eq__cancel2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 173.13/173.38 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))
% 173.13/173.38 <=> V_A_2 = V_B_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__cartesian__product,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__cartesian__product,axiom,
% 173.13/173.38 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__empty2,axiom,
% 173.13/173.38 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__empty,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))
% 173.13/173.38 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Compl__Times__UNIV1,axiom,
% 173.13/173.38 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Compl__Times__UNIV2,axiom,
% 173.13/173.38 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setprod__cartesian__product,axiom,
% 173.13/173.38 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__mult(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Un__distrib2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__Un__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Un__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_swap__product,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__cartesian__product,axiom,
% 173.13/173.38 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_equiv__type,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Int__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__Int__distrib1,axiom,
% 173.13/173.38 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__Int__distrib2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Id__on__subset__Times,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UNIV__Times__UNIV,axiom,
% 173.13/173.38 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_mem__Sigma__iff,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SigmaD1,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SigmaD2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SigmaE2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 173.13/173.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__cartesian__product__singleton,axiom,
% 173.13/173.38 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Times__subset__cancel2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Image__subset,axiom,
% 173.13/173.38 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__cartesian__productD2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__cartesian__productD1,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fst__image__times,axiom,
% 173.13/173.38 ! [V_A_2,T_b,T_a,V_B_2] :
% 173.13/173.38 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.38 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_snd__image__times,axiom,
% 173.13/173.38 ! [V_B_2,T_b,T_a,V_A_2] :
% 173.13/173.38 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.38 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_refl__on__def,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.13/173.38 & ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__times__insert,axiom,
% 173.13/173.38 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__equiv__class,axiom,
% 173.13/173.38 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_vimage__Times,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_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))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UN__Times__distrib,axiom,
% 173.13/173.38 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),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(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sigma__def,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__quotient,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 173.13/173.38 ! [V_A_2,V_I_2,T_b,T_a] :
% 173.13/173.38 ? [B_f] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_refl__onI,axiom,
% 173.13/173.38 ! [V_A_2,V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
% 173.13/173.38 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold__image__Sigma,axiom,
% 173.13/173.38 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 173.13/173.38 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),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)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setprod__Sigma,axiom,
% 173.13/173.38 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__Sigma,axiom,
% 173.13/173.38 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__SigmaI,axiom,
% 173.13/173.38 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 173.13/173.38 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__SigmaI,axiom,
% 173.13/173.38 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ! [B_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SigmaE,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 173.13/173.38 => ~ ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => ! [B_y] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 173.13/173.38 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__surj,axiom,
% 173.13/173.38 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__imageI,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_snd__prod__fun,axiom,
% 173.13/173.38 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fst__map__pair,axiom,
% 173.13/173.38 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__ident,axiom,
% 173.13/173.38 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__simp,axiom,
% 173.13/173.38 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_snd__comp__map__pair,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fst__comp__map__pair,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair_Ocompositionality,axiom,
% 173.13/173.38 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__compose,axiom,
% 173.13/173.38 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair_Ocomp,axiom,
% 173.13/173.38 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__def,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,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_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__surj__on,axiom,
% 173.13/173.38 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 173.13/173.38 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,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))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair__inj__on,axiom,
% 173.13/173.38 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 173.13/173.38 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_prod__fun__imageE,axiom,
% 173.13/173.38 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2)))
% 173.13/173.38 => ~ ! [B_x,B_y] :
% 173.13/173.38 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__Un,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__antimono,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__singleton__def,axiom,
% 173.13/173.38 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 173.13/173.38 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 173.13/173.38 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__singleton,axiom,
% 173.13/173.38 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one_Oeq__fold,axiom,
% 173.13/173.38 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__def,axiom,
% 173.13/173.38 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Sup__fin_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Olattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Inf__fin_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Olattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Min_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Max_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__belowI,axiom,
% 173.13/173.38 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_below__fold1__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)))
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Ofold1__belowI,axiom,
% 173.13/173.38 ! [V_a_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__insert__idem,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__below__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
% 173.13/173.38 <=> ? [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__Un2,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_strict__below__fold1__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__strict__below__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
% 173.13/173.38 <=> ? [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__insert,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_semilattice__big_OF__eq,axiom,
% 173.13/173.38 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fold1__in,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( class_Groups_Oab__semigroup__mult(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_hom__fold1__commute,axiom,
% 173.13/173.38 ! [V_N_2,V_h_2,T_a] :
% 173.13/173.38 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.38 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.38 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setprod__pos__nat,axiom,
% 173.13/173.38 ! [V_f_2,V_S_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.13/173.38 => 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))) )
% 173.13/173.38 => 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_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 173.13/173.38 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.13/173.38 => ( ! [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))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.38 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Rep__Integ__cases,axiom,
% 173.13/173.38 ! [V_y_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 173.13/173.38 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Rep__Integ__induct,axiom,
% 173.13/173.38 ! [V_P_2,V_y_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 173.13/173.38 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => hAPP(V_g_2,B_x) = V_z_2 )
% 173.13/173.38 => 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)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem__remove,axiom,
% 173.13/173.38 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 173.13/173.38 ! [V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.13/173.38 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 173.13/173.38 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 173.13/173.38 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem__insert,axiom,
% 173.13/173.38 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem__inf,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Lattices_Osemilattice__inf(T_a)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fun__left__comm__idem__sup,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Lattices_Osemilattice__sup(T_a)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__less__Suc,axiom,
% 173.13/173.38 ! [V_i_2,V_M_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 173.13/173.38 => 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))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__less,axiom,
% 173.13/173.38 ! [V_i_2,V_M_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__less__Suc2,axiom,
% 173.13/173.38 ! [V_i_2,V_M_2] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 173.13/173.38 => 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))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_CollectI,axiom,
% 173.13/173.38 ! [T_a,V_a_2,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,V_a_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__conjI,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__less__nat,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__le__nat,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__split,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_SetCompr__Sigma__eq,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_vimage__Collect__eq,axiom,
% 173.13/173.38 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__neg__eq,axiom,
% 173.13/173.38 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__Collect,axiom,
% 173.13/173.38 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_CollectE,axiom,
% 173.13/173.38 ! [V_P_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_CollectD,axiom,
% 173.13/173.38 ! [V_P_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_mem__Collect__eq,axiom,
% 173.13/173.38 ! [V_P_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__mem__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__disjI,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2))))
% 173.13/173.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__conj__eq,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__disj__eq,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_UNIV__def,axiom,
% 173.13/173.38 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__def,axiom,
% 173.13/173.38 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_empty__Collect__eq,axiom,
% 173.13/173.38 ! [V_P_2,T_a] :
% 173.13/173.38 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 173.13/173.38 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__empty__eq,axiom,
% 173.13/173.38 ! [V_P_2,T_a] :
% 173.13/173.38 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_empty__def,axiom,
% 173.13/173.38 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__compr__raw,axiom,
% 173.13/173.38 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__compr,axiom,
% 173.13/173.38 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Un__def,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Int__Collect,axiom,
% 173.13/173.38 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Int__def,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_singleton__conv2,axiom,
% 173.13/173.38 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_singleton__conv,axiom,
% 173.13/173.38 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__conv__if2,axiom,
% 173.13/173.38 ! [T_a,V_a_2,V_P_2] :
% 173.13/173.38 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 173.13/173.38 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 173.13/173.38 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__conv__if,axiom,
% 173.13/173.38 ! [T_a,V_a_2,V_P_2] :
% 173.13/173.38 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 173.13/173.38 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 173.13/173.38 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__diff__eq,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__not,axiom,
% 173.13/173.38 ! [V_P_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))))
% 173.13/173.38 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insert__def,axiom,
% 173.13/173.38 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Compl__eq,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_vimage__def,axiom,
% 173.13/173.38 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Collect__imp__eq,axiom,
% 173.13/173.38 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__def,axiom,
% 173.13/173.38 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__M__bounded__by__nat,axiom,
% 173.13/173.38 ! [V_i_2,V_P_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_P_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))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__setsum__restrict,axiom,
% 173.13/173.38 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_if__image__distrib,axiom,
% 173.13/173.38 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__if,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nat__seg__image__imp__finite,axiom,
% 173.13/173.38 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 173.13/173.38 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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)))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__restrict__set_H,axiom,
% 173.13/173.38 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__image__gen,axiom,
% 173.13/173.38 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Image__singleton,axiom,
% 173.13/173.38 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,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_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__cases,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),V_P_2)),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_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__override__on,axiom,
% 173.13/173.38 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__multicount,axiom,
% 173.13/173.38 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 173.13/173.38 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_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_b),V_T_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__subsets,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Pow__Compl,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Pow__def,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Collect__bounded__ex,axiom,
% 173.13/173.38 ! [V_Q_2,T_b,V_P_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2)))))
% 173.13/173.38 <=> ! [B_y] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,B_y))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__image__set,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_P_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,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_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_override__on__apply__notin,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_override__on__apply__in,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_override__on__emptyset,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__graph,axiom,
% 173.13/173.38 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 173.13/173.38 ! [V_P_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_P_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_override__on__def,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__psubset__def,axiom,
% 173.13/173.38 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ran__def,axiom,
% 173.13/173.38 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inv__image__def,axiom,
% 173.13/173.38 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,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_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),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_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 173.13/173.38 ! [V_P_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_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_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 173.13/173.38 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_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_P_2),c_Int_Onat)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_add__Max__commute,axiom,
% 173.13/173.38 ! [V_k_2,V_N_2,T_a] :
% 173.13/173.38 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.38 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_add__Min__commute,axiom,
% 173.13/173.38 ! [V_k_2,V_N_2,T_a] :
% 173.13/173.38 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 173.13/173.38 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sup__Inf1__distrib,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sup__Inf2__distrib,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inf__Sup1__distrib,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inf__Sup2__distrib,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Lattices_Odistrib__lattice(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 173.13/173.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Oprod__def,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_int__ge__less__than2__def,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_int__ge__less__than__def,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_reflp__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Predicate_Oreflp(T_a,V_r_2)
% 173.13/173.38 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_c)
% 173.13/173.38 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))
% 173.13/173.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),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_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),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_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),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))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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))))))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_def__lfp__induct__set,axiom,
% 173.13/173.38 ! [V_P_2,V_a_2,V_f_2,T_a,V_A_2] :
% 173.13/173.38 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.38 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__on__id,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_id__o,axiom,
% 173.13/173.38 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_o__id,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_o__eq__id__dest,axiom,
% 173.13/173.38 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 173.13/173.38 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_ca_2)
% 173.13/173.38 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_of__int__eq__id,axiom,
% 173.13/173.38 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Option_Omap_Oidentity,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_apsnd__id,axiom,
% 173.13/173.38 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Option_Omap_Oid,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_id__apply,axiom,
% 173.13/173.38 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 173.13/173.38
% 173.13/173.38 fof(fact_reflpE,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Predicate_Oreflp(T_a,V_r_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_id__def,axiom,
% 173.13/173.38 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_apfst__id,axiom,
% 173.13/173.38 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_vimage__id,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair_Oid,axiom,
% 173.13/173.38 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__pair_Oidentity,axiom,
% 173.13/173.38 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_image__id,axiom,
% 173.13/173.38 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_surj__id,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_folding_Oempty,axiom,
% 173.13/173.38 ! [V_F_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.13/173.38 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_apsnd__def,axiom,
% 173.13/173.38 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_apfst__def,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_split__Pair,axiom,
% 173.13/173.38 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__reindex__id,axiom,
% 173.13/173.38 ! [V_B_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setprod__reindex__id,axiom,
% 173.13/173.38 ! [V_B_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lfp__induct__set,axiom,
% 173.13/173.38 ! [V_P_2,V_f_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))
% 173.13/173.38 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2)))))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_def__Collect__coinduct,axiom,
% 173.13/173.38 ! [V_X_2,V_a_2,V_P_2,T_a,V_A_2] :
% 173.13/173.38 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_OCollect(T_a)),V_P_2))
% 173.13/173.38 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_OCollect(T_a)),V_P_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 173.13/173.38 => ( ! [B_z] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_z),V_X_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lfp__induct2,axiom,
% 173.13/173.38 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_2)))
% 173.13/173.38 => ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_2)
% 173.13/173.38 => ( ! [B_a,B_b] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__multicount__gen,axiom,
% 173.13/173.38 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 173.13/173.38 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__conv__nat__seg__image,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__def,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),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_a,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(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_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(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_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),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_s_2))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__Collect__split,axiom,
% 173.13/173.38 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__compI,axiom,
% 173.13/173.38 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_ca_2)),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_RangeI,axiom,
% 173.13/173.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__UNION__distrib2,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__UNION__distrib,axiom,
% 173.13/173.38 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__distrib,axiom,
% 173.13/173.38 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__distrib2,axiom,
% 173.13/173.38 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_O__assoc,axiom,
% 173.13/173.38 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__mono,axiom,
% 173.13/173.38 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__empty2,axiom,
% 173.13/173.38 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__empty1,axiom,
% 173.13/173.38 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__Id__on,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_union__comp__emptyL,axiom,
% 173.13/173.38 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.38 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_union__comp__emptyR,axiom,
% 173.13/173.38 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.38 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.38 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__empty,axiom,
% 173.13/173.38 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__empty__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_rel__comp__subset__Sigma,axiom,
% 173.13/173.38 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_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))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__Un__eq,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Range,axiom,
% 173.13/173.38 ! [V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_snd__eq__Range,axiom,
% 173.13/173.38 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_b,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 173.13/173.38 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__insert,axiom,
% 173.13/173.38 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__Int__subset,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Range__Diff__subset,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_max__ext__compat,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__ext__compat,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_RangeP__Range__eq,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_RangeE,axiom,
% 173.13/173.38 ! [V_r_2,T_b,V_b_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 173.13/173.38 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_RangeP_Ointros,axiom,
% 173.13/173.38 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 173.13/173.38 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_RangeP_Oequations,axiom,
% 173.13/173.38 ! [V_a2_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 173.13/173.38 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_pred__comp__rel__comp__eq,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 173.13/173.38 ( c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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)
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_reduction__pairI,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 173.13/173.38 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__less__than,axiom,
% 173.13/173.38 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_pred__comp_Ointros,axiom,
% 173.13/173.38 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 173.13/173.38 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__empty,axiom,
% 173.13/173.38 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__inv__image,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__lex__prod,axiom,
% 173.13/173.38 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 173.13/173.38 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__measure,axiom,
% 173.13/173.38 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__comp__self,axiom,
% 173.13/173.38 ! [V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_min__ext__wf,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__subset,axiom,
% 173.13/173.38 ! [V_p_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2))
% 173.13/173.38 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__Int2,axiom,
% 173.13/173.38 ! [V_r_H_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__Int1,axiom,
% 173.13/173.38 ! [V_r_H_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_pred__comp_Oequations,axiom,
% 173.13/173.38 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 173.13/173.38 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 173.13/173.38 <=> ? [B_b] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 173.13/173.38 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_max__ext__wf,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__pair__less,axiom,
% 173.13/173.38 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__mlex,axiom,
% 173.13/173.38 ! [V_f_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__finite__psubset,axiom,
% 173.13/173.38 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__not__refl,axiom,
% 173.13/173.38 ! [V_a_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__not__sym,axiom,
% 173.13/173.38 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__asym,axiom,
% 173.13/173.38 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__irrefl,axiom,
% 173.13/173.38 ! [V_a_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__int__ge__less__than,axiom,
% 173.13/173.38 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__int__ge__less__than2,axiom,
% 173.13/173.38 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__less,axiom,
% 173.13/173.38 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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_acc__wfD,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__acc__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__no__loop,axiom,
% 173.13/173.38 ! [V_R_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.13/173.38 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__union__merge,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
% 173.13/173.38 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 <=> ~ ? [B_f] :
% 173.13/173.38 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfE__pf,axiom,
% 173.13/173.38 ! [V_A_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2)))
% 173.13/173.38 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__union__compatible,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Orderings_Owellorder(T_a)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_reduction__pair__def,axiom,
% 173.13/173.38 ! [V_P_2,T_a] :
% 173.13/173.38 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 173.13/173.38 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_reduction__pair__lemma,axiom,
% 173.13/173.38 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 173.13/173.38 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
% 173.13/173.38 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__map__pair__image,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.38 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__lenlex,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__Un,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 173.13/173.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_DomainI,axiom,
% 173.13/173.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__Id__on,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__empty__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_b,T_a] :
% 173.13/173.38 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__empty,axiom,
% 173.13/173.38 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__mono,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__Un__eq,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__Domain,axiom,
% 173.13/173.38 ! [V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_fst__eq__Domain,axiom,
% 173.13/173.38 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_b,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 173.13/173.38 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__insert,axiom,
% 173.13/173.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__Int__subset,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__Diff__subset,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Field__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Domain__Collect__split,axiom,
% 173.13/173.38 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_pred__nat__def,axiom,
% 173.13/173.38 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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_DomainP__Domain__eq,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_DomainP_Ointros,axiom,
% 173.13/173.38 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 173.13/173.38 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_DomainP_Oequations,axiom,
% 173.13/173.38 ! [V_a1_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 173.13/173.38 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__pred__nat,axiom,
% 173.13/173.38 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__lex,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__lexn,axiom,
% 173.13/173.38 ! [V_n_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lex__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexn_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_DomainE,axiom,
% 173.13/173.38 ! [V_r_2,T_b,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 173.13/173.38 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__same__fst,axiom,
% 173.13/173.38 ! [T_a,V_R_2,T_b,V_P_2] :
% 173.13/173.38 ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.38 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 173.13/173.38 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__if__measure,axiom,
% 173.13/173.38 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 173.13/173.38 ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.38 => 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))) )
% 173.13/173.38 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 173.13/173.38 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__empty,axiom,
% 173.13/173.38 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_accp__wfPD,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 173.13/173.38 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__accp__iff,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 173.13/173.38 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__subset,axiom,
% 173.13/173.38 ! [V_p_2,V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2))
% 173.13/173.38 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__in__rel,axiom,
% 173.13/173.38 ! [V_R_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_R_2)
% 173.13/173.38 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__wf__eq,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
% 173.13/173.38 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wfP__acyclicP,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_pigeonhole__infinite,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_A_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 173.13/173.38 => ? [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.38 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__acyclic,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_acyclic__subset,axiom,
% 173.13/173.38 ! [V_r_2,V_s_2,T_a] :
% 173.13/173.38 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.13/173.38 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__acyclic__wf,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 173.13/173.38 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 173.13/173.38 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 173.13/173.38 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.13/173.38 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Owf_H__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] :
% 173.13/173.38 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 173.13/173.38 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 173.13/173.38 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 173.13/173.38 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Abs__Integ__cases,axiom,
% 173.13/173.38 ! [V_x_2] :
% 173.13/173.38 ~ ! [B_y] :
% 173.13/173.38 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Abs__Integ__induct,axiom,
% 173.13/173.38 ! [V_x_2,V_P_2] :
% 173.13/173.38 ( ! [B_y] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__range__map__of__map__add,axiom,
% 173.13/173.38 ! [V_l_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__dom__map__of,axiom,
% 173.13/173.38 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__range__map__of,axiom,
% 173.13/173.38 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__add__map__of__foldr,axiom,
% 173.13/173.38 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_body__def,axiom,
% 173.13/173.38 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__mapk__SomeI,axiom,
% 173.13/173.38 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.38 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2)
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,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_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__mapI,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.38 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_foldr__map,axiom,
% 173.13/173.38 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__injective,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 173.13/173.38 => V_xs_2 = V_ys_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__mapD,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
% 173.13/173.38 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__map__eq__map,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.13/173.38 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
% 173.13/173.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__map,axiom,
% 173.13/173.38 ! [V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
% 173.13/173.38 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__ident,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Omap_Ocompositionality,axiom,
% 173.13/173.38 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__comp__map,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Omap_Ocomp,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Omap_Oid,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Omap_Oidentity,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__map__restrict,axiom,
% 173.13/173.38 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__map__keys,axiom,
% 173.13/173.38 ! [V_m_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 173.13/173.38 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__set,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__eq__conv,axiom,
% 173.13/173.38 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 173.13/173.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_infinite__UNIV__listI,axiom,
% 173.13/173.38 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__inj__on,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
% 173.13/173.38 => ( c_Fun_Oinj__on(T_b,T_a,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)))
% 173.13/173.38 => V_xs_2 = V_ys_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_inj__on__map__eq__map,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
% 173.13/173.38 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
% 173.13/173.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__fun__upd,axiom,
% 173.13/173.38 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__eq__dom,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 173.13/173.38 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 173.13/173.38 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__is__SomeD,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__SomeD,axiom,
% 173.13/173.38 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__map__of__conv__image__fst,axiom,
% 173.13/173.38 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__eq__None__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_xys_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 173.13/173.38 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_WT__bodies__def,axiom,
% 173.13/173.38 ( c_Com_OWT__bodies
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_ran__distinct,axiom,
% 173.13/173.38 ! [V_al_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2)))
% 173.13/173.38 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__map__of__compr,axiom,
% 173.13/173.38 ! [V_xs_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
% 173.13/173.38 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 173.13/173.38 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 173.13/173.38 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__inject__set,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)))
% 173.13/173.38 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 173.13/173.38 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Some__eq__map__of__iff,axiom,
% 173.13/173.38 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 173.13/173.38 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2)
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__eq__Some__iff,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 173.13/173.38 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__is__SomeI,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_greaterThanLessThan__upto,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_weak__map__of__SomeI,axiom,
% 173.13/173.38 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2)))
% 173.13/173.38 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__upto,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeastAtMost__upto,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__upto,axiom,
% 173.13/173.38 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_atLeastLessThan__upto,axiom,
% 173.13/173.38 ! [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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_greaterThanAtMost__upto,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nat__list__def,axiom,
% 173.13/173.38 ! [V_l_2] :
% 173.13/173.38 ( c_List_Onat__list(V_l_2)
% 173.13/173.38 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__remove1__eq,axiom,
% 173.13/173.38 ! [V_x_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_remove1__commute,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__remove1,axiom,
% 173.13/173.38 ! [V_x,V_xs,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_remove1__idem,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_notin__set__remove1,axiom,
% 173.13/173.38 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__remove1,axiom,
% 173.13/173.38 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 173.13/173.38 ( V_a_2 != V_b_2
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2))))
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__remove1__subset,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sorted__list__of__set__remove,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__zip__map,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__zipI1,axiom,
% 173.13/173.38 ! [V_ys,T_b,V_xs,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__zipI2,axiom,
% 173.13/173.38 ! [V_xs,T_b,V_ys,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__same__conv__map,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__map__fst__snd,axiom,
% 173.13/173.38 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__zip__map,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__zip__map2,axiom,
% 173.13/173.38 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__same,axiom,
% 173.13/173.38 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2))))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 & V_a_2 = V_b_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__zip__leftD,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__zip__rightD,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__zipE,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 173.13/173.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__map__map,axiom,
% 173.13/173.38 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__map1,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__map2,axiom,
% 173.13/173.38 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sorted__list__of__set__insert,axiom,
% 173.13/173.38 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__zip__upd,axiom,
% 173.13/173.38 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 173.13/173.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 173.13/173.38 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2))
% 173.13/173.38 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__zip,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexn__length,axiom,
% 173.13/173.38 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))
% 173.13/173.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 173.13/173.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__key__left__comm,axiom,
% 173.13/173.38 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__left__comm,axiom,
% 173.13/173.38 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_neq__if__length__neq,axiom,
% 173.13/173.38 ! [V_ys,V_xs,T_a] :
% 173.13/173.38 ( 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)
% 173.13/173.38 => V_xs != V_ys ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__insort,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__eq__imp__length__eq,axiom,
% 173.13/173.38 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2)
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_remove1__insort,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__insort,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__length,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_card__distinct,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__card,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__zip__inject,axiom,
% 173.13/173.38 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 173.13/173.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 173.13/173.38 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))
% 173.13/173.38 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__fst__zip,axiom,
% 173.13/173.38 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__snd__zip,axiom,
% 173.13/173.38 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__insort,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)))
% 173.13/173.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__pos__if__in__set,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => 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_a)),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__eq__conv,axiom,
% 173.13/173.38 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 173.13/173.38 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2
% 173.13/173.38 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lenlex__conv,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lenlex__def,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__lists__length__eq,axiom,
% 173.13/173.38 ! [V_n_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__eq__iff__zip__eq,axiom,
% 173.13/173.38 ! [T_a,V_ys_2,V_xs_2] :
% 173.13/173.38 ( V_xs_2 = V_ys_2
% 173.13/173.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 173.13/173.38 & ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__zip__is__None,axiom,
% 173.13/173.38 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b)
% 173.13/173.38 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__zip__is__Some,axiom,
% 173.13/173.38 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__remove1,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,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_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__map__of__zip,axiom,
% 173.13/173.38 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_finite__lists__length__le,axiom,
% 173.13/173.38 ! [V_n_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__iff__zip,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 173.13/173.38 & ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__sublist,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,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_a)),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)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__eq__len,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__sublistI,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__mono,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_notin__set__sublistI,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__sublistD,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__sublist__subset,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrelp__listrel__eq,axiom,
% 173.13/173.38 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 173.13/173.38 ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2)
% 173.13/173.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexn_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_impossible__Cons,axiom,
% 173.13/173.38 ! [V_x,V_ys,V_xs,T_a] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__ConsD,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))))
% 173.13/173.38 => ( V_y_2 = V_x_2
% 173.13/173.38 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__Cons__Cons,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__subset__Cons,axiom,
% 173.13/173.38 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_foldr_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrelp_OCons,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 173.13/173.38 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 173.13/173.38 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrelp_Oequations_I2_J,axiom,
% 173.13/173.38 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 173.13/173.38 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 173.13/173.38 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Oinject,axiom,
% 173.13/173.38 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)
% 173.13/173.38 <=> ( V_a_2 = V_a_H_2
% 173.13/173.38 & V_list_2 = V_list_H_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_not__Cons__self2,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 173.13/173.38
% 173.13/173.38 fof(fact_not__Cons__self,axiom,
% 173.13/173.38 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_remove1_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_xs,T_a,V_y,V_x] :
% 173.13/173.38 ( ( V_x = V_y
% 173.13/173.38 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 173.13/173.38 & ( V_x != V_y
% 173.13/173.38 => 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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__key_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 173.13/173.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__Cons__code_I2_J,axiom,
% 173.13/173.38 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 173.13/173.38 ( ( V_l = V_k
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) )
% 173.13/173.38 & ( V_l != V_k
% 173.13/173.38 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osize_I4_J,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel_OCons,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Cons__in__lex,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2)))
% 173.13/173.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
% 173.13/173.38 | ( V_x_2 = V_y_2
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Cons,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__Cons__def,axiom,
% 173.13/173.38 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Cons2,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => ~ ! [B_x,B_xs] :
% 173.13/173.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Cons1,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => ~ ! [B_y,B_ys] :
% 173.13/173.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__insert__insort__key,axiom,
% 173.13/173.38 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
% 173.13/173.38 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__cons__cons,axiom,
% 173.13/173.38 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.13/173.38 | ( V_a_2 = V_b_2
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__insort__insert,axiom,
% 173.13/173.38 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__insert__triv,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__insort__insert,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__insert__key__triv,axiom,
% 173.13/173.38 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
% 173.13/173.38 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__lex,axiom,
% 173.13/173.38 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2)))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__insert__insort,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__zip,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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)),tc_prod(T_a,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)),tc_prod(T_a,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(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osize_I2_J,axiom,
% 173.13/173.38 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),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_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__Cons__0,axiom,
% 173.13/173.38 ! [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 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__Cons__Suc,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__zip,axiom,
% 173.13/173.38 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => ( 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)))
% 173.13/173.38 => 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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__eq__iff__nth__eq,axiom,
% 173.13/173.38 ! [T_a,V_ys_2,V_xs_2] :
% 173.13/173.38 ( V_xs_2 = V_ys_2
% 173.13/173.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 173.13/173.38 & ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__size__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth_Osimps,axiom,
% 173.13/173.38 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_all__set__conv__all__nth,axiom,
% 173.13/173.38 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.38 ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.38 <=> ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__map,axiom,
% 173.13/173.38 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__conv__nth,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 <=> ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => ! [B_j] :
% 173.13/173.38 ( 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_2)))
% 173.13/173.38 => ( B_i != B_j
% 173.13/173.38 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__eq__iff__index__eq,axiom,
% 173.13/173.38 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2)
% 173.13/173.38 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__mem,axiom,
% 173.13/173.38 ! [V_xs_2,T_a,V_n_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__conv__nth,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 <=> ? [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__Cons_H,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a,V_n] :
% 173.13/173.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 173.13/173.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__conv__nth,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__Cons__number__of,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a,V_v] :
% 173.13/173.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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 )
% 173.13/173.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__size__estimation,axiom,
% 173.13/173.38 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__size__estimation_H,axiom,
% 173.13/173.38 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__sublist,axiom,
% 173.13/173.38 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),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))))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__iff__nth,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 173.13/173.38 & ! [B_n] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__take__index__conv,axiom,
% 173.13/173.38 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))
% 173.13/173.38 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 )
% 173.13/173.38 | ? [B_i] :
% 173.13/173.38 ( 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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))))
% 173.13/173.38 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__list__update,axiom,
% 173.13/173.38 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__take,axiom,
% 173.13/173.38 ! [V_xs,T_a,V_n,V_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__list__update__neq,axiom,
% 173.13/173.38 ! [V_x,V_xs,T_a,V_j,V_i] :
% 173.13/173.38 ( V_i != V_j
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__id,axiom,
% 173.13/173.38 ! [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 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__beyond,axiom,
% 173.13/173.38 ! [V_x,V_i,V_xs,T_a] :
% 173.13/173.38 ( 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))
% 173.13/173.38 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__all,axiom,
% 173.13/173.38 ! [V_n,V_xs,T_a] :
% 173.13/173.38 ( 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))
% 173.13/173.38 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__take__subset,axiom,
% 173.13/173.38 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__take,axiom,
% 173.13/173.38 ! [V_i,V_xs,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__update,axiom,
% 173.13/173.38 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__overwrite,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__swap,axiom,
% 173.13/173.38 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 173.13/173.38 ( V_i != V_i_H
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__take,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_update__zip,axiom,
% 173.13/173.38 ! [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))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__zip,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__update,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__take,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__list__update,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__takeD,axiom,
% 173.13/173.38 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__code_I3_J,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__Suc__Cons,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__code_I2_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sublist__upt__eq__take,axiom,
% 173.13/173.38 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__take__subset__set__take,axiom,
% 173.13/173.38 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__update__subsetI,axiom,
% 173.13/173.38 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__update__subset__insert,axiom,
% 173.13/173.38 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__list__update,axiom,
% 173.13/173.38 ! [V_x,V_j,V_xs,T_a,V_i] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => ( ( V_i = V_j
% 173.13/173.38 => 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 )
% 173.13/173.38 & ( V_i != V_j
% 173.13/173.38 => 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) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__same__conv,axiom,
% 173.13/173.38 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 173.13/173.38 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__list__update__eq,axiom,
% 173.13/173.38 ! [V_x,V_xs,T_a,V_i] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => 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 ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__update__memI,axiom,
% 173.13/173.38 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upd__upds__conv__if,axiom,
% 173.13/173.38 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
% 173.13/173.38 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
% 173.13/173.38 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__subset,axiom,
% 173.13/173.38 ! [V_A_2,V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__le__upds,axiom,
% 173.13/173.38 ! [V_bs_2,V_as_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 173.13/173.38 => c_Map_Omap__le(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_f_2,V_as_2,V_bs_2),c_Map_Omap__upds(T_a,T_b,V_g_2,V_as_2,V_bs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__add__upds,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__mono,axiom,
% 173.13/173.38 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__apply__nontin,axiom,
% 173.13/173.38 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__UNIV,axiom,
% 173.13/173.38 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_equiv__listrel,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.13/173.38 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__refl__on,axiom,
% 173.13/173.38 ! [V_r_2,V_A_2,T_a] :
% 173.13/173.38 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.13/173.38 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__Cons,axiom,
% 173.13/173.38 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Cons__in__lists__iff,axiom,
% 173.13/173.38 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2)))
% 173.13/173.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__lists__conv__set,axiom,
% 173.13/173.38 ! [V_A_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__list__update2__drop,axiom,
% 173.13/173.38 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 173.13/173.38 ( 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_2)),V_i_2))
% 173.13/173.38 => ( 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_ys_2)))
% 173.13/173.38 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__twist,axiom,
% 173.13/173.38 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 173.13/173.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 173.13/173.38 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__eq__set,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_restrict__map__upds,axiom,
% 173.13/173.38 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2))
% 173.13/173.38 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_dom__map__upds,axiom,
% 173.13/173.38 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1__subset__listrel,axiom,
% 173.13/173.38 ! [V_r_H_2,V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 173.13/173.38 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__irreflexive,axiom,
% 173.13/173.38 ! [V_y_2,V_r_2,T_a] :
% 173.13/173.38 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
% 173.13/173.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Cons__acc__listrel1I,axiom,
% 173.13/173.38 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1__mono,axiom,
% 173.13/173.38 ! [V_s_2,V_r_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1I2,axiom,
% 173.13/173.38 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1__eq__len,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__accI,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__accD,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1I1,axiom,
% 173.13/173.38 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Cons__listrel1__Cons,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.38 & V_xs_2 = V_ys_2 )
% 173.13/173.38 | ( V_x_2 = V_y_2
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel1__iff__update,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.38 <=> ? [B_y,B_n] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2))
% 173.13/173.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.38 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__linear,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 173.13/173.38 ( ! [B_a,B_b] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2))
% 173.13/173.38 | B_a = B_b
% 173.13/173.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) )
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.38 | V_x_2 = V_y_2
% 173.13/173.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__setsum__nth,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__size__pointwise,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 173.13/173.38 ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 173.13/173.38 ! [V_ns_2] :
% 173.13/173.38 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 <=> ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 173.13/173.38 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__simps_I2_J,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a] :
% 173.13/173.38 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.38 => 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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_elem__le__listsum__nat,axiom,
% 173.13/173.38 ! [V_ns,V_k] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => 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))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__0,axiom,
% 173.13/173.38 ! [V_xs_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__addf,axiom,
% 173.13/173.38 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__mult__const,axiom,
% 173.13/173.38 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_ca_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__const__mult,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__0(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__subtractf,axiom,
% 173.13/173.38 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__update__nat,axiom,
% 173.13/173.38 ! [V_n,V_ns,V_k] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => 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)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__abs,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_uminus__listsum__map,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( class_Groups_Oab__group__add(T_a)
% 173.13/173.38 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__size__conv__listsum,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,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_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 173.13/173.38 ! [V_f_2,V_xs_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 173.13/173.38 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 173.13/173.38 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__triv,axiom,
% 173.13/173.38 ! [V_xs_2,V_r_2,T_b,T_a] :
% 173.13/173.38 ( class_Rings_Osemiring__1(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__map__remove1,axiom,
% 173.13/173.38 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 173.13/173.38 ! [V_f_2,V_A_2,T_a,T_b] :
% 173.13/173.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 173.13/173.38 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__mono,axiom,
% 173.13/173.38 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 173.13/173.38 ( ( class_Groups_Omonoid__add(T_b)
% 173.13/173.38 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_someI,axiom,
% 173.13/173.38 ! [T_a,V_x_2,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_tfl__some,axiom,
% 173.13/173.38 ! [T_a,B_P] :
% 173.13/173.38 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 173.13/173.38 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_someI__ex,axiom,
% 173.13/173.38 ! [T_a,V_P_2] :
% 173.13/173.38 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_some__eq__ex,axiom,
% 173.13/173.38 ! [T_a,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 173.13/173.38 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_some__eq__trivial,axiom,
% 173.13/173.38 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_some__sym__eq__trivial,axiom,
% 173.13/173.38 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_exE__some,axiom,
% 173.13/173.38 ! [T_a,V_ca_2,V_P_2] :
% 173.13/173.38 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.13/173.38 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 173.13/173.38 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nitpick_Ocard_H__def,axiom,
% 173.13/173.38 ! [V_A_2,T_a] :
% 173.13/173.38 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.38 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_LeastM__def,axiom,
% 173.13/173.38 ! [V_P_2,V_m_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Oord(T_b)
% 173.13/173.38 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_LeastM__nat__lemma,axiom,
% 173.13/173.38 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,V_k_2))
% 173.13/173.38 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 173.13/173.38 & ! [B_y] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,B_y))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_LeastM__nat__le,axiom,
% 173.13/173.38 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_split__paired__Eps,axiom,
% 173.13/173.38 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Eps__split__eq,axiom,
% 173.13/173.38 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Eps__split,axiom,
% 173.13/173.38 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_GreatestM__def,axiom,
% 173.13/173.38 ! [V_P_2,V_m_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Oord(T_b)
% 173.13/173.38 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_butlast__take,axiom,
% 173.13/173.38 ! [V_xs,T_a,V_n] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_LeastM__natI,axiom,
% 173.13/173.38 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 173.13/173.38 ( hBOOL(hAPP(V_P_2,V_k_2))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__butlast,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_in__set__butlastD,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 173.13/173.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__butlast,axiom,
% 173.13/173.38 ! [V_xs,T_a,V_n] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => 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) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__butlast,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_butlast__conv__take,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_butlast__list__update,axiom,
% 173.13/173.38 ! [V_x,V_xs,T_a,V_k] :
% 173.13/173.38 ( ( 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))
% 173.13/173.38 => 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) )
% 173.13/173.38 & ( 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))
% 173.13/173.38 => 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) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Greatest__def,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Orderings_Oord(T_a)
% 173.13/173.38 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_nth__take__lemma,axiom,
% 173.13/173.38 ! [V_ys,V_xs,T_a,V_k] :
% 173.13/173.38 ( 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)))
% 173.13/173.38 => ( 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)))
% 173.13/173.38 => ( ! [B_i] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 173.13/173.38 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 173.13/173.38 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__Cons__number__of,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a,V_v] :
% 173.13/173.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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) )
% 173.13/173.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_partition__set,axiom,
% 173.13/173.38 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 173.13/173.38 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
% 173.13/173.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists_ONil,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Nil2,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Nil1,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.13/173.38 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sorted__list__of__set__empty,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_a)
% 173.13/173.38 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osimps_I3_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osimps_I2_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__key_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_x_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_partition_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sublist__nil,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_upto__empty,axiom,
% 173.13/173.38 ! [V_i,V_j] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 173.13/173.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip__Nil,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_zip_Osimps_I1_J,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_foldr_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of__Cons__code_I1_J,axiom,
% 173.13/173.38 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_remove1_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct_Osimps_I1_J,axiom,
% 173.13/173.38 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_insort__not__Nil,axiom,
% 173.13/173.38 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( class_Orderings_Olinorder(T_b)
% 173.13/173.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrelp_Oequations_I1_J,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrelp_ONil,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osize_I1_J,axiom,
% 173.13/173.38 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__Nil1,axiom,
% 173.13/173.38 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__upds__Nil2,axiom,
% 173.13/173.38 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__eq__Nil,axiom,
% 173.13/173.38 ! [V_xs_2,V_n_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.38 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__0,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__Nil,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__nonempty,axiom,
% 173.13/173.38 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update_Osimps_I1_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list__update__code_I1_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__is__Nil__conv,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.38 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nil__is__map__conv,axiom,
% 173.13/173.38 ! [V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.38 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_list_Osize_I3_J,axiom,
% 173.13/173.38 ! [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) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__0__conv,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 173.13/173.38 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__empty2,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__empty,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listsum__simps_I1_J,axiom,
% 173.13/173.38 ! [T_a] :
% 173.13/173.38 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_distinct__butlast,axiom,
% 173.13/173.38 ! [T_a,V_xs] :
% 173.13/173.38 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_butlast_Osimps_I1_J,axiom,
% 173.13/173.38 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_butlast_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_x,T_a,V_xs] :
% 173.13/173.38 ( ( V_xs = c_List_Olist_ONil(T_a)
% 173.13/173.38 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 173.13/173.38 & ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.38 => 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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sublist__empty,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_map__of_Osimps_I1_J,axiom,
% 173.13/173.38 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_length__greater__0__conv,axiom,
% 173.13/173.38 ! [V_xs_2,T_a] :
% 173.13/173.38 ( 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_a)),V_xs_2)))
% 173.13/173.38 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__1__Cons,axiom,
% 173.13/173.38 ! [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)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_not__listrel1__Nil,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_not__Nil__listrel1,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel_ONil,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lexord__Nil__right,axiom,
% 173.13/173.38 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nil__notin__lex,axiom,
% 173.13/173.38 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_Nil2__notin__lex,axiom,
% 173.13/173.38 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_partition__P,axiom,
% 173.13/173.38 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 173.13/173.38 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
% 173.13/173.38 => ( ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 173.13/173.38 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.13/173.38 & ! [B_x] :
% 173.13/173.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 173.13/173.38 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__Cons,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_upto_Osimps,axiom,
% 173.13/173.38 ! [V_j,V_i] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 173.13/173.38 => 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)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 173.13/173.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_sublist__singleton,axiom,
% 173.13/173.38 ! [V_x_2,T_a,V_A_2] :
% 173.13/173.38 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 173.13/173.38 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) )
% 173.13/173.38 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 173.13/173.38 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_partition_Osimps_I2_J,axiom,
% 173.13/173.38 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_lists__empty,axiom,
% 173.13/173.38 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_take__Cons_H,axiom,
% 173.13/173.38 ! [V_xs,V_x,T_a,V_n] :
% 173.13/173.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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) )
% 173.13/173.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.38 => 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)) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_upto__rec__number__of,axiom,
% 173.13/173.38 ! [V_n,V_m] :
% 173.13/173.38 ( ( 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)))
% 173.13/173.38 => 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))) )
% 173.13/173.38 & ( ~ 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)))
% 173.13/173.38 => 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) ) ) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_listrel__Nil,axiom,
% 173.13/173.38 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 173.13/173.38
% 173.13/173.38 fof(fact_set__Cons__sing__Nil,axiom,
% 173.13/173.38 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upto_Opsimps,axiom,
% 173.13/173.39 ! [V_j_2,V_i_2] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 173.13/173.39 => 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)) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 173.13/173.39 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_anamorph_Osimps,axiom,
% 173.13/173.39 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 173.13/173.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.39 => hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) )
% 173.13/173.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.13/173.39 => hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oanamorph(T_b,T_a,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)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listset_Osimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__Cons,axiom,
% 173.13/173.39 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_list_Osimps_I5_J,axiom,
% 173.13/173.39 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_list_Osimps_I4_J,axiom,
% 173.13/173.39 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listset_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__Cons1,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upto_Opinduct,axiom,
% 173.13/173.39 ! [V_P_2,V_a1_2,V_a0_2] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => ( ! [B_i,B_j] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 173.13/173.39 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 173.13/173.39 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 173.13/173.39 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__upds__append1,axiom,
% 173.13/173.39 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))
% 173.13/173.39 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append1__eq__conv,axiom,
% 173.13/173.39 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))
% 173.13/173.39 <=> ( V_xs_2 = V_ys_2
% 173.13/173.39 & V_x_2 = V_y_2 ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Cons__eq__append__conv,axiom,
% 173.13/173.39 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)
% 173.13/173.39 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 173.13/173.39 | ? [B_ys_H] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 173.13/173.39 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__eq__Cons__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
% 173.13/173.39 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 173.13/173.39 | ? [B_ys_H] :
% 173.13/173.39 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 173.13/173.39 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_eq__Nil__appendI,axiom,
% 173.13/173.39 ! [T_a,V_ys,V_xs] :
% 173.13/173.39 ( V_xs = V_ys
% 173.13/173.39 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__self__conv2,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__self__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 173.13/173.39 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__is__Nil__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_self__append__conv2,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_ys_2] :
% 173.13/173.39 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_self__append__conv,axiom,
% 173.13/173.39 ! [V_ys_2,T_a,V_xs_2] :
% 173.13/173.39 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 173.13/173.39 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__Nil2,axiom,
% 173.13/173.39 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Nil__is__append__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 173.13/173.39 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__Nil,axiom,
% 173.13/173.39 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 173.13/173.39
% 173.13/173.39 fof(fact_butlast__append,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_ys] :
% 173.13/173.39 ( ( V_ys = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 173.13/173.39 & ( V_ys != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsum__append,axiom,
% 173.13/173.39 ! [V_ys,V_xs,T_a] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__append,axiom,
% 173.13/173.39 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 173.13/173.39 ( 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)
% 173.13/173.39 => ( 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)
% 173.13/173.39 => 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)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__append,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_fun__upds__append2__drop,axiom,
% 173.13/173.39 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.39 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_fun__upds__append__drop,axiom,
% 173.13/173.39 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.13/173.39 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__in__lists__conv,axiom,
% 173.13/173.39 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2)))
% 173.13/173.39 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__assoc,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__eq__append__conv2,axiom,
% 173.13/173.39 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)
% 173.13/173.39 <=> ? [B_us] :
% 173.13/173.39 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 173.13/173.39 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 173.13/173.39 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 173.13/173.39 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_same__append__eq,axiom,
% 173.13/173.39 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)
% 173.13/173.39 <=> V_ys_2 = V_zs_2 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__same__eq,axiom,
% 173.13/173.39 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)
% 173.13/173.39 <=> V_ys_2 = V_zs_2 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__eq__appendI,axiom,
% 173.13/173.39 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 173.13/173.39 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 173.13/173.39 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__of__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldr__append,axiom,
% 173.13/173.39 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Cons__eq__appendI,axiom,
% 173.13/173.39 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 173.13/173.39 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 173.13/173.39 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__Cons,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__append__length,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__append__length__plus,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__append,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_list__update__append1,axiom,
% 173.13/173.39 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_list__update__length,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remove1__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_in__set__butlast__appendI,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 173.13/173.39 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_butlast__snoc,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__listrel1I,axiom,
% 173.13/173.39 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.39 & V_us_2 = V_vs_2 )
% 173.13/173.39 | ( V_xs_2 = V_ys_2
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) )
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lexord__append__leftI,axiom,
% 173.13/173.39 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 173.13/173.39 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 173.13/173.39 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__append,axiom,
% 173.13/173.39 ! [V_ys,V_xs,T_a,V_n] :
% 173.13/173.39 ( ( 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)))
% 173.13/173.39 => 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) )
% 173.13/173.39 & ( ~ 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)))
% 173.13/173.39 => 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))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_list__update__append,axiom,
% 173.13/173.39 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 173.13/173.39 ( ( 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)))
% 173.13/173.39 => 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) )
% 173.13/173.39 & ( ~ 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)))
% 173.13/173.39 => 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)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublist__append,axiom,
% 173.13/173.39 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,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_a)),V_l_2)))),V_A_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listrel1I,axiom,
% 173.13/173.39 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 173.13/173.39 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2))
% 173.13/173.39 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lexord__append__left__rightI,axiom,
% 173.13/173.39 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__Suc__conv__app__nth,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 173.13/173.39 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.39 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.39 & V_x_2 = V_y_2 )
% 173.13/173.39 | ( V_xs_2 = V_ys_2
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublist__Cons,axiom,
% 173.13/173.39 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),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_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,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)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listrel1E,axiom,
% 173.13/173.39 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.13/173.39 => ~ ! [B_x,B_y] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
% 173.13/173.39 => ! [B_us,B_vs] :
% 173.13/173.39 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 173.13/173.39 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lexord__append__leftD,axiom,
% 173.13/173.39 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.39 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate1__def,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upd__conv__take__nth__drop,axiom,
% 173.13/173.39 ! [V_a,V_xs,T_a,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__take__drop__id,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate1__is__Nil__conv,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Nil,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__butlast,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_butlast__drop,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__drop__subset,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_in__set__dropD,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__drop,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__rotate1,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__rotate1,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__drop,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__take,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__drop,axiom,
% 173.13/173.39 ! [V_i,V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct1__rotate,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 173.13/173.39 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__drop,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__0,axiom,
% 173.13/173.39 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__zip,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__via__drop,axiom,
% 173.13/173.39 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__1__Cons,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Suc__Cons,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__drop__subset__set__drop,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__all,axiom,
% 173.13/173.39 ! [V_n,V_xs,T_a] :
% 173.13/173.39 ( 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))
% 173.13/173.39 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__eq__Nil,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> 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_2)),V_n_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__append,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__eq__conv__conj,axiom,
% 173.13/173.39 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 173.13/173.39 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)
% 173.13/173.39 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Cons,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Cons_H,axiom,
% 173.13/173.39 ! [V_xs,V_x,T_a,V_n] :
% 173.13/173.39 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => 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) )
% 173.13/173.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => 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) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__drop,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_i,V_n] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__eq__append__conv__if,axiom,
% 173.13/173.39 ! [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_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 173.13/173.39 <=> ( ( 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_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
% 173.13/173.39 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 173.13/173.39 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 173.13/173.39 & ( ~ 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_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
% 173.13/173.39 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 173.13/173.39 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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 ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__drop_H,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__simps,axiom,
% 173.13/173.39 ! [V_xs,V_x,T_b,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 173.13/173.39 & 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Cons__number__of,axiom,
% 173.13/173.39 ! [V_xs,V_x,T_a,V_v] :
% 173.13/173.39 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => 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) )
% 173.13/173.39 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => 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) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__add,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_j,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate1__length01,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__append2,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__append1,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_id__take__nth__drop,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_i] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__hd__drop,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_n] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__drop__conv__nth,axiom,
% 173.13/173.39 ! [V_n,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => ( 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)))
% 173.13/173.39 => 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) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd_Osimps,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__map,axiom,
% 173.13/173.39 ! [V_f_2,T_b,T_a,V_xs_2] :
% 173.13/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__append,axiom,
% 173.13/173.39 ! [V_ys,T_a,V_xs] :
% 173.13/173.39 ( ( V_xs = c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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) )
% 173.13/173.39 & ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__append2,axiom,
% 173.13/173.39 ! [V_ys,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__in__set,axiom,
% 173.13/173.39 ! [T_a,V_xs_2] :
% 173.13/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__conv__nth,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate1__hd__tl,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__rotate__conv__nth,axiom,
% 173.13/173.39 ! [V_n,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl__drop,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__tl,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__is__Nil__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl_Osimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__rotate,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__rotate,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__tl,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__tl,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__rotate,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 173.13/173.39 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__rotate,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl_Osimps_I2_J,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate1__rotate__swap,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl__append2,axiom,
% 173.13/173.39 ! [V_ys,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__tl,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__conv__mod,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__Suc,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__Suc,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate0,axiom,
% 173.13/173.39 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__add,axiom,
% 173.13/173.39 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__id,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_n] :
% 173.13/173.39 ( 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)
% 173.13/173.39 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__length01,axiom,
% 173.13/173.39 ! [V_n,V_xs,T_a] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__tl,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_tl__take,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__Suc,axiom,
% 173.13/173.39 ! [V_n,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__drop__take,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_fold1__set,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 173.13/173.39 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lexord__append__rightI,axiom,
% 173.13/173.39 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 173.13/173.39 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__Cons,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_start__le__sum,axiom,
% 173.13/173.39 ! [V_ns_2,V_n_2,V_m_2] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__assoc,axiom,
% 173.13/173.39 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Groups_Osemigroup__add(T_a)
% 173.13/173.39 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__absorb0,axiom,
% 173.13/173.39 ! [V_zs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldr__conv__foldl,axiom,
% 173.13/173.39 ! [V_a_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Groups_Oab__semigroup__add(T_a)
% 173.13/173.39 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__Nil,axiom,
% 173.13/173.39 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsum__foldl,axiom,
% 173.13/173.39 ! [T_a] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.39 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__foldr1,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.39 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__foldr1__lemma,axiom,
% 173.13/173.39 ! [V_xs_2,V_a_2,T_a] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_a)
% 173.13/173.39 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sum__eq__0__conv,axiom,
% 173.13/173.39 ! [V_ns_2,V_m_2] :
% 173.13/173.39 ( 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)
% 173.13/173.39 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 & ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 173.13/173.39 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Sup__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Lattices_Olattice(T_a)
% 173.13/173.39 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Inf__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Lattices_Olattice(T_a)
% 173.13/173.39 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Min__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Max__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_SUPR__set__fold,axiom,
% 173.13/173.39 ! [V_f_2,V_xs_2,T_b,T_a] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__upds__fold__map__upd,axiom,
% 173.13/173.39 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_elem__le__sum,axiom,
% 173.13/173.39 ! [V_ns_2,V_n_2] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lexord__Nil__left,axiom,
% 173.13/173.39 ! [V_r_2,V_y_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 173.13/173.39 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__list__update,axiom,
% 173.13/173.39 ! [V_x,V_k,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => ( ( 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))
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 173.13/173.39 & ( 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))
% 173.13/173.39 => 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) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__ConsL,axiom,
% 173.13/173.39 ! [V_x,T_a,V_xs] :
% 173.13/173.39 ( V_xs = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__ConsR,axiom,
% 173.13/173.39 ! [V_x,T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last_Osimps,axiom,
% 173.13/173.39 ! [V_x,T_a,V_xs] :
% 173.13/173.39 ( ( V_xs = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 173.13/173.39 & ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__map,axiom,
% 173.13/173.39 ! [V_f_2,T_b,T_a,V_xs_2] :
% 173.13/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__appendL,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_ys] :
% 173.13/173.39 ( V_ys = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__appendR,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_ys] :
% 173.13/173.39 ( V_ys != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__append,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_ys] :
% 173.13/173.39 ( ( V_ys = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 173.13/173.39 & ( V_ys != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__in__set,axiom,
% 173.13/173.39 ! [T_a,V_as_2] :
% 173.13/173.39 ( V_as_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__snoc,axiom,
% 173.13/173.39 ! [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 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__drop,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_n] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_snoc__eq__iff__butlast,axiom,
% 173.13/173.39 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2
% 173.13/173.39 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 173.13/173.39 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__butlast__last__id,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__conv__nth,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lists_Osimps,axiom,
% 173.13/173.39 ! [V_A_2,V_a_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 173.13/173.39 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 | ? [B_a,B_l] :
% 173.13/173.39 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INFI__set__fold,axiom,
% 173.13/173.39 ! [V_f_2,V_xs_2,T_b,T_a] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF1__E,axiom,
% 173.13/173.39 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 173.13/173.39 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 173.13/173.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF1__D,axiom,
% 173.13/173.39 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__D,axiom,
% 173.13/173.39 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__E,axiom,
% 173.13/173.39 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 173.13/173.39 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF2__E,axiom,
% 173.13/173.39 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 173.13/173.39 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 173.13/173.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF2__D,axiom,
% 173.13/173.39 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_finite__INT,axiom,
% 173.13/173.39 ! [V_A_2,T_b,V_I_2,T_a] :
% 173.13/173.39 ( ? [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 173.13/173.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 173.13/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I10_J,axiom,
% 173.13/173.39 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I10_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__INT__eq2,axiom,
% 173.13/173.39 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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))
% 173.13/173.39 <=> 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_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_le__INF__iff,axiom,
% 173.13/173.39 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2)))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__subset__iff,axiom,
% 173.13/173.39 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Image__INT__subset,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__lower,axiom,
% 173.13/173.39 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__absorb,axiom,
% 173.13/173.39 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 173.13/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__insert,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I1_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I2_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__const,axiom,
% 173.13/173.39 ! [V_M_2,T_a,V_A_2,T_b] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I5_J,axiom,
% 173.13/173.39 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I5_J,axiom,
% 173.13/173.39 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__constant,axiom,
% 173.13/173.39 ! [V_ca_2,T_b,T_a,V_A_2] :
% 173.13/173.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 173.13/173.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__empty,axiom,
% 173.13/173.39 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__INT__eq,axiom,
% 173.13/173.39 ! [V_x_2,V_r_2,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
% 173.13/173.39 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__insert__distrib,axiom,
% 173.13/173.39 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__iff,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Collect__ball__eq,axiom,
% 173.13/173.39 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.39 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.39 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.39 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.39 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I7_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I6_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I7_J,axiom,
% 173.13/173.39 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Un__INT__distrib,axiom,
% 173.13/173.39 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I6_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Un__INT__distrib2,axiom,
% 173.13/173.39 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_vimage__INT,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Pow__INT__eq,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INFI__apply,axiom,
% 173.13/173.39 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__commute,axiom,
% 173.13/173.39 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__less__iff,axiom,
% 173.13/173.39 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 173.13/173.39 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.13/173.39 & class_Orderings_Olinorder(T_a) )
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2))
% 173.13/173.39 <=> ? [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 173.13/173.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_UN__extend__simps_I7_J,axiom,
% 173.13/173.39 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_UN__simps_I7_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I9_J,axiom,
% 173.13/173.39 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I9_J,axiom,
% 173.13/173.39 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Compl__INT,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Compl__UN,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INFI__bool__eq,axiom,
% 173.13/173.39 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__Int__distrib,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__Un,axiom,
% 173.13/173.39 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__subset,axiom,
% 173.13/173.39 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INTER__def,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I2_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I1_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(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)) )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Collect__all__eq,axiom,
% 173.13/173.39 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I3_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(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)) )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I3_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_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_B_2) )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__extend__simps_I4_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF__leI,axiom,
% 173.13/173.39 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 173.13/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__greaterThan__UNIV,axiom,
% 173.13/173.39 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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INT__simps_I4_J,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 173.13/173.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(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)) )
% 173.13/173.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.13/173.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__aux__max,axiom,
% 173.13/173.39 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_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_a)),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)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lists__IntI,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 173.13/173.39 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp_ONil,axiom,
% 173.13/173.39 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF1__iff,axiom,
% 173.13/173.39 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_INF2__iff,axiom,
% 173.13/173.39 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_append__in__listsp__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 173.13/173.39 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 173.13/173.39 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp_Oequations_I1_J,axiom,
% 173.13/173.39 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter_Osimps_I1_J,axiom,
% 173.13/173.39 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__empty__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_partition__filter1,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__filter__le,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,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)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__is__subset,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sum__length__filter__compl,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_in__listsp__conv__set,axiom,
% 173.13/173.39 ! [V_xs_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__id__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp__inf__eq,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp__infI,axiom,
% 173.13/173.39 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 173.13/173.39 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__insort__triv,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_b)
% 173.13/173.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__filter,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remove1__filter__not,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 173.13/173.39 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__remove1,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp__conj__eq,axiom,
% 173.13/173.39 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2))
% 173.13/173.39 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 173.13/173.39 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__filter,axiom,
% 173.13/173.39 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp_Oequations_I2_J,axiom,
% 173.13/173.39 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 173.13/173.39 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 173.13/173.39 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 173.13/173.39 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_partition__filter2,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__filter,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__filter__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__filter__less,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_partition__filter__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp__mono,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__minus__filter__out,axiom,
% 173.13/173.39 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__in__sublist,axiom,
% 173.13/173.39 ! [V_s_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsp__lists__eq,axiom,
% 173.13/173.39 ! [V_x_2,V_A_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
% 173.13/173.39 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__filter__conv__card,axiom,
% 173.13/173.39 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_lists__Int__eq,axiom,
% 173.13/173.39 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__filter__def,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),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,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__max__length,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Osimps_I2_J,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__map__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__filter__simps_I2_J,axiom,
% 173.13/173.39 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__empty,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.39 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Osimps_I1_J,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__of__filter__in,axiom,
% 173.13/173.39 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 173.13/173.39 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 173.13/173.39 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__filter__simps_I1_J,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublist__shift__lemma__Suc,axiom,
% 173.13/173.39 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__transpose,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_i_2] :
% 173.13/173.39 ( 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_a))),c_List_Otranspose(T_a,V_xs_2))))
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__transpose,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__filter__map__filter,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_insort__key__remove1,axiom,
% 173.13/173.39 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_b)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 173.13/173.39 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 173.13/173.39 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublist__def,axiom,
% 173.13/173.39 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted_ONil,axiom,
% 173.13/173.39 ! [T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__single,axiom,
% 173.13/173.39 ! [V_x,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__map__same,axiom,
% 173.13/173.39 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__filter,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__same,axiom,
% 173.13/173.39 ! [V_xs_2,V_g_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_atLeastLessThan__upt,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__upt,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__drop,axiom,
% 173.13/173.39 ! [V_n,V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_drop__upt,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__upt,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__Suc__append,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__Suc,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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))) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__add__eq__append,axiom,
% 173.13/173.39 ! [V_k,V_j,V_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__eq__Nil__conv,axiom,
% 173.13/173.39 ! [V_j_2,V_i_2] :
% 173.13/173.39 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 173.13/173.39 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__conv__Nil,axiom,
% 173.13/173.39 ! [V_i,V_j] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 173.13/173.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__0,axiom,
% 173.13/173.39 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted_Oequations_I1_J,axiom,
% 173.13/173.39 ! [T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__butlast,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__map__remove1,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__insort__key,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)))
% 173.13/173.39 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__Suc__upt,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__distinct__set__unique,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 173.13/173.39 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 173.13/173.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__take,axiom,
% 173.13/173.39 ! [V_n,V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__insort,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))
% 173.13/173.39 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__upt,axiom,
% 173.13/173.39 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__remove1,axiom,
% 173.13/173.39 ! [V_a,V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__upt,axiom,
% 173.13/173.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__upto,axiom,
% 173.13/173.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__list__of__set__range,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__insort__insert,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_take__upt,axiom,
% 173.13/173.39 ! [V_n,V_m,V_i] :
% 173.13/173.39 ( 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))
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__conv__Cons,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__many,axiom,
% 173.13/173.39 ! [V_zs,V_y,V_x,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 173.13/173.39 => 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))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__many__eq,axiom,
% 173.13/173.39 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)))
% 173.13/173.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 173.13/173.39 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__rec,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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)) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__insort__insert__key,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__tl,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__upt,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__Cons,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 173.13/173.39 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 & ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__append,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 173.13/173.39 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 173.13/173.39 & ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ! [B_xa] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__rec__number__of,axiom,
% 173.13/173.39 ! [V_n,V_m] :
% 173.13/173.39 ( ( 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)))
% 173.13/173.39 => 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))) )
% 173.13/173.39 & ( ~ 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)))
% 173.13/173.39 => 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) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_upt__eq__Cons__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 173.13/173.39 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 173.13/173.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 173.13/173.39 & V_i_2 = V_x_2
% 173.13/173.39 & 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 ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__upt,axiom,
% 173.13/173.39 ! [V_j,V_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__insort,axiom,
% 173.13/173.39 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 173.13/173.39 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__nth,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_atLeastAtMost__upt,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_atLeast__upt,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 173.13/173.39 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 173.13/173.39 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.39 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 173.13/173.39 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 173.13/173.39 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__upt,axiom,
% 173.13/173.39 ! [V_j,V_k,V_i] :
% 173.13/173.39 ( 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))
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_greaterThanAtMost__upt,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted_Oequations_I2_J,axiom,
% 173.13/173.39 ! [V_a1_2,V_a2_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 173.13/173.39 <=> ( ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 173.13/173.39 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_greaterThanLessThan__upt,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__map__upt,axiom,
% 173.13/173.39 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__list__of__set,axiom,
% 173.13/173.39 ! [V_A_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.13/173.39 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 173.13/173.39 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 173.13/173.39 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_atMost__upto,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_insort__remove1,axiom,
% 173.13/173.39 ! [V_xs_2,V_a_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__nth__mono,axiom,
% 173.13/173.39 ! [V_j,V_i,V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => ( 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)))
% 173.13/173.39 => 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))) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__equals__nth__mono,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 <=> ! [B_j] :
% 173.13/173.39 ( 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_2)))
% 173.13/173.39 => ! [B_i] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__sorted__distinct__set__unique,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_b)
% 173.13/173.39 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 173.13/173.39 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 173.13/173.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublist__shift__lemma,axiom,
% 173.13/173.39 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__rectangle,axiom,
% 173.13/173.39 ! [V_n_2,T_a,V_xs_2] :
% 173.13/173.39 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 173.13/173.39 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.39 => ( ! [B_i] :
% 173.13/173.39 ( 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_a))),V_xs_2)))
% 173.13/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 )
% 173.13/173.39 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Opsimps_I2_J,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)))
% 173.13/173.39 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Opsimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))))
% 173.13/173.39 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__column,axiom,
% 173.13/173.39 ! [V_i_2,V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 173.13/173.39 => ( 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_a))),V_xs_2)))
% 173.13/173.39 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__aux__filter__head,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_inj__on__rev,axiom,
% 173.13/173.39 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__is__Nil__conv,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Nil__is__rev__conv,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 173.13/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev_Osimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__concat,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__singleton__conv,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
% 173.13/173.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_singleton__rev__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2)
% 173.13/173.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__conv__foldl,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__foldl__cons,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__conv__concat,axiom,
% 173.13/173.39 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__rev,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 173.13/173.39 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__append,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__append,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldl__foldr,axiom,
% 173.13/173.39 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldr__foldl,axiom,
% 173.13/173.39 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat_Osimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__rev,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsum__rev,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( class_Groups_Ocomm__monoid__add(T_a)
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__rev__ident,axiom,
% 173.13/173.39 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__swap,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 173.13/173.39 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__is__rev__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 173.13/173.39 <=> V_xs_2 = V_ys_2 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__rev,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__rev,axiom,
% 173.13/173.39 ! [V_ys,T_b,V_xs,T_a] :
% 173.13/173.39 ( 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)
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__filter,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat_Osimps_I2_J,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__eq__Nil__conv,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] :
% 173.13/173.39 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 173.13/173.39 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_Nil__eq__concat__conv,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] :
% 173.13/173.39 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 173.13/173.39 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__concat,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__concat,axiom,
% 173.13/173.39 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__eq__Cons__iff,axiom,
% 173.13/173.39 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 173.13/173.39 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev_Osimps_I2_J,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__concat,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__concat,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__rev,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_last__rev,axiom,
% 173.13/173.39 ! [T_a,V_xs] :
% 173.13/173.39 ( V_xs != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__transpose,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__drop,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__take,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rotate__rev,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Osimps_I3_J,axiom,
% 173.13/173.39 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__nth,axiom,
% 173.13/173.39 ! [V_xs,T_a,V_n] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__injective,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 173.13/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
% 173.13/173.39 => ( ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
% 173.13/173.39 => V_xs_2 = V_ys_2 ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__eq__concat__iff,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a] :
% 173.13/173.39 ( ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
% 173.13/173.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
% 173.13/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
% 173.13/173.39 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 173.13/173.39 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_rev__update,axiom,
% 173.13/173.39 ! [V_y,V_xs,T_a,V_k] :
% 173.13/173.39 ( 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)))
% 173.13/173.39 => 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) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_concat__map__singleton,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__rev__nth__mono,axiom,
% 173.13/173.39 ! [V_j,V_i,V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 173.13/173.39 => ( 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)))
% 173.13/173.39 => 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))) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_foldr__max__sorted,axiom,
% 173.13/173.39 ! [V_y_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 173.13/173.39 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 173.13/173.39 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose_Opsimps_I3_J,axiom,
% 173.13/173.39 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)))
% 173.13/173.39 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__transpose__sorted,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 173.13/173.39 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 173.13/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.13/173.39 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 173.13/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__column__length,axiom,
% 173.13/173.39 ! [V_i_2,V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 173.13/173.39 => ( 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_a))),V_xs_2)))
% 173.13/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__aux__filter__tail,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__nth__transpose__sorted,axiom,
% 173.13/173.39 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 173.13/173.39 => ( 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_a))),c_List_Otranspose(T_a,V_xs_2))))
% 173.13/173.39 => ( 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_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2))))
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transpose__transpose,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 173.13/173.39 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 173.13/173.39 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__takeWhile__fst,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_zip__takeWhile__snd,axiom,
% 173.13/173.39 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__takeWhileD,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__eq__all__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__takeWhile__le,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,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_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__eq__take,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__takeWhile,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 173.13/173.39 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__takeWhile,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 173.13/173.39 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__tail,axiom,
% 173.13/173.39 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 173.13/173.39 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_return__list__def,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__append1,axiom,
% 173.13/173.39 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__nth,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_nth__length__takeWhile,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.13/173.39 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__upds__def,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__not__last,axiom,
% 173.13/173.39 ! [T_a,V_xs_2] :
% 173.13/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 173.13/173.39 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 173.13/173.39 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 173.13/173.39 ! [V_l] :
% 173.13/173.39 ( c_List_Onat__list(V_l)
% 173.13/173.39 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__remdups__concat,axiom,
% 173.13/173.39 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__remdups,axiom,
% 173.13/173.39 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__remdups__leq,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__map__remdups,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__remdups,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remove1__remdups,axiom,
% 173.13/173.39 ! [V_x,V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => 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)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__eq__nil__iff,axiom,
% 173.13/173.39 ! [V_x_2,T_a] :
% 173.13/173.39 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__eq__nil__right__iff,axiom,
% 173.13/173.39 ! [V_x_2,T_a] :
% 173.13/173.39 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 173.13/173.39 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups_Osimps_I1_J,axiom,
% 173.13/173.39 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__remdups,axiom,
% 173.13/173.39 ! [V_l,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__id__iff__distinct,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 173.13/173.39 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__remdups__id,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__remdups__eq,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
% 173.13/173.39 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__remdups,axiom,
% 173.13/173.39 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups__filter,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_embed__list__def,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_remdups_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__remdups__card__conv,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__neq__rev,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__neq__rev,axiom,
% 173.13/173.39 ! [V_x_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__dropWhile__le,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,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_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__dropWhile,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 173.13/173.39 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) )
% 173.13/173.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__dropWhile,axiom,
% 173.13/173.39 ! [V_P_2,V_xs_2,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 173.13/173.39 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 173.13/173.39 <=> ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_takeWhile__dropWhile__id,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ).
% 173.13/173.39
% 173.13/173.39 fof(fact_hd__dropWhile,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 173.13/173.39 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__map,axiom,
% 173.13/173.39 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__append1,axiom,
% 173.13/173.39 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.13/173.39 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 173.13/173.39 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 173.13/173.39 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 173.13/173.39 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))
% 173.13/173.39 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__eq__drop,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_dropWhile__nth,axiom,
% 173.13/173.39 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
% 173.13/173.39 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_listsum__map__filter,axiom,
% 173.13/173.39 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 173.13/173.39 ( class_Groups_Omonoid__add(T_b)
% 173.13/173.39 => ( ! [B_x] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.13/173.39 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 173.13/173.39 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 173.13/173.39 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sorted__nth__monoI,axiom,
% 173.13/173.39 ! [V_xs,T_a] :
% 173.13/173.39 ( class_Orderings_Olinorder(T_a)
% 173.13/173.39 => ( ! [B_i,B_j] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 173.13/173.39 => ( 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)))
% 173.13/173.39 => 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))) ) )
% 173.13/173.39 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_n__lists_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__sublists,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__n__lists,axiom,
% 173.13/173.39 ! [V_n,V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__set__sublists,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__n__lists,axiom,
% 173.13/173.39 ! [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) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_length__n__lists__elem,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))))
% 173.13/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublists__powset,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublists_Osimps_I1_J,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_n__lists_Osimps_I1_J,axiom,
% 173.13/173.39 ! [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))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_n__lists__Nil,axiom,
% 173.13/173.39 ! [T_a,V_n] :
% 173.13/173.39 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => 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))) )
% 173.13/173.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.13/173.39 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sublists_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_set__n__lists,axiom,
% 173.13/173.39 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_product_Osimps_I2_J,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_enum__the__def,axiom,
% 173.13/173.39 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_product_Osimps_I1_J,axiom,
% 173.13/173.39 ! [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)) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_distinct__product,axiom,
% 173.13/173.39 ! [V_ys,T_b,V_xs,T_a] :
% 173.13/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.13/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 173.13/173.39 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_product__list__set,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_map__of__zip__enum__inject,axiom,
% 173.13/173.39 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 173.13/173.39 ( ( class_Enum_Oenum(T_b)
% 173.13/173.39 & class_Enum_Oenum(T_a) )
% 173.13/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
% 173.13/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
% 173.13/173.39 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2)))
% 173.13/173.39 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 173.13/173.39
% 173.13/173.39 fof(fact_sort__foldl__insort,axiom,
% 173.13/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__prod__def,axiom,
% 173.49/173.39 ! [T_b,T_a] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_a)
% 173.49/173.39 & class_Enum_Oenum(T_b) )
% 173.49/173.39 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__distinct,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__option__def,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_distinct__sort,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 173.49/173.39 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_filter__sort,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_length__sort,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sorted__sort,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sort__key__simps_I1_J,axiom,
% 173.49/173.39 ! [V_f_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_set__sort,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_in__enum,axiom,
% 173.49/173.39 ! [V_x_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_UNIV__enum,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__UNIV,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sorted__sort__key,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_b,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sort__key__simps_I2_J,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__fun__code,axiom,
% 173.49/173.39 ! [T_b,T_a] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_a)
% 173.49/173.39 & class_HOL_Oequal(T_a)
% 173.49/173.39 & class_Enum_Oenum(T_b) )
% 173.49/173.39 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__fun__def,axiom,
% 173.49/173.39 ! [T_b,T_a] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_a)
% 173.49/173.39 & class_Enum_Oenum(T_b) )
% 173.49/173.39 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_all__n__lists__def,axiom,
% 173.49/173.39 ! [V_n_2,V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 173.49/173.39 <=> ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a)))))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_ex__n__lists__def,axiom,
% 173.49/173.39 ! [V_n_2,V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 173.49/173.39 <=> ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a)))))
% 173.49/173.39 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__all__fun__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__ex__fun__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_all__code,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.49/173.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_exists__code,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 173.49/173.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__all,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 173.49/173.39 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__ex,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 173.49/173.39 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__all__option__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 173.49/173.39 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 173.49/173.39 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__ex__option__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 173.49/173.39 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 173.49/173.39 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__ex__prod__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__all__prod__def,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_order__fun_I1_J,axiom,
% 173.49/173.39 ! [V_g_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Orderings_Oorder(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.49/173.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_order__fun_I2_J,axiom,
% 173.49/173.39 ! [V_g_2,V_f_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Orderings_Oorder(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.49/173.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 173.49/173.39 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__ex__fun__code,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a)
% 173.49/173.39 & class_HOL_Oequal(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_enum__all__fun__code,axiom,
% 173.49/173.39 ! [V_P_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Enum_Oenum(T_b)
% 173.49/173.39 & class_Enum_Oenum(T_a)
% 173.49/173.39 & class_HOL_Oequal(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 173.49/173.39 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_image__INT,axiom,
% 173.49/173.39 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 173.49/173.39 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 173.49/173.39 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,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_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_map__of__zip__enum__is__Some,axiom,
% 173.49/173.39 ! [V_x,V_ys,T_b,T_a] :
% 173.49/173.39 ( class_Enum_Oenum(T_a)
% 173.49/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))
% 173.49/173.39 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_takeWhile__eq__filter,axiom,
% 173.49/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.49/173.39 ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
% 173.49/173.39 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_inj__on__mapI,axiom,
% 173.49/173.39 ! [V_A_2,V_f_2,T_b,T_a] :
% 173.49/173.39 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2)))
% 173.49/173.39 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_UnionI,axiom,
% 173.49/173.39 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_image__Union,axiom,
% 173.49/173.39 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),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_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__image__eq,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_UNION__eq__Union__image,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Field__Union,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_INT__simps_I8_J,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_INT__extend__simps_I8_J,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__upper,axiom,
% 173.49/173.39 ! [V_A_2,V_x_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__UNIV,axiom,
% 173.49/173.39 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__le__iff,axiom,
% 173.49/173.39 ! [V_b_2,V_A_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2))
% 173.49/173.39 <=> ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__mono,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__quotient,axiom,
% 173.49/173.39 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.39 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__upper,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_subset__Pow__Union,axiom,
% 173.49/173.39 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__UnionD,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__empty,axiom,
% 173.49/173.39 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__insert,axiom,
% 173.49/173.39 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__Pow__eq,axiom,
% 173.49/173.39 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__Sup__iff,axiom,
% 173.49/173.39 ! [V_S_2,V_a_2,T_a] :
% 173.49/173.39 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 & class_Orderings_Olinorder(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 173.49/173.39 <=> ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__Un__distrib,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__disjoint,axiom,
% 173.49/173.39 ! [V_A_2,V_C_2,T_a] :
% 173.49/173.39 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.49/173.39 <=> ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__insert,axiom,
% 173.49/173.39 ! [V_A_2,V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__singleton,axiom,
% 173.49/173.39 ! [V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__empty,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__UNIV,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Int__Union,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Int__Union2,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sigma__Union,axiom,
% 173.49/173.39 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Domain__Union,axiom,
% 173.49/173.39 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__def,axiom,
% 173.49/173.39 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_UN__extend__simps_I8_J,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_UN__simps_I8_J,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_vimage__Union,axiom,
% 173.49/173.39 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Range__Union,axiom,
% 173.49/173.39 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Un__eq__Union,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Un__Union__image,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Union__Int__subset,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__binary,axiom,
% 173.49/173.39 ! [V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__fin__Sup,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.49/173.39 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__set__fold,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__Union,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 173.49/173.39 => ( ! [B_M] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_insert__partition,axiom,
% 173.49/173.39 ! [V_F_2,V_x_2,T_a] :
% 173.49/173.39 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
% 173.49/173.39 => ! [B_xa] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
% 173.49/173.39 => ( B_x != B_xa
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 173.49/173.39 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 173.49/173.39 ( ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 173.49/173.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 173.49/173.39 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_length__takeWhile__less__P__nth,axiom,
% 173.49/173.39 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 173.49/173.39 ( ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 173.49/173.39 => ( 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_a)),V_xs_2)))
% 173.49/173.39 => 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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sup__Inf,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__Sup,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__Inter,axiom,
% 173.49/173.39 ! [V_M_2,T_a] :
% 173.49/173.39 ( ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 173.49/173.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_InterD,axiom,
% 173.49/173.39 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_InterE,axiom,
% 173.49/173.39 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__eq,axiom,
% 173.49/173.39 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,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_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__singleton,axiom,
% 173.49/173.39 ! [V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__empty,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__UNIV,axiom,
% 173.49/173.39 ! [T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__insert,axiom,
% 173.49/173.39 ! [V_A_2,V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__Un__distrib,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__insert,axiom,
% 173.49/173.39 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__UNIV,axiom,
% 173.49/173.39 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__lower,axiom,
% 173.49/173.39 ! [V_A_2,V_x_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__less__iff,axiom,
% 173.49/173.39 ! [V_a_2,V_S_2,T_a] :
% 173.49/173.39 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 & class_Orderings_Olinorder(T_a) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 173.49/173.39 <=> ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__lower,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_le__Inf__iff,axiom,
% 173.49/173.39 ! [V_A_2,V_b_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
% 173.49/173.39 <=> ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__empty,axiom,
% 173.49/173.39 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__anti__mono,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__image__eq,axiom,
% 173.49/173.39 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_INTER__eq__Inter__image,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__def,axiom,
% 173.49/173.39 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Un__Inter,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Int__eq__Inter,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Int__Inter__image,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__Un__subset,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__binary,axiom,
% 173.49/173.39 ! [V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__fin__Inf,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.49/173.39 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inf__set__fold,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.39 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__def,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.49/173.39 & ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sorted_Osimps,axiom,
% 173.49/173.39 ! [V_a_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 173.49/173.39 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 173.49/173.39 | ? [B_xs,B_x] :
% 173.49/173.39 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 173.49/173.39 & ! [B_xa] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 173.49/173.39 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__Cons,axiom,
% 173.49/173.39 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 173.49/173.39 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 173.49/173.39 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__map1,axiom,
% 173.49/173.39 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2)
% 173.49/173.39 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__map2,axiom,
% 173.49/173.39 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2))
% 173.49/173.39 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__eq,axiom,
% 173.49/173.39 ! [T_a,V_ys_2,V_xs_2] :
% 173.49/173.39 ( V_xs_2 = V_ys_2
% 173.49/173.39 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__lengthD,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__dropI,axiom,
% 173.49/173.39 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__takeI,axiom,
% 173.49/173.39 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__Nil,axiom,
% 173.49/173.39 ! [V_ys_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 173.49/173.39 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__Nil2,axiom,
% 173.49/173.39 ! [V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 173.49/173.39 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__rev,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2))
% 173.49/173.39 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__rev1,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 173.49/173.39 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__append,axiom,
% 173.49/173.39 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.49/173.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.49/173.39 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))
% 173.49/173.39 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__appendI,axiom,
% 173.49/173.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 173.49/173.39 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2)
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__conv__all__nth,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 173.49/173.39 & ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__nthD,axiom,
% 173.49/173.39 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__nthD2,axiom,
% 173.49/173.39 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => ( 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_ys_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__update__cong,axiom,
% 173.49/173.39 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__update__cong2,axiom,
% 173.49/173.39 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 173.49/173.39 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 173.49/173.39 => ( 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_ys_2)))
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2I,axiom,
% 173.49/173.39 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 173.49/173.39 ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2))))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 173.49/173.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_card__partition,axiom,
% 173.49/173.39 ! [V_k_2,V_C_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 173.49/173.39 => ( ! [B_c] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 173.49/173.39 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 173.49/173.39 => ( ! [B_c1] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 173.49/173.39 => ! [B_c2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 173.49/173.39 => ( B_c1 != B_c2
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 173.49/173.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_all__nth__imp__all__set,axiom,
% 173.49/173.39 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 173.49/173.39 ( ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_map__removeAll__inj__on,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 173.49/173.39 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll__id,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll_Osimps_I2_J,axiom,
% 173.49/173.39 ! [V_xs,T_a,V_y,V_x] :
% 173.49/173.39 ( ( V_x = V_y
% 173.49/173.39 => 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) )
% 173.49/173.39 & ( V_x != V_y
% 173.49/173.39 => 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)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_distinct__removeAll,axiom,
% 173.49/173.39 ! [V_x,V_xs,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.49/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll__filter__not__eq,axiom,
% 173.49/173.39 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll__filter__not,axiom,
% 173.49/173.39 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 173.49/173.39 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 173.49/173.39 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll_Osimps_I1_J,axiom,
% 173.49/173.39 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_removeAll__append,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_distinct__remove1__removeAll,axiom,
% 173.49/173.39 ! [V_x,V_xs,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.49/173.39 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_map__removeAll__inj,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 173.49/173.39 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 173.49/173.39 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_set__removeAll,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_not__in__set__insert,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_List_Oinsert__def,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.39 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 173.49/173.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_insert__remdups,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_distinct__insert,axiom,
% 173.49/173.39 ! [V_x,V_xs,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 173.49/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_in__set__insert,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_List_Oset__insert,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_insert__Nil,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_concat__map__maps,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_maps__def,axiom,
% 173.49/173.39 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_maps__simps_I2_J,axiom,
% 173.49/173.39 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_maps__simps_I1_J,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_distinct__concat,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 173.49/173.39 => ( ! [B_ys] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 173.49/173.39 => ( ! [B_ys] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => ! [B_zs] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => ( B_ys != B_zs
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 173.49/173.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_measures__lesseq,axiom,
% 173.49/173.39 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 173.49/173.39 ( 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)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_wf__measures,axiom,
% 173.49/173.39 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_in__measures_I1_J,axiom,
% 173.49/173.39 ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_measures__def,axiom,
% 173.49/173.39 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_measures__less,axiom,
% 173.49/173.39 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 173.49/173.39 ( 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)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_in__measures_I2_J,axiom,
% 173.49/173.39 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 173.49/173.39 <=> ( 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)))
% 173.49/173.39 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_inj__on__Inter,axiom,
% 173.49/173.39 ! [V_f_2,T_b,T_a,V_S_2] :
% 173.49/173.39 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 173.49/173.39 => ( ! [B_A] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 173.49/173.39 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 173.49/173.39 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Inter__subset,axiom,
% 173.49/173.39 ! [V_B_2,V_A_2,T_a] :
% 173.49/173.39 ( ! [B_X] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 173.49/173.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_foldl__apply,axiom,
% 173.49/173.39 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 173.49/173.39 ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) )
% 173.49/173.39 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_inj__on__INTER,axiom,
% 173.49/173.39 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 173.49/173.39 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.49/173.39 => ( ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 173.49/173.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 173.49/173.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_zip__obtain__same__length,axiom,
% 173.49/173.39 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 173.49/173.39 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = 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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) )
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_map__of__eqI,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 173.49/173.39 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))))
% 173.49/173.39 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) )
% 173.49/173.39 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__UN__I,axiom,
% 173.49/173.39 ! [V_B_2,T_b,V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( ! [B_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 173.49/173.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_wfP__SUP,axiom,
% 173.49/173.39 ! [T_a,V_r_2,T_b] :
% 173.49/173.39 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 173.49/173.39 => ( ! [B_i,B_j] :
% 173.49/173.39 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 173.49/173.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 173.49/173.39 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_dropWhile__append2,axiom,
% 173.49/173.39 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 173.49/173.39 ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__all2__all__nthI,axiom,
% 173.49/173.39 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 173.49/173.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
% 173.49/173.39 => ( ! [B_n] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) )
% 173.49/173.39 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__map__freshness,axiom,
% 173.49/173.39 ! [V_f_2,T_b,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 173.49/173.39 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 173.49/173.39 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_mem__splitI2,axiom,
% 173.49/173.39 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 173.49/173.39 ( ! [B_a,B_b] :
% 173.49/173.39 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_mem__splitE,axiom,
% 173.49/173.39 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),V_p_2)))
% 173.49/173.39 => ~ ! [B_x,B_y] :
% 173.49/173.39 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 173.49/173.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__sorted__distinct__unique,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ? [B_x] :
% 173.49/173.39 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 173.49/173.39 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 173.49/173.39 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 173.49/173.39 & ! [B_y] :
% 173.49/173.39 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 173.49/173.39 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 173.49/173.39 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 173.49/173.39 => B_y = B_x ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_setsum__SucD,axiom,
% 173.49/173.39 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 173.49/173.39 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 173.49/173.39 => ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 & 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))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__mod__eq__lemma,axiom,
% 173.49/173.39 ! [V_y,V_n,V_x] :
% 173.49/173.39 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 173.49/173.39 => ? [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)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_takeWhile__append2,axiom,
% 173.49/173.39 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 173.49/173.39 ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_insort__is__Cons,axiom,
% 173.49/173.39 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_b)
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 173.49/173.39 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_wfI__pf,axiom,
% 173.49/173.39 ! [V_R_2,T_a] :
% 173.49/173.39 ( ! [B_A] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A)))
% 173.49/173.39 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 173.49/173.39 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_filter__eq__Cons__iff,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 173.49/173.39 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
% 173.49/173.39 <=> ? [B_us,B_vs] :
% 173.49/173.39 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs))
% 173.49/173.39 & ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 173.49/173.39 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 & hBOOL(hAPP(V_P_2,V_x_2))
% 173.49/173.39 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Cons__eq__filter__iff,axiom,
% 173.49/173.39 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 173.49/173.39 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)
% 173.49/173.39 <=> ? [B_us,B_vs] :
% 173.49/173.39 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs))
% 173.49/173.39 & ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 173.49/173.39 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 & hBOOL(hAPP(V_P_2,V_x_2))
% 173.49/173.39 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Sigma__mono,axiom,
% 173.49/173.39 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_not__acc__down,axiom,
% 173.49/173.39 ! [V_R_2,V_x_2,T_a] :
% 173.49/173.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 173.49/173.39 => ~ ! [B_z] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_acc_OaccI,axiom,
% 173.49/173.39 ! [V_r_2,V_x_2,T_a] :
% 173.49/173.39 ( ! [B_y] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_fold__image__1,axiom,
% 173.49/173.39 ! [V_f_2,V_S_2,T_a,T_b] :
% 173.49/173.39 ( class_Groups_Ocomm__monoid__mult(T_b)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 173.49/173.39 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 173.49/173.39 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_card_Oneutral,axiom,
% 173.49/173.39 ! [V_A_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 173.49/173.39 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_max__ext_Osimps,axiom,
% 173.49/173.39 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 173.49/173.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 173.49/173.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 173.49/173.39 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 173.49/173.39 & ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 173.49/173.39 => ? [B_xa] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ball__nth,axiom,
% 173.49/173.39 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,B_x)) )
% 173.49/173.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_mod__induct__0,axiom,
% 173.49/173.39 ! [V_i_2,V_P_2,V_p_2] :
% 173.49/173.39 ( ! [B_i] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 173.49/173.39 => ( hBOOL(hAPP(V_P_2,B_i))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 173.49/173.39 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 173.49/173.39 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_sorted_OCons,axiom,
% 173.49/173.39 ! [V_x_2,V_xs_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 173.49/173.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 173.49/173.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_InterI,axiom,
% 173.49/173.39 ! [V_A_2,V_C_2,T_a] :
% 173.49/173.39 ( ! [B_X] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_fold__image__cong,axiom,
% 173.49/173.39 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 173.49/173.39 ( class_Groups_Oab__semigroup__mult(T_b)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.39 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 173.49/173.39 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Min__eqI,axiom,
% 173.49/173.39 ! [V_x_2,V_A_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( ! [B_y] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.49/173.39 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Max__eqI,axiom,
% 173.49/173.39 ! [V_x_2,V_A_2,T_a] :
% 173.49/173.39 ( class_Orderings_Olinorder(T_a)
% 173.49/173.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.39 => ( ! [B_y] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.49/173.39 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_wf__no__infinite__down__chainE,axiom,
% 173.49/173.39 ! [V_f_2,V_r_2,T_a] :
% 173.49/173.39 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.49/173.39 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__length,axiom,
% 173.49/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.49/173.39 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 173.49/173.39 <=> ? [B_n] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__simps_I2_J,axiom,
% 173.49/173.39 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__append,axiom,
% 173.49/173.39 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 173.49/173.39 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 173.49/173.39 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 173.49/173.39 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__rev,axiom,
% 173.49/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.49/173.39 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 173.49/173.39 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__iff,axiom,
% 173.49/173.39 ! [V_xs_2,V_P_2,T_a] :
% 173.49/173.39 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 173.49/173.39 <=> ? [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.39 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_list__ex__simps_I1_J,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 173.49/173.39 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 173.49/173.39 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 173.49/173.39 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_setsum__reindex__cong,axiom,
% 173.49/173.39 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 173.49/173.39 ( class_Groups_Ocomm__monoid__add(T_c)
% 173.49/173.39 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 173.49/173.39 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 173.49/173.39 => ( ! [B_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 173.49/173.39 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 173.49/173.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_scomp__unfold,axiom,
% 173.49/173.39 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_scomp__def,axiom,
% 173.49/173.39 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_scomp__apply,axiom,
% 173.49/173.39 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Pair__scomp,axiom,
% 173.49/173.39 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_scomp__Pair,axiom,
% 173.49/173.39 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ).
% 173.49/173.39
% 173.49/173.39 fof(fact_scomp__scomp,axiom,
% 173.49/173.39 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_iterate_Osimps,axiom,
% 173.49/173.39 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 173.49/173.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.49/173.39 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) )
% 173.49/173.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 173.49/173.39 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,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)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_setsum__ivl__cong,axiom,
% 173.49/173.39 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] :
% 173.49/173.39 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 173.49/173.39 & class_Orderings_Oord(T_a) )
% 173.49/173.39 => ( V_a_2 = V_ca_2
% 173.49/173.39 => ( V_b_2 = V_d_2
% 173.49/173.39 => ( ! [B_x] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 173.49/173.39 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 173.49/173.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) ) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_log_Osimps,axiom,
% 173.49/173.39 ! [V_i,V_b] :
% 173.49/173.39 ( ( ( 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)))
% 173.49/173.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 173.49/173.39 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 173.49/173.39 & ( ~ ( 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)))
% 173.49/173.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 173.49/173.39 => 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(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral,V_i),V_b))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_minus__shift__def,axiom,
% 173.49/173.39 ! [V_r,V_l,V_k] :
% 173.49/173.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 173.49/173.39 => 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) )
% 173.49/173.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 173.49/173.39 => 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) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_inc__shift__def,axiom,
% 173.49/173.39 ! [V_k,V_v] :
% 173.49/173.39 ( ( V_v = V_k
% 173.49/173.39 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 173.49/173.39 & ( V_v != V_k
% 173.49/173.39 => 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)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select,axiom,
% 173.49/173.39 ! [V_s_2,T_a,V_xs_2] :
% 173.49/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__weight__member,axiom,
% 173.49/173.39 ! [V_s_2,V_xs_2,T_a] :
% 173.49/173.39 ( 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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__weigth__select,axiom,
% 173.49/173.39 ! [T_a,V_xs_2] :
% 173.49/173.39 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 173.49/173.39 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__weight__cons__zero,axiom,
% 173.49/173.39 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__weigth__drop__zero,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_pick__member,axiom,
% 173.49/173.39 ! [V_xs_2,T_a,V_i_2] :
% 173.49/173.39 ( 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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_pick_Osimps,axiom,
% 173.49/173.39 ! [V_xs,V_x,T_a,V_i] :
% 173.49/173.39 ( ( 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)))
% 173.49/173.39 => 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) )
% 173.49/173.39 & ( ~ 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)))
% 173.49/173.39 => 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))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_pick__drop__zero,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__weight__def,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,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_a,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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_pick__same,axiom,
% 173.49/173.39 ! [V_xs_2,T_a,V_l_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 173.49/173.39 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),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_a),V_xs_2),V_l_2) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_number__of__code__numeral__def,axiom,
% 173.49/173.39 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) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 173.49/173.39 ! [V_y_2,V_x_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 173.49/173.39 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 173.49/173.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_one__code__numeral__def,axiom,
% 173.49/173.39 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_zero__code__numeral__def,axiom,
% 173.49/173.39 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_times__code__numeral__code,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 173.49/173.39 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 173.49/173.39 ! [V_m_2,V_n_2] :
% 173.49/173.39 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 173.49/173.39 <=> V_n_2 = V_m_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__code__numeral__code,axiom,
% 173.49/173.39 ! [V_m_2,V_n_2] :
% 173.49/173.39 ( 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)))
% 173.49/173.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_plus__code__numeral__code,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__eq__code__numeral__code,axiom,
% 173.49/173.39 ! [V_m_2,V_n_2] :
% 173.49/173.39 ( 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)))
% 173.49/173.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_code__numeral__not__eq__zero,axiom,
% 173.49/173.39 ! [V_i_2] :
% 173.49/173.39 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.49/173.39 <=> 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)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_range,axiom,
% 173.49/173.39 ! [V_s,V_k] :
% 173.49/173.39 ( 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))
% 173.49/173.39 => 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)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_select__def,axiom,
% 173.49/173.39 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,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_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_subtract__code__numeral__code,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_type__definition__code__numeral,axiom,
% 173.49/173.39 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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of__inverse,axiom,
% 173.49/173.39 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 173.49/173.39
% 173.49/173.39 fof(fact_of__nat__nat__of,axiom,
% 173.49/173.39 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of__of__nat,axiom,
% 173.49/173.39 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 173.49/173.39
% 173.49/173.39 fof(fact_times__code__numeral__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of__code,axiom,
% 173.49/173.39 ! [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)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__eq__code__numeral__def,axiom,
% 173.49/173.39 ! [V_m_2,V_n_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 173.49/173.39 <=> 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))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__code__numeral__def,axiom,
% 173.49/173.39 ! [V_m_2,V_n_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 173.49/173.39 <=> 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))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of__number,axiom,
% 173.49/173.39 ! [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) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of,axiom,
% 173.49/173.39 ! [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)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 173.49/173.39 ! [V_l_2,V_k_2] :
% 173.49/173.39 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 173.49/173.39 <=> V_k_2 = V_l_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_code__numeral_Onat__of__inject,axiom,
% 173.49/173.39 ! [V_y_2,V_x_2] :
% 173.49/173.39 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 173.49/173.39 <=> V_x_2 = V_y_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_int__of__def,axiom,
% 173.49/173.39 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) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_nat__of__aux__def,axiom,
% 173.49/173.39 ! [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) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Suc__code__numeral__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_minus__code__numeral__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_of__nat__inverse,axiom,
% 173.49/173.39 ! [V_y_2] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 173.49/173.39 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_plus__code__numeral__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_div__code__numeral__def,axiom,
% 173.49/173.39 ! [V_m,V_n] : hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral,V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_subtract__code__numeral__def,axiom,
% 173.49/173.39 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_minus__code__numeral__code,axiom,
% 173.49/173.39 ! [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) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_mod__code__numeral__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_code__numeral__decr,axiom,
% 173.49/173.39 ! [V_k] :
% 173.49/173.39 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 173.49/173.39 => 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))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 173.49/173.39 ! [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))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__eq,axiom,
% 173.49/173.39 ! [V_n_2,V_m_2] :
% 173.49/173.39 ( 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)))
% 173.49/173.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_wf__trancl,axiom,
% 173.49/173.39 ! [V_r_2,T_a] :
% 173.49/173.39 ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.49/173.39 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_less__than__def,axiom,
% 173.49/173.39 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_acyclic__def,axiom,
% 173.49/173.39 ! [V_r_2,T_a] :
% 173.49/173.39 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 173.49/173.39 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl_Or__into__trancl,axiom,
% 173.49/173.39 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__subset__Field2,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_r__into__trancl_H,axiom,
% 173.49/173.39 ! [V_r_2,V_p_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__empty,axiom,
% 173.49/173.39 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__domain,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__range,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_finite__trancl,axiom,
% 173.49/173.39 ! [V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_r__r__into__trancl,axiom,
% 173.49/173.39 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_R_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__into__trancl2,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__trans,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__mono,axiom,
% 173.49/173.39 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__unfold,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__subset__Sigma,axiom,
% 173.49/173.39 ! [V_A_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__Int__subset,axiom,
% 173.49/173.39 ! [V_s_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__insert,axiom,
% 173.49/173.39 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_reflcl__set__eq,axiom,
% 173.49/173.39 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 173.49/173.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_r__into__rtrancl,axiom,
% 173.49/173.39 ! [V_r_2,V_p_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 173.49/173.39 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_IdI,axiom,
% 173.49/173.39 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__into__rtrancl,axiom,
% 173.49/173.39 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_listrel__rtrancl__refl,axiom,
% 173.49/173.39 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__unfold__left,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__unfold__right,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__reflcl,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_reflcl__trancl,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__trancl__absorb,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__rtrancl__absorb,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__trancl__trancl,axiom,
% 173.49/173.39 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_trancl__rtrancl__trancl,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__into__trancl1,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtranclD,axiom,
% 173.49/173.39 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.39 => ( V_a_2 = V_b_2
% 173.49/173.39 | ( V_a_2 != V_b_2
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__into__trancl2,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__eq__or__trancl,axiom,
% 173.49/173.39 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.39 <=> ( V_x_2 = V_y_2
% 173.49/173.39 | ( V_x_2 != V_y_2
% 173.49/173.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__trans,axiom,
% 173.49/173.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__mono,axiom,
% 173.49/173.39 ! [V_s_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__subset,axiom,
% 173.49/173.39 ! [V_S_2,V_R_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.39 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__subset__rtrancl,axiom,
% 173.49/173.39 ! [V_s_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__Un__subset,axiom,
% 173.49/173.39 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Image__closed__trancl,axiom,
% 173.49/173.39 ! [V_X_2,V_r_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2))
% 173.49/173.39 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__Int__subset,axiom,
% 173.49/173.39 ! [V_r_2,V_s_2,T_a] :
% 173.49/173.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2))
% 173.49/173.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__idemp,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__r__diff__Id,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__reflcl__absorb,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__Un__rtrancl,axiom,
% 173.49/173.39 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__reflcl,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__idemp__self__comp,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_r__comp__rtrancl__eq,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__unfold,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Domain__rtrancl,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_Range__rtrancl,axiom,
% 173.49/173.39 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_in__rtrancl__UnI,axiom,
% 173.49/173.39 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 173.49/173.39 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.39 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 173.49/173.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_rtrancl__empty,axiom,
% 173.49/173.39 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ).
% 173.49/173.39
% 173.49/173.39 fof(fact_refl__rtrancl,axiom,
% 173.49/173.39 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 173.49/173.39
% 173.49/173.40 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Image__Id,axiom,
% 173.49/173.40 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_R__O__Id,axiom,
% 173.49/173.40 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Id__O__R,axiom,
% 173.49/173.40 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Range__Id,axiom,
% 173.49/173.40 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Domain__Id,axiom,
% 173.49/173.40 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_refl__Id,axiom,
% 173.49/173.40 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_pair__in__Id__conv,axiom,
% 173.49/173.40 ! [V_b_2,V_a_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a)))
% 173.49/173.40 <=> V_a_2 = V_b_2 ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_listrel__rtrancl__trans,axiom,
% 173.49/173.40 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 173.49/173.40 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_pair__leq__def,axiom,
% 173.49/173.40 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))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Not__Domain__rtrancl,axiom,
% 173.49/173.40 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.40 <=> V_x_2 = V_y_2 ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_acc__downwards__aux,axiom,
% 173.49/173.40 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_acc__downwards,axiom,
% 173.49/173.40 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_wf__insert,axiom,
% 173.49/173.40 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 173.49/173.40 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
% 173.49/173.40 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 173.49/173.40 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 173.49/173.40 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 173.49/173.40 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 173.49/173.40 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_acyclic__insert,axiom,
% 173.49/173.40 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 173.49/173.40 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
% 173.49/173.40 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 173.49/173.40 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 173.49/173.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 173.49/173.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_refl__reflcl,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Id__def,axiom,
% 173.49/173.40 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_irrefl__diff__Id,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_pred__nat__trancl__eq__le,axiom,
% 173.49/173.40 ! [V_n_2,V_m_2] :
% 173.49/173.40 ( 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)))
% 173.49/173.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_trancl__subset__Sigma__aux,axiom,
% 173.49/173.40 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 173.49/173.40 => ( V_a_2 = V_b_2
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_irrefl__tranclI,axiom,
% 173.49/173.40 ! [V_x_2,V_r_2,T_a] :
% 173.49/173.40 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 173.49/173.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_sequence__trans,axiom,
% 173.49/173.40 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 173.49/173.40 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__converseI,axiom,
% 173.49/173.40 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__converseD,axiom,
% 173.49/173.40 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__Id,axiom,
% 173.49/173.40 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_in__listrel1__converse,axiom,
% 173.49/173.40 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 173.49/173.40 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__iff,axiom,
% 173.49/173.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 173.49/173.40 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converseI,axiom,
% 173.49/173.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converseD,axiom,
% 173.49/173.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__inv__image,axiom,
% 173.49/173.40 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__Int,axiom,
% 173.49/173.40 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Range__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Domain__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Range__def,axiom,
% 173.49/173.40 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_finite__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 173.49/173.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_acyclic__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] :
% 173.49/173.40 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 173.49/173.40 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__Id__on,axiom,
% 173.49/173.40 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Field__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__Un,axiom,
% 173.49/173.40 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__rel__comp,axiom,
% 173.49/173.40 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_equiv__comp__eq,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 173.49/173.40 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_refl__on__converse,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 173.49/173.40 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_listrel1__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__INTER,axiom,
% 173.49/173.40 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__UNION,axiom,
% 173.49/173.40 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Image__subset__eq,axiom,
% 173.49/173.40 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2))
% 173.49/173.40 <=> 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)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_trancl__converseI,axiom,
% 173.49/173.40 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_trancl__converseD,axiom,
% 173.49/173.40 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_trancl__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_wf__converse__trancl,axiom,
% 173.49/173.40 ! [V_r_2,T_a] :
% 173.49/173.40 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 173.49/173.40 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_refl__on__comp__subset,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_comp__equivI,axiom,
% 173.49/173.40 ! [V_A_2,V_r_2,T_a] :
% 173.49/173.40 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2
% 173.49/173.40 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 173.49/173.40 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_finite__acyclic__wf__converse,axiom,
% 173.49/173.40 ! [V_r_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 173.49/173.40 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 173.49/173.40 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_converse__def,axiom,
% 173.49/173.40 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),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_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Image__INT__eq,axiom,
% 173.49/173.40 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 173.49/173.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 173.49/173.40 => hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_total__on__diff__Id,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))
% 173.49/173.40 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__Id,axiom,
% 173.49/173.40 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_total__on__converse,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 173.49/173.40 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valuedD,axiom,
% 173.49/173.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2))
% 173.49/173.40 => V_y_2 = V_z_2 ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__def,axiom,
% 173.49/173.40 ! [V_r_2,T_b,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 173.49/173.40 <=> ! [B_x,B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2))
% 173.49/173.40 => ! [B_z] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2))
% 173.49/173.40 => B_y = B_z ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__Id__on,axiom,
% 173.49/173.40 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__rel__comp,axiom,
% 173.49/173.40 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 173.49/173.40 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 173.49/173.40 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_total__on__empty,axiom,
% 173.49/173.40 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__subset,axiom,
% 173.49/173.40 ! [V_s_2,V_r_2,T_b,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 173.49/173.40 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 173.49/173.40 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_total__on__def,axiom,
% 173.49/173.40 ! [V_r_2,V_A_2,T_a] :
% 173.49/173.40 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 173.49/173.40 <=> ! [B_x] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 173.49/173.40 => ! [B_xa] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 173.49/173.40 => ( B_x != B_xa
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__confluent,axiom,
% 173.49/173.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Image__Int__eq,axiom,
% 173.49/173.40 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 173.49/173.40 => hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 173.49/173.40 ! [V_R_2,V_p_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_acyclicI,axiom,
% 173.49/173.40 ! [V_r_2,T_a] :
% 173.49/173.40 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 173.49/173.40 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_single__valued__rel__pow,axiom,
% 173.49/173.40 ! [V_n_2,V_R_2,T_a] :
% 173.49/173.40 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 173.49/173.40 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_comp__funpow,axiom,
% 173.49/173.40 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow_Osimps_I2_J,axiom,
% 173.49/173.40 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow__add,axiom,
% 173.49/173.40 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow__swap1,axiom,
% 173.49/173.40 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_wf__exp,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,T_a] :
% 173.49/173.40 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))
% 173.49/173.40 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow__mult,axiom,
% 173.49/173.40 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_relpow_Osimps_I2_J,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__commute,axiom,
% 173.49/173.40 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__1,axiom,
% 173.49/173.40 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__add,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__0__E,axiom,
% 173.49/173.40 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 173.49/173.40 => V_x_2 = V_y_2 ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__0__I,axiom,
% 173.49/173.40 ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__Suc__I2,axiom,
% 173.49/173.40 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__Suc__I,axiom,
% 173.49/173.40 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow_Osimps_I1_J,axiom,
% 173.49/173.40 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__power,axiom,
% 173.49/173.40 ! [V_R_2,V_p_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.40 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__imp__rtrancl,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_relpow_Osimps_I1_J,axiom,
% 173.49/173.40 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_trancl__power,axiom,
% 173.49/173.40 ! [V_R_2,V_p_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 173.49/173.40 <=> ? [B_n] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 173.49/173.40 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 173.49/173.40 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_funpow__code__def,axiom,
% 173.49/173.40 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__E2,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.49/173.40 => V_x_2 != V_z_2 )
% 173.49/173.40 => ~ ! [B_y,B_m] :
% 173.49/173.40 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 173.49/173.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rotate__def,axiom,
% 173.49/173.40 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__E,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 173.49/173.40 => V_x_2 != V_z_2 )
% 173.49/173.40 => ~ ! [B_y,B_m] :
% 173.49/173.40 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2)))
% 173.49/173.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_pos__not__random__dseq__def,axiom,
% 173.49/173.40 ! [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)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 173.49/173.40 => ( ! [B_x] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
% 173.49/173.40 => ! [B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2))
% 173.49/173.40 => B_y = B_x ) )
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rtrancl__Un__separatorE,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 173.49/173.40 => ( ! [B_x] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
% 173.49/173.40 => ! [B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2))
% 173.49/173.40 => B_x = B_y ) )
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__Suc__E,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 173.49/173.40 => ~ ! [B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 173.49/173.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__Suc__E2,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 173.49/173.40 => ~ ! [B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 173.49/173.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_rel__pow__Suc__D2,axiom,
% 173.49/173.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 173.49/173.40 => ? [B_y] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 173.49/173.40 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_tranclD,axiom,
% 173.49/173.40 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 173.49/173.40 => ? [B_z] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2))
% 173.49/173.40 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_tranclD2,axiom,
% 173.49/173.40 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 173.49/173.40 => ? [B_z] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 173.49/173.40 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_IdE,axiom,
% 173.49/173.40 ! [V_p_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 173.49/173.40 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_in__set__conv__decomp,axiom,
% 173.49/173.40 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.40 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_in__set__conv__decomp__last,axiom,
% 173.49/173.40 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.40 <=> ? [B_ys,B_zs] :
% 173.49/173.40 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs))
% 173.49/173.40 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_in__set__conv__decomp__first,axiom,
% 173.49/173.40 ! [V_xs_2,V_x_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 173.49/173.40 <=> ? [B_ys] :
% 173.49/173.40 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs))
% 173.49/173.40 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 173.49/173.40 ! [V_x_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Orderings_Olinorder(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 173.49/173.40 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_inf__INFI__fold__inf,axiom,
% 173.49/173.40 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 173.49/173.40 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 173.49/173.40 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 173.49/173.40 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 173.49/173.40 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_inf__Inf__fold__inf,axiom,
% 173.49/173.40 ! [V_B_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_min__max_Ofold__inf__insert,axiom,
% 173.49/173.40 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Orderings_Olinorder(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_min__max_Ofold__sup__insert,axiom,
% 173.49/173.40 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Orderings_Olinorder(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__inf__insert,axiom,
% 173.49/173.40 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Lattices_Osemilattice__inf(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_folding_Oeq__fold,axiom,
% 173.49/173.40 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 173.49/173.40 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__image__def,axiom,
% 173.49/173.40 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__empty,axiom,
% 173.49/173.40 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__def,axiom,
% 173.49/173.40 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 173.49/173.40 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
% 173.49/173.40 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_sup__Sup__fold__sup,axiom,
% 173.49/173.40 ! [V_B_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__sup__insert,axiom,
% 173.49/173.40 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Lattices_Osemilattice__sup(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_union__fold__insert,axiom,
% 173.49/173.40 ! [V_B_2,V_A_2,T_a] :
% 173.49/173.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_sup__SUPR__fold__sup,axiom,
% 173.49/173.40 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 173.49/173.40 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 173.49/173.40 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 173.49/173.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_sup__le__fold__sup,axiom,
% 173.49/173.40 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Lattices_Osemilattice__sup(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_fold__inf__le__inf,axiom,
% 173.49/173.40 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Lattices_Osemilattice__inf(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 173.49/173.40 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Orderings_Olinorder(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 173.49/173.40 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 173.49/173.40 ( class_Orderings_Olinorder(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 173.49/173.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ).
% 173.49/173.40
% 173.49/173.40 fof(fact_Sup__fold__sup,axiom,
% 173.49/173.40 ! [V_A_2,T_a] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 173.49/173.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 173.49/173.40 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ).
% 173.49/173.40
% 173.49/173.40 %----Arity declarations (220)
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 173.49/173.40 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Obounded__lattice(T_1)
% 173.49/173.40 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 173.49/173.40 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Obounded__lattice(T_1)
% 173.49/173.40 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Obounded__lattice(T_1)
% 173.49/173.40 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Olattice(T_1)
% 173.49/173.40 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Olattice(T_1)
% 173.49/173.40 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Odistrib__lattice(T_1)
% 173.49/173.40 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Oboolean__algebra(T_1)
% 173.49/173.40 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Orderings_Opreorder,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Orderings_Opreorder(T_1)
% 173.49/173.40 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Finite__Set_Ofinite(T_2)
% 173.49/173.40 & class_Finite__Set_Ofinite(T_1) )
% 173.49/173.40 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Lattices_Olattice,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Lattices_Olattice(T_1)
% 173.49/173.40 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Orderings_Oorder,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Orderings_Oorder(T_1)
% 173.49/173.40 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Orderings_Otop,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Orderings_Otop(T_1)
% 173.49/173.40 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Orderings_Oord,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Orderings_Oord(T_1)
% 173.49/173.40 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Orderings_Obot,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Orderings_Obot(T_1)
% 173.49/173.40 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Groups_Ouminus,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Groups_Ouminus(T_1)
% 173.49/173.40 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Groups_Ominus,axiom,
% 173.49/173.40 ! [T_2,T_1] :
% 173.49/173.40 ( class_Groups_Ominus(T_1)
% 173.49/173.40 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Enum_Oenum(T_2)
% 173.49/173.40 & class_HOL_Oequal(T_1) )
% 173.49/173.40 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_fun__Enum_Oenum,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Enum_Oenum(T_2)
% 173.49/173.40 & class_Enum_Oenum(T_1) )
% 173.49/173.40 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Com_Ocom) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 173.49/173.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 173.49/173.40 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 173.49/173.40 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 173.49/173.40 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 173.49/173.40 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 173.49/173.40 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 173.49/173.40 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 173.49/173.40 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 173.49/173.40 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 173.49/173.40 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 173.49/173.40 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 173.49/173.40 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 173.49/173.40 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 173.49/173.40 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 173.49/173.40 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 173.49/173.40 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 173.49/173.40 class_Orderings_Opreorder(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 173.49/173.40 class_Orderings_Olinorder(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 173.49/173.40 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 173.49/173.40 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 173.49/173.40 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 173.49/173.40 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 173.49/173.40 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 173.49/173.40 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 173.49/173.40 class_Lattices_Olattice(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 173.49/173.40 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 173.49/173.40 class_Divides_Oring__div(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 173.49/173.40 class_Rings_Omult__zero(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 173.49/173.40 class_Orderings_Oorder(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 173.49/173.40 class_Int_Oring__char__0(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 173.49/173.40 class_Int_Onumber__ring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 173.49/173.40 class_Rings_Osemiring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 173.49/173.40 class_Orderings_Oord(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 173.49/173.40 class_Groups_Ouminus(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 173.49/173.40 class_Groups_Osgn__if(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 173.49/173.40 class_Groups_Oabs__if(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 173.49/173.40 class_Rings_Oring__1(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 173.49/173.40 class_Groups_Ominus(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Power_Opower,axiom,
% 173.49/173.40 class_Power_Opower(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 173.49/173.40 class_Groups_Ozero(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oring,axiom,
% 173.49/173.40 class_Rings_Oring(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 173.49/173.40 class_Rings_Oidom(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Int_Onumber,axiom,
% 173.49/173.40 class_Int_Onumber(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__Groups_Oone,axiom,
% 173.49/173.40 class_Groups_Oone(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Int_Oint) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 173.49/173.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 173.49/173.40 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 173.49/173.40 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 173.49/173.40 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 173.49/173.40 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 173.49/173.40 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 173.49/173.40 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 173.49/173.40 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 173.49/173.40 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 173.49/173.40 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 173.49/173.40 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 173.49/173.40 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 173.49/173.40 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 173.49/173.40 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 173.49/173.40 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 173.49/173.40 class_Lattices_Olattice(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 173.49/173.40 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 173.49/173.40 class_Orderings_Oorder(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 173.49/173.40 class_Rings_Osemiring(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 173.49/173.40 class_Orderings_Oord(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 173.49/173.40 class_Orderings_Obot(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 173.49/173.40 class_Groups_Ominus(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Power_Opower,axiom,
% 173.49/173.40 class_Power_Opower(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 173.49/173.40 class_Groups_Ozero(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 173.49/173.40 class_Int_Onumber(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 173.49/173.40 class_Groups_Oone(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Nat_Onat) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 173.49/173.40 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 173.49/173.40 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 173.49/173.40 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 173.49/173.40 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 173.49/173.40 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 173.49/173.40 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 173.49/173.40 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 173.49/173.40 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 173.49/173.40 class_Lattices_Olattice(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 173.49/173.40 class_Orderings_Oorder(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 173.49/173.40 class_Orderings_Otop(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 173.49/173.40 class_Orderings_Oord(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 173.49/173.40 class_Orderings_Obot(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 173.49/173.40 class_Groups_Ouminus(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 173.49/173.40 class_Groups_Ominus(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 173.49/173.40 class_Enum_Oenum(tc_HOL_Obool) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Com_Ostate) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Com_Ovname) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_List__Olist__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Finite__Set_Ofinite(T_2)
% 173.49/173.40 & class_Finite__Set_Ofinite(T_1) )
% 173.49/173.40 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_sum__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_sum__Enum_Oenum,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Enum_Oenum(T_2)
% 173.49/173.40 & class_Enum_Oenum(T_1) )
% 173.49/173.40 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 173.49/173.40 ! [T_1] :
% 173.49/173.40 ( class_Finite__Set_Ofinite(T_1)
% 173.49/173.40 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 173.49/173.40 ! [T_1] :
% 173.49/173.40 ( class_Enum_Oenum(T_1)
% 173.49/173.40 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Finite__Set_Ofinite(T_2)
% 173.49/173.40 & class_Finite__Set_Ofinite(T_1) )
% 173.49/173.40 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_prod__Smallcheck_Osmall,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Smallcheck_Osmall(T_2)
% 173.49/173.40 & class_Smallcheck_Osmall(T_1) )
% 173.49/173.40 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_prod__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_prod__Enum_Oenum,axiom,
% 173.49/173.40 ! [T_1,T_2] :
% 173.49/173.40 ( ( class_Enum_Oenum(T_2)
% 173.49/173.40 & class_Enum_Oenum(T_1) )
% 173.49/173.40 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 173.49/173.40 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 173.49/173.40 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 173.49/173.40 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 173.49/173.40 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 173.49/173.40 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 173.49/173.40 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 173.49/173.40 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 173.49/173.40 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 173.49/173.40 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 173.49/173.40 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 173.49/173.40 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 173.49/173.40 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 173.49/173.40 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 173.49/173.40 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 173.49/173.40 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 173.49/173.40 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 173.49/173.40 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 173.49/173.40 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 173.49/173.40 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 173.49/173.40 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 173.49/173.40 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 173.49/173.40 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 173.49/173.40 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 173.49/173.40 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 173.49/173.40 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 173.49/173.40 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 173.49/173.40 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 173.49/173.40 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 173.49/173.40 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 173.49/173.40 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 173.49/173.40
% 173.49/173.40 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 173.49/173.40 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 173.49/173.40
% 173.49/173.40 %----Helper facts (20)
% 173.49/173.40 fof(help_c__COMBI__1,axiom,
% 173.49/173.40 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__COMBK__1,axiom,
% 173.49/173.40 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__COMBB__1,axiom,
% 173.49/173.40 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__COMBC__1,axiom,
% 173.49/173.40 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__COMBS__1,axiom,
% 173.49/173.40 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fequal__1,axiom,
% 173.49/173.40 ! [V_y_2,V_x_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 173.49/173.40 | V_x_2 = V_y_2 ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fequal__2,axiom,
% 173.49/173.40 ! [V_y_2,V_x_2] :
% 173.49/173.40 ( V_x_2 != V_y_2
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fFalse__1,axiom,
% 173.49/173.40 ~ hBOOL(c_fFalse) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fTrue__1,axiom,
% 173.49/173.40 hBOOL(c_fTrue) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fNot__1,axiom,
% 173.49/173.40 ! [V_P_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 173.49/173.40 | ~ hBOOL(V_P_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fNot__2,axiom,
% 173.49/173.40 ! [V_P_2] :
% 173.49/173.40 ( ~ ~ hBOOL(V_P_2)
% 173.49/173.40 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fconj__1,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(V_P_2)
% 173.49/173.40 | ~ hBOOL(V_Q_2)
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fconj__2,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 173.49/173.40 | hBOOL(V_P_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fconj__3,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 173.49/173.40 | hBOOL(V_Q_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fdisj__1,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(V_P_2)
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fdisj__2,axiom,
% 173.49/173.40 ! [V_P_2,V_Q_2] :
% 173.49/173.40 ( ~ hBOOL(V_Q_2)
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fdisj__3,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 173.49/173.40 | hBOOL(V_P_2)
% 173.49/173.40 | hBOOL(V_Q_2) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fimplies__1,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( hBOOL(V_P_2)
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fimplies__2,axiom,
% 173.49/173.40 ! [V_P_2,V_Q_2] :
% 173.49/173.40 ( ~ hBOOL(V_Q_2)
% 173.49/173.40 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 173.49/173.40
% 173.49/173.40 fof(help_c__fimplies__3,axiom,
% 173.49/173.40 ! [V_Q_2,V_P_2] :
% 173.49/173.40 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 173.49/173.40 | ~ hBOOL(V_P_2)
% 173.49/173.40 | hBOOL(V_Q_2) ) ).
% 173.49/173.40
% 173.49/173.40 %----Conjectures (3)
% 173.49/173.40 fof(conj_0,hypothesis,
% 173.49/173.40 c_Hoare__Mirabelle_Ostate__not__singleton ).
% 173.49/173.40
% 173.49/173.40 fof(conj_1,hypothesis,
% 173.49/173.40 ! [B_Z_H] :
% 173.49/173.40 ( ! [B_s1] :
% 173.49/173.40 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),B_s1))
% 173.49/173.40 => B_Z_H = B_s1 )
% 173.49/173.40 => B_Z_H = v_s_H ) ).
% 173.49/173.40
% 173.49/173.40 fof(conj_2,conjecture,
% 173.49/173.40 hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)) ).
% 173.49/173.40
% 173.49/173.40 %------------------------------------------------------------------------------
% 173.49/173.40 %-------------------------------------------
% 173.49/173.40 % Proof found
% 173.49/173.40 % SZS status Theorem for theBenchmark
% 173.49/173.40 % SZS output start Proof
% 173.49/173.40 %ClaNum:10096(EqnAxiom:2803)
% 173.49/173.40 %VarNum:70177(SingletonVarNum:20591)
% 173.49/173.40 %MaxLitNum:8
% 173.49/173.40 %MaxfuncDepth:15
% 173.49/173.40 %SharedTerms:1102
% 173.49/173.40 %goalClause: 4460
% 173.49/173.40 %singleGoalClaCount:1
% 173.49/173.40 [2804]P1(a5000)
% 173.49/173.40 [2808]P22(a188)
% 173.49/173.40 [2809]P23(a852)
% 173.49/173.40 [2810]P23(a1)
% 173.49/173.40 [2811]P23(a113)
% 173.49/173.40 [2812]P24(a852)
% 173.49/173.40 [2813]P24(a845)
% 173.49/173.40 [2814]P101(a852)
% 173.49/173.40 [2815]P25(a852)
% 173.49/173.40 [2816]P25(a1)
% 173.49/173.40 [2817]P25(a113)
% 173.49/173.40 [2818]P107(a852)
% 173.49/173.40 [2819]P107(a1)
% 173.49/173.40 [2820]P107(a113)
% 173.49/173.40 [2821]P26(a852)
% 173.49/173.40 [2822]P26(a1)
% 173.49/173.40 [2823]P26(a113)
% 173.49/173.40 [2824]P70(a1)
% 173.49/173.40 [2825]P136(a852)
% 173.49/173.40 [2826]P136(a1)
% 173.49/173.40 [2827]P75(a852)
% 173.49/173.40 [2828]P75(a1)
% 173.49/173.40 [2829]P75(a113)
% 173.49/173.40 [2830]P27(a852)
% 173.49/173.40 [2831]P27(a1)
% 173.49/173.40 [2832]P27(a113)
% 173.49/173.40 [2833]P28(a852)
% 173.49/173.40 [2834]P28(a1)
% 173.49/173.40 [2835]P28(a113)
% 173.49/173.40 [2836]P29(a852)
% 173.49/173.40 [2837]P29(a1)
% 173.49/173.40 [2838]P29(a113)
% 173.49/173.40 [2839]P30(a1)
% 173.49/173.40 [2840]P71(a1)
% 173.49/173.40 [2841]P73(a852)
% 173.49/173.40 [2842]P73(a845)
% 173.49/173.40 [2843]P73(a1)
% 173.49/173.40 [2844]P73(a113)
% 173.49/173.40 [2845]P76(a1)
% 173.49/173.40 [2846]P79(a845)
% 173.49/173.40 [2847]P79(a1)
% 173.49/173.40 [2848]P87(a852)
% 173.49/173.40 [2849]P87(a845)
% 173.49/173.40 [2850]P87(a1)
% 173.49/173.40 [2851]P88(a845)
% 173.49/173.40 [2852]P98(a852)
% 173.49/173.40 [2853]P98(a845)
% 173.49/173.40 [2854]P98(a1)
% 173.49/173.40 [2855]P94(a845)
% 173.49/173.40 [2856]P108(a1)
% 173.49/173.40 [2857]P89(a1)
% 173.49/173.40 [2858]P77(a852)
% 173.49/173.40 [2859]P77(a1)
% 173.49/173.40 [2860]P77(a113)
% 173.49/173.40 [2861]P99(a852)
% 173.49/173.40 [2862]P99(a845)
% 173.49/173.40 [2863]P99(a1)
% 173.49/173.40 [2864]P111(a1)
% 173.49/173.40 [2865]P96(a852)
% 173.49/173.40 [2866]P96(a845)
% 173.49/173.40 [2867]P96(a1)
% 173.49/173.40 [2868]P137(a852)
% 173.49/173.40 [2869]P137(a1)
% 173.49/173.40 [2870]P137(a113)
% 173.49/173.40 [2871]P112(a1)
% 173.49/173.40 [2872]P102(a852)
% 173.49/173.40 [2873]P102(a845)
% 173.49/173.40 [2874]P102(a1)
% 173.49/173.40 [2875]P102(a113)
% 173.49/173.40 [2876]P117(a852)
% 173.49/173.40 [2877]P117(a1)
% 173.49/173.40 [2878]P117(a113)
% 173.49/173.40 [2879]P110(a852)
% 173.49/173.40 [2880]P110(a1)
% 173.49/173.40 [2881]P110(a113)
% 173.49/173.40 [2882]P132(a852)
% 173.49/173.40 [2883]P132(a1)
% 173.49/173.40 [2884]P132(a113)
% 173.49/173.40 [2885]P120(a1)
% 173.49/173.40 [2886]P113(a1)
% 173.49/173.40 [2887]P106(a845)
% 173.49/173.40 [2888]P103(a852)
% 173.49/173.40 [2889]P103(a1)
% 173.49/173.40 [2890]P103(a113)
% 173.49/173.40 [2891]P104(a852)
% 173.49/173.40 [2892]P104(a845)
% 173.49/173.40 [2893]P104(a1)
% 173.49/173.40 [2894]P104(a113)
% 173.49/173.40 [2895]P105(a852)
% 173.49/173.40 [2896]P105(a845)
% 173.49/173.40 [2897]P105(a1)
% 173.49/173.40 [2898]P105(a113)
% 173.49/173.40 [2899]P100(a852)
% 173.49/173.40 [2900]P100(a1)
% 173.49/173.40 [2901]P100(a113)
% 173.49/173.40 [2902]P121(a852)
% 173.49/173.40 [2903]P121(a1)
% 173.49/173.40 [2904]P121(a113)
% 173.49/173.40 [2905]P128(a1)
% 173.49/173.40 [2906]P122(a852)
% 173.49/173.40 [2907]P122(a1)
% 173.49/173.40 [2908]P122(a113)
% 173.49/173.40 [2909]P123(a852)
% 173.49/173.40 [2910]P123(a1)
% 173.49/173.40 [2911]P123(a113)
% 173.49/173.40 [2912]P130(a852)
% 173.49/173.40 [2913]P130(a1)
% 173.49/173.40 [2914]P130(a113)
% 173.49/173.40 [2915]P118(a1)
% 173.49/173.40 [2916]P129(a852)
% 173.49/173.40 [2917]P129(a1)
% 173.49/173.40 [2918]P129(a113)
% 173.49/173.40 [2919]P116(a852)
% 173.49/173.40 [2920]P116(a1)
% 173.49/173.40 [2921]P116(a113)
% 173.49/173.40 [2922]P119(a1)
% 173.49/173.40 [2923]P68(a852)
% 173.49/173.40 [2924]P68(a1)
% 173.49/173.40 [2925]P68(a113)
% 173.49/173.40 [2926]P80(a852)
% 173.49/173.40 [2927]P80(a1)
% 173.49/173.40 [2928]P80(a113)
% 173.49/173.40 [2929]P126(a852)
% 173.49/173.40 [2930]P126(a1)
% 173.49/173.40 [2931]P126(a113)
% 173.49/173.40 [2932]P133(a1)
% 173.49/173.40 [2933]P127(a852)
% 173.49/173.40 [2934]P127(a1)
% 173.49/173.40 [2935]P127(a113)
% 173.49/173.40 [2936]P124(a1)
% 173.49/173.40 [2937]P84(a852)
% 173.49/173.40 [2938]P84(a1)
% 173.49/173.40 [2939]P84(a113)
% 173.49/173.40 [2940]P125(a1)
% 173.49/173.40 [2941]P81(a852)
% 173.49/173.40 [2942]P81(a1)
% 173.49/173.40 [2943]P81(a113)
% 173.49/173.40 [2944]P82(a852)
% 173.49/173.40 [2945]P82(a1)
% 173.49/173.40 [2946]P82(a113)
% 173.49/173.40 [2947]P78(a852)
% 173.49/173.40 [2948]P78(a1)
% 173.49/173.40 [2949]P78(a113)
% 173.49/173.40 [2950]P72(a852)
% 173.49/173.40 [2951]P72(a1)
% 173.49/173.40 [2952]P72(a113)
% 173.49/173.40 [2953]P134(a1)
% 173.49/173.40 [2954]P97(a845)
% 173.49/173.40 [2955]P85(a1)
% 173.49/173.40 [2956]P83(a1)
% 173.49/173.40 [2957]P131(a1)
% 173.49/173.40 [2958]P69(a1)
% 173.49/173.40 [2959]P90(a1)
% 173.49/173.40 [2960]P91(a852)
% 173.49/173.40 [2961]P91(a1)
% 173.49/173.40 [2962]P91(a113)
% 173.49/173.40 [2963]P31(a845)
% 173.49/173.40 [2964]P109(a852)
% 173.49/173.40 [2965]P109(a1)
% 173.49/173.40 [2966]P109(a113)
% 173.49/173.40 [2967]P135(a852)
% 173.49/173.40 [2968]P135(a1)
% 173.49/173.40 [2969]P135(a113)
% 173.49/173.40 [2970]P60(a852)
% 173.49/173.40 [2971]P60(a1)
% 173.49/173.40 [2972]P60(a113)
% 173.49/173.40 [2973]P61(a1)
% 173.49/173.40 [2974]P138(a1)
% 173.49/173.40 [2975]P138(a855)
% 173.49/173.40 [2976]P62(a845)
% 173.49/173.40 [2977]P62(a855)
% 173.49/173.40 [2978]P74(a852)
% 173.49/173.40 [2979]P74(a1)
% 173.49/173.40 [2980]P74(a113)
% 173.49/173.40 [2981]P86(a852)
% 173.49/173.40 [2982]P86(a1)
% 173.49/173.40 [2983]P86(a113)
% 173.49/173.40 [2984]P63(a845)
% 173.49/173.40 [2985]P63(a855)
% 173.49/173.40 [2986]P92(a846)
% 173.49/173.40 [2987]P92(a852)
% 173.49/173.40 [2988]P92(a847)
% 173.49/173.40 [2989]P92(a845)
% 173.49/173.40 [2990]P92(a850)
% 173.49/173.40 [2991]P92(a1)
% 173.49/173.40 [2992]P92(a308)
% 173.49/173.40 [2993]P92(a113)
% 173.49/173.40 [2994]P92(a855)
% 173.49/173.40 [2995]P95(a845)
% 173.49/173.40 [3011]P41(a852,a232)
% 173.49/173.40 [3012]P41(a852,a302)
% 173.49/173.40 [3098]P49(a852,a852,a126)
% 173.49/173.40 [4378]~E(a111,a92)
% 173.49/173.40 [4379]~P22(a224)
% 173.49/173.40 [2805]E(f2(a1),a92)
% 173.49/173.40 [2806]E(f114(a113),a3)
% 173.49/173.40 [2807]E(f21(a113),a22)
% 173.49/173.40 [2996]E(f189(a852),f2(a852))
% 173.49/173.40 [2997]E(f34(a23),f2(a852))
% 173.49/173.40 [2998]E(f93(a224),f2(a852))
% 173.49/173.40 [2999]E(f93(a188),f2(a852))
% 173.49/173.40 [3000]E(f115(a852),f225(a852))
% 173.49/173.40 [3001]E(f124(a852),f226(a852))
% 173.49/173.40 [3002]E(f116(a1),f39(a1))
% 173.49/173.40 [3003]P32(f2(a1))
% 173.49/173.40 [3004]P32(f87(a1))
% 173.49/173.40 [3051]P22(f312(a24,a23))
% 173.49/173.40 [3066]P41(f859(a852,a852),a45)
% 173.49/173.40 [3414]E(f304(a852,a852,a232,a232),a45)
% 173.49/173.40 [4380]~E(f87(a1),f2(a1))
% 173.49/173.40 [3005]E(f125(f2(a852)),f2(a852))
% 173.49/173.40 [3006]E(f4(f2(a113)),f2(a852))
% 173.49/173.40 [3016]E(f312(f88(a1),a92),a92)
% 173.49/173.40 [3020]E(f312(a3,f2(a852)),f2(a113))
% 173.49/173.40 [3021]E(f312(a126,f2(a852)),f87(a852))
% 173.49/173.40 [3022]E(f312(a118,f87(a1)),f87(a852))
% 173.49/173.40 [3023]E(f312(a3,f87(a852)),f87(a113))
% 173.49/173.40 [3025]E(f312(f117(a1),a92),f2(a1))
% 173.49/173.40 [3026]E(f312(f117(a113),a92),f2(a113))
% 173.49/173.40 [3027]E(f312(a118,f2(a1)),f2(a852))
% 173.49/173.40 [3028]E(f312(f190(a846),a23),f2(a852))
% 173.49/173.40 [3029]E(f312(f190(a845),a224),f2(a852))
% 173.49/173.40 [3030]E(f312(f190(a845),a188),f2(a852))
% 173.49/173.40 [3031]E(f312(f117(a852),a92),f2(a852))
% 173.49/173.40 [3036]E(f312(f88(a1),f87(a1)),a111)
% 173.49/173.40 [3044]E(f312(f190(a113),f2(a113)),f2(a852))
% 173.49/173.40 [3045]E(f312(f88(a1),f2(a1)),f2(a1))
% 173.49/173.40 [3046]E(f312(f114(a1),f2(a852)),f2(a1))
% 173.49/173.40 [3047]E(f312(f114(a1),f87(a852)),f87(a1))
% 173.49/173.40 [3061]E(f312(a118,f87(a1)),f312(a126,f2(a852)))
% 173.49/173.40 [3063]E(f312(f173(a848,a846),a29),a30)
% 173.49/173.40 [3064]E(f303(f859(a852,a852),a45),a46)
% 173.49/173.40 [3065]E(f305(f859(a852,a852),a45),a77)
% 173.49/173.40 [3088]E(f312(f234(a852),f2(a852)),f235(f860(a852,a845)))
% 173.49/173.40 [3089]E(f312(f279(a852),f2(a852)),f189(f860(a852,a845)))
% 173.49/173.40 [3100]P43(f189(f860(a1,a845)))
% 173.49/173.40 [3132]E(f312(f312(f21(a113),f2(a113)),f87(a113)),f2(a113))
% 173.49/173.40 [3205]P22(f312(f312(f228(a1),a111),f2(a1)))
% 173.49/173.40 [3230]P22(f312(f312(f228(a1),f2(a1)),f87(a1)))
% 173.49/173.40 [3232]P22(f312(f312(f227(a1),f2(a1)),f87(a1)))
% 173.49/173.40 [3407]P22(f312(f70(a848),f179(a848,a846,a30)))
% 173.49/173.40 [3444]E(f312(f312(f267(a852,a852,a852),a302),f287(a852,a302)),a232)
% 173.49/173.40 [3486]P44(a1,a852,a118,f312(f227(a1),f2(a1)))
% 173.49/173.40 [3490]E(f312(f312(f50(a852,f860(a852,a845)),f235(f860(a852,a845))),f281(a852)),f235(f860(a852,a845)))
% 173.49/173.40 [3491]E(f312(f312(f50(a852,f860(a852,a845)),f235(f860(a852,a845))),f234(a852)),f235(f860(a852,a845)))
% 173.49/173.40 [3492]E(f312(f312(f50(a852,f860(a852,a845)),f235(f860(a852,a845))),f279(a852)),f235(f860(a852,a845)))
% 173.49/173.40 [3493]E(f312(f312(f51(a852,f860(a852,a845)),f235(f860(a852,a845))),f280(a852)),f189(f860(a852,a845)))
% 173.49/173.40 [3507]P19(a852,a1,f114(a1),f235(f860(a852,a845)))
% 173.49/173.40 [3648]E(f312(f82(a852,a113,a1,a3),a118),f117(a113))
% 173.49/173.40 [3873]P56(a113,a852,a19,a3,f235(f860(a852,a845)))
% 173.49/173.40 [3882]P56(a1,f860(f859(a852,a852),a845),a121,a98,a112)
% 173.49/173.40 [4143]E(f250(a1,a1,a1,a1,f39(a1),f88(a1)),a59)
% 173.49/173.40 [4413]~E(f312(f117(a1),a111),f312(f117(a1),a92))
% 173.49/173.40 [4414]~P22(f312(a194,f2(a1)))
% 173.49/173.40 [4415]~P22(f312(a194,f87(a1)))
% 173.49/173.40 [4469]~P22(f312(f312(f228(a1),a92),f2(a1)))
% 173.49/173.40 [3081]E(f312(f312(f21(a1),a111),a111),a92)
% 173.49/173.40 [3097]E(f312(f114(a1),f312(a126,f2(a852))),f87(a1))
% 173.49/173.40 [3156]E(f312(f53(a855),f235(f860(a855,a845))),f87(a852))
% 173.49/173.40 [3180]P22(f312(a194,f312(f117(a1),a111)))
% 173.49/173.40 [3181]P22(f312(f312(f228(a1),a111),a92))
% 173.49/173.40 [3183]P22(f312(f312(f227(a1),a111),a92))
% 173.49/173.40 [3242]E(f312(f312(f289(a852),f2(a852)),f189(f860(a852,a845))),f312(f281(a852),f2(a852)))
% 173.49/173.40 [3297]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),a92)))
% 173.49/173.40 [3311]E(f312(f290(a852,a852,a126),f235(f860(a852,a845))),f312(f280(a852),f2(a852)))
% 173.49/173.40 [3349]P3(f859(a852,a852),f235(f860(f859(a852,a852),a845)),a122)
% 173.49/173.40 [3656]E(f312(f82(a852,a1,a113,f114(a1)),a19),a20)
% 173.49/173.40 [3714]P41(a852,f312(f233(f859(a852,a852)),f312(f249(a852,a852,a845),f228(a852))))
% 173.49/173.40 [4459]~P22(f312(a194,f312(f117(a1),a92)))
% 173.49/173.40 [4460]~P22(f312(f312(f195(a861),a862),a863))
% 173.49/173.40 [4461]~P22(f312(f312(f228(a1),a92),a92))
% 173.49/173.40 [4462]~P22(f312(f312(f228(a1),a92),a111))
% 173.49/173.40 [4463]~P22(f312(f312(f228(a1),a111),a111))
% 173.49/173.40 [4464]~P22(f312(f312(f227(a1),a92),a111))
% 173.49/173.40 [4479]~P22(f312(f70(a852),f235(f860(a852,a845))))
% 173.49/173.40 [4480]~P22(f312(f70(a1),f235(f860(a1,a845))))
% 173.49/173.40 [4311]E(f312(f249(a1,a1,a845),f312(f312(f8(f860(a1,a845),f860(a1,a845),a1),f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f228(a1),f2(a1))))),f312(f312(f7(a1,a1,f860(a1,a845)),f312(f312(f8(f860(a1,f860(a1,a845)),f860(a1,f860(a1,a845)),a1),f7(a1,a1,a845)),f312(f312(f8(f860(a1,a1),f860(a1,f860(a1,a845)),a1),f312(f8(a1,f860(a1,a845),a1),a309)),a200))),f87(a1)))),a205)
% 173.49/173.40 [3387]E(f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111),f312(f88(a1),a111))
% 173.49/173.40 [3429]E(f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111),f312(f312(f21(a1),a92),a111))
% 173.49/173.40 [3584]E(f312(f312(f69(f859(a852,a852)),f235(f860(f859(a852,a852),a845))),a122),a112)
% 173.49/173.40 [3612]E(f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a1))
% 173.49/173.40 [3613]E(f312(f117(a113),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a113))
% 173.49/173.40 [3614]E(f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a852))
% 173.49/173.40 [3618]E(f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(a126,f2(a852)))
% 173.49/173.40 [4007]E(f312(f312(f124(f860(f859(f859(a852,a852),f859(a852,a852)),a845)),a45),f287(f859(a852,a852),f189(f860(f859(f859(a852,a852),f859(a852,a852)),a845)))),a79)
% 173.49/173.40 [4077]E(f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),f2(a852)),f2(a852))),f189(f860(f859(a852,a852),a845))))),f2(a1))
% 173.49/173.40 [4078]E(f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),f87(a852)),f2(a852))),f189(f860(f859(a852,a852),a845))))),f87(a1))
% 173.49/173.40 [4094]E(f312(f233(f859(a852,a852)),f312(f249(a852,a852,a845),f312(f312(f8(a852,f860(a852,a845),a852),f312(f7(a852,a852,a845),a309)),a126))),a302)
% 173.49/173.40 [4063]E(f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),f312(a126,f312(a126,f2(a852))))
% 173.49/173.40 [4066]E(f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),f312(f312(f89(a852),f87(a852)),f87(a852)))
% 173.49/173.40 [4067]E(f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),f312(f53(a845),f235(f860(a845,a845))))
% 173.49/173.40 [4129]P32(f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))
% 173.49/173.40 [4203]P20(f860(f859(a852,a852),a845),f312(f312(f239(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845),f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)),a46),a78))
% 173.49/173.40 [4204]P20(f860(f859(a852,a852),a845),f312(f312(f239(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845),f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)),a77),a80))
% 173.49/173.40 [4243]E(f312(f312(f124(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)),f305(f859(a852,a852),a79)),f312(f312(f289(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f189(f860(f859(a852,a852),a845))),f189(f860(f859(a852,a852),a845)))),f189(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)))),a80)
% 173.49/173.40 [4244]E(f312(f312(f124(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)),f303(f859(a852,a852),a79)),f312(f312(f289(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f189(f860(f859(a852,a852),a845))),f189(f860(f859(a852,a852),a845)))),f189(f860(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a845)))),a78)
% 173.49/173.40 [4131]E(f312(a118,f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(a126,f312(a126,f2(a852))))
% 173.49/173.40 [4180]E(f312(f114(a1),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))
% 173.49/173.40 [4215]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.49/173.40 [4216]E(f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111)),f312(a126,f312(a126,f312(a126,f2(a852)))))
% 173.49/173.40 [4257]P32(f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111)))
% 173.49/173.40 [4283]E(f312(f114(a1),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111)))
% 173.49/173.40 [4298]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))))
% 173.49/173.40 [3013]P2(x30131,a309)
% 173.49/173.40 [3415]P19(a852,a852,a126,x34151)
% 173.49/173.40 [3007]P92(f851(x30071))
% 173.49/173.40 [3008]P92(f856(x30081))
% 173.49/173.40 [3009]P92(f853(x30091))
% 173.49/173.40 [3010]P92(f854(x30101))
% 173.49/173.40 [3032]P41(a1,f119(x30321))
% 173.49/173.40 [3033]P41(a1,f120(x30331))
% 173.49/173.40 [3035]P42(x30351,f192(x30351))
% 173.49/173.40 [3085]P41(f860(x30851,a845),f286(x30851))
% 173.49/173.40 [3123]E(f54(a1,x31231,x31231),f2(a1))
% 173.49/173.40 [3177]P11(x31771,f860(x31771,a845),f289(x31771))
% 173.49/173.40 [4384]~E(f312(a27,x43841),a23)
% 173.49/173.40 [4386]~E(f312(a126,x43861),x43861)
% 173.49/173.40 [4398]~E(f312(a126,x43981),f2(a852))
% 173.49/173.40 [3014]E(f42(f40(x30141)),f2(a852))
% 173.49/173.40 [3015]E(f42(f41(x30151)),f2(a852))
% 173.49/173.40 [3017]E(f312(f190(a852),x30171),x30171)
% 173.49/173.40 [3018]E(f312(f117(a1),x30181),x30181)
% 173.49/173.40 [3034]E(f312(a98,f313(x30341)),x30341)
% 173.49/173.40 [3048]E(f128(x30481,f127(x30481)),f127(x30481))
% 173.49/173.40 [3049]E(f148(x30491,f127(x30491)),f127(x30491))
% 173.49/173.40 [3052]E(f312(f190(a850),f40(x30521)),f2(a852))
% 173.49/173.40 [3053]E(f312(f190(a850),f41(x30531)),f2(a852))
% 173.49/173.40 [3054]E(f34(f312(a27,x30541)),f2(a852))
% 173.49/173.40 [3058]E(f312(f164(x30581),f127(x30581)),f127(x30581))
% 173.49/173.40 [3059]E(f312(f167(x30591),f127(x30591)),f127(x30591))
% 173.49/173.40 [3060]E(f312(f165(x30601),f127(x30601)),f127(x30601))
% 173.49/173.40 [3067]E(f312(f117(a1),x30671),f312(f116(a1),x30671))
% 173.49/173.40 [3068]E(f312(a98,f312(a121,x30681)),x30681)
% 173.49/173.40 [3070]E(f312(a3,f312(a19,x30701)),x30701)
% 173.49/173.40 [3071]E(f312(a19,f312(a3,x30711)),x30711)
% 173.49/173.40 [3072]P32(f312(f114(a1),x30721))
% 173.49/173.40 [3077]E(f312(f190(f856(x30771)),f192(x30771)),f2(a852))
% 173.49/173.40 [3078]E(f312(f190(f853(x30781)),f127(x30781)),f2(a852))
% 173.49/173.40 [3083]E(f312(f190(a846),f312(a27,x30831)),f2(a852))
% 173.49/173.40 [3084]E(f312(f47(a1,x30841),f2(a1)),f2(a1))
% 173.49/173.40 [3095]E(f218(x30951,f192(x30951)),f189(f860(x30951,a845)))
% 173.49/173.40 [3103]E(f312(f312(f89(a852),x31031),f2(a852)),x31031)
% 173.49/173.40 [3104]E(f312(f312(f89(a1),x31041),f2(a1)),x31041)
% 173.49/173.40 [3105]E(f312(f312(f21(a852),x31051),f2(a852)),x31051)
% 173.49/173.40 [3106]E(f312(f312(f90(a852),x31061),f87(a852)),x31061)
% 173.49/173.40 [3107]E(f312(f312(f90(a1),x31071),f87(a1)),x31071)
% 173.49/173.40 [3108]E(f312(f312(f226(a852),x31081),f2(a852)),x31081)
% 173.49/173.40 [3109]E(f312(f312(f90(a852),x31091),f2(a852)),f2(a852))
% 173.49/173.40 [3110]E(f312(f312(f225(a852),x31101),f2(a852)),f2(a852))
% 173.49/173.40 [3116]E(f312(f168(x31161),f127(x31161)),f189(f860(x31161,a845)))
% 173.49/173.40 [3119]P22(f312(f133(x31191),f127(x31191)))
% 173.49/173.40 [3124]E(f312(f193(x31241,x31241),f5(x31241)),f39(f856(x31241)))
% 173.49/173.40 [3125]E(f312(f193(x31251,x31251),f39(x31251)),f39(f856(x31251)))
% 173.49/173.40 [3126]E(f312(f150(x31261,x31261),f5(x31261)),f39(f853(x31261)))
% 173.49/173.40 [3127]E(f312(f150(x31271,x31271),f39(x31271)),f39(f853(x31271)))
% 173.49/173.40 [3128]E(f54(a1,x31281,f2(a1)),x31281)
% 173.49/173.40 [3129]E(f312(f227(a852),f312(a126,x31291)),f312(f228(a852),x31291))
% 173.49/173.40 [3130]E(f312(f234(a852),f312(a126,x31301)),f312(f280(a852),x31301))
% 173.49/173.40 [3131]E(f312(f279(a852),f312(a126,x31311)),f312(f281(a852),x31311))
% 173.49/173.40 [3133]E(f54(a1,f2(a1),x31331),f2(a1))
% 173.49/173.40 [3140]E(f312(f312(f89(a852),x31401),f87(a852)),f312(a126,x31401))
% 173.49/173.40 [3150]E(f312(f282(a852,x31501),f2(a852)),f189(f860(a852,a845)))
% 173.49/173.40 [3163]E(f283(a852,f2(a852),x31631),f312(f281(a852),x31631))
% 173.49/173.40 [3208]E(f312(f312(f21(a852),f312(a126,x32081)),f87(a852)),x32081)
% 173.49/173.40 [3221]E(f55(f2(a1),x32211),f312(f312(f239(a1,a1),f2(a1)),f2(a1)))
% 173.49/173.40 [3272]P22(f312(f312(f228(a852),x32721),f312(a126,x32721)))
% 173.49/173.40 [3284]P22(f312(f312(f228(a852),f2(a852)),f312(a126,x32841)))
% 173.49/173.40 [3572]E(f312(f312(f21(a113),f312(a3,f312(a126,f312(a19,x35721)))),f87(a113)),x35721)
% 173.49/173.40 [3640]P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x36401))),f2(a1)))
% 173.49/173.40 [3790]P22(f312(f312(f228(a1),f312(f88(a1),f312(f114(a1),f312(a126,x37901)))),f2(a1)))
% 173.49/173.40 [4421]~E(f235(f860(x44211,a845)),f189(f860(x44211,a845)))
% 173.49/173.40 [4472]~P22(f312(f312(f228(a852),x44721),f2(a852)))
% 173.49/173.40 [4488]~P22(f312(f312(f228(a1),f312(f114(a1),x44881)),f2(a1)))
% 173.49/173.40 [3082]E(f175(x30821,f127(f853(x30821))),f127(f853(x30821)))
% 173.49/173.40 [3086]E(f312(f312(f90(a1),a92),x30861),a92)
% 173.49/173.40 [3087]E(f312(f312(f89(a1),a92),x30871),x30871)
% 173.49/173.40 [3090]E(f312(a118,f312(f114(a1),x30901)),x30901)
% 173.49/173.40 [3091]E(f312(f312(f89(a1),x30911),a92),x30911)
% 173.49/173.40 [3092]E(f312(f312(f21(a1),x30921),a92),x30921)
% 173.49/173.40 [3094]E(f312(f47(a1,f2(a1)),x30941),f2(a1))
% 173.49/173.40 [3096]E(f312(f312(f21(a852),x30961),x30961),f2(a852))
% 173.49/173.40 [3101]E(f312(f88(a1),f312(f88(a1),x31011)),x31011)
% 173.49/173.40 [3102]E(f312(f53(a852),f312(f279(a852),x31021)),x31021)
% 173.49/173.40 [3111]E(f312(f312(f89(a852),f2(a852)),x31111),x31111)
% 173.49/173.40 [3112]E(f312(f312(f89(a1),f2(a1)),x31121),x31121)
% 173.49/173.40 [3113]E(f312(f312(f90(a852),f87(a852)),x31131),x31131)
% 173.49/173.40 [3114]E(f312(f312(f90(a1),f87(a1)),x31141),x31141)
% 173.49/173.40 [3115]E(f312(f312(f226(a852),f2(a852)),x31151),x31151)
% 173.49/173.40 [3120]E(f312(f312(f21(a852),f2(a852)),x31201),f2(a852))
% 173.49/173.40 [3121]E(f312(f312(f90(a852),f2(a852)),x31211),f2(a852))
% 173.49/173.40 [3122]E(f312(f312(f225(a852),f2(a852)),x31221),f2(a852))
% 173.49/173.40 [3138]E(f312(f282(a852,f2(a852)),x31381),f312(f279(a852),x31381))
% 173.49/173.40 [3139]E(f312(f312(f90(a1),a111),x31391),f312(f88(a1),x31391))
% 173.49/173.40 [3142]E(f312(a118,f312(f117(a1),x31421)),f312(f117(a852),x31421))
% 173.49/173.40 [3143]E(f312(a19,f312(f117(a113),x31431)),f312(f117(a852),x31431))
% 173.49/173.40 [3144]E(f312(f53(a852),f312(f281(a852),x31441)),f312(a126,x31441))
% 173.49/173.40 [3154]E(f312(f312(f89(a852),f87(a852)),x31541),f312(a126,x31541))
% 173.49/173.40 [3158]E(f312(f84(a1),f312(f114(a1),x31581)),f312(f114(a1),x31581))
% 173.49/173.40 [3159]E(f312(f116(a1),f312(f114(a1),x31591)),f312(f114(a1),x31591))
% 173.49/173.40 [3162]E(f312(f47(a852,x31621),f312(a126,f2(a852))),x31621)
% 173.49/173.40 [3165]E(f312(f53(x31651),f189(f860(x31651,a845))),f2(a852))
% 173.49/173.40 [3176]E(f312(f47(a1,x31761),f312(f117(a1),a111)),f312(f88(a1),x31761))
% 173.49/173.40 [3178]E(f54(a852,x31781,f312(a126,f2(a852))),f2(a852))
% 173.49/173.40 [3179]E(f54(a1,x31791,f312(f117(a1),a111)),f2(a1))
% 173.49/173.40 [3195]E(f135(a852,f312(f282(a852,x31951),f2(a852))),f127(a852))
% 173.49/173.40 [3196]E(f312(f312(f21(a1),x31961),f87(a1)),f312(f312(f89(a1),x31961),a111))
% 173.49/173.40 [3197]E(f312(f312(f89(a1),x31971),f87(a1)),f312(f312(f21(a1),x31971),a111))
% 173.49/173.40 [3202]P22(f312(f312(f195(a23),x32021),x32021))
% 173.49/173.40 [3203]P22(f312(f312(f227(a852),x32031),x32031))
% 173.49/173.40 [3204]P22(f312(f312(f227(a1),x32041),x32041))
% 173.49/173.40 [3209]E(f312(f88(a1),f312(f117(a1),x32091)),f312(f117(a1),f312(f88(a1),x32091)))
% 173.49/173.40 [3211]P22(f312(f70(a852),f312(f281(a852),x32111)))
% 173.49/173.40 [3212]P22(f312(f70(a852),f312(f279(a852),x32121)))
% 173.49/173.40 [3220]E(f157(x32201,f235(f860(x32201,a845))),f235(f860(f853(x32201),a845)))
% 173.49/173.40 [3224]P22(f312(f312(f227(a852),f2(a852)),x32241))
% 173.49/173.40 [3235]E(f312(f312(f89(a852),f125(x32351)),f312(a126,f2(a852))),f125(f312(a126,x32351)))
% 173.49/173.40 [3236]E(f312(f233(x32361),f312(f16(a845,x32361),a224)),f189(f860(x32361,a845)))
% 173.49/173.40 [3237]E(f312(f233(x32371),f312(f16(a845,x32371),a188)),f235(f860(x32371,a845)))
% 173.49/173.40 [3241]E(f312(f312(f289(a852),x32411),f312(f279(a852),x32411)),f312(f279(a852),f312(a126,x32411)))
% 173.49/173.40 [3253]E(f312(f312(f89(a1),f87(a1)),f312(f114(a1),x32531)),f312(f114(a1),f312(a126,x32531)))
% 173.49/173.40 [3256]E(f312(f312(f147(f853(x32561)),f127(x32561)),f127(f853(x32561))),f62(x32561,f127(x32561)))
% 173.49/173.40 [3275]E(f189(f860(f859(x32751,x32751),a845)),f237(x32751,f189(f860(x32751,a845))))
% 173.49/173.40 [3276]E(f312(f288(x32761),f235(f860(x32761,a845))),f235(f860(f860(x32761,a845),a845)))
% 173.49/173.40 [3277]E(f312(f88(f860(x32771,a845)),f189(f860(x32771,a845))),f235(f860(x32771,a845)))
% 173.49/173.40 [3278]E(f312(f88(f860(x32781,a845)),f235(f860(x32781,a845))),f189(f860(x32781,a845)))
% 173.49/173.40 [3280]P22(f312(f70(x32801),f189(f860(x32801,a845))))
% 173.49/173.40 [3282]E(f312(f282(a852,x32821),f312(a126,x32821)),f312(f312(f289(a852),x32821),f189(f860(a852,a845))))
% 173.49/173.40 [3283]E(f94(f859(a852,a852),f56(x32831,f2(a852))),f312(f312(f239(a852,a852),f2(a852)),x32831))
% 173.49/173.40 [3296]E(f312(f312(f289(a852),f312(a126,x32961)),f312(f281(a852),x32961)),f312(f281(a852),f312(a126,x32961)))
% 173.49/173.40 [3300]P41(x33001,f189(f860(f859(x33001,x33001),a845)))
% 173.49/173.40 [3305]P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x33051)))
% 173.49/173.40 [3313]E(f312(f312(f89(a852),f312(f190(a852),x33131)),f312(a126,f2(a852))),f312(f190(a852),f312(a126,x33131)))
% 173.49/173.40 [3422]P43(f312(f290(a852,a1,f114(a1)),x34221))
% 173.49/173.40 [3458]P50(x34581,f189(f860(x34581,a845)),f189(f860(f859(x34581,x34581),a845)))
% 173.49/173.40 [3483]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f21(a1),x34831),f87(a1))),f58(f312(f117(a1),a111),x34831))
% 173.49/173.40 [3529]P59(x35291,f312(f16(f860(x35291,a845),x35291),f312(f16(a845,x35291),a224)))
% 173.49/173.40 [3726]P22(f312(f312(f314(f860(f859(a852,a852),a845)),f313(x37261)),a112))
% 173.49/173.40 [3750]P22(f312(f312(f314(f860(f859(a852,a852),a845)),f312(a121,x37501)),a112))
% 173.49/173.40 [3891]P19(x38911,f860(x38911,a845),f312(f312(f7(x38911,f860(x38911,a845),f860(x38911,a845)),f289(x38911)),f189(f860(x38911,a845))),f235(f860(x38911,a845)))
% 173.49/173.40 [4417]~E(f312(f312(f89(a1),x44171),x44171),a111)
% 173.49/173.40 [4458]~E(f312(a3,f312(a126,f312(a19,x44581))),f2(a113))
% 173.49/173.40 [4465]~P22(f312(a194,f312(f114(a1),x44651)))
% 173.49/173.40 [4468]~P22(f312(f312(f228(a852),x44681),x44681))
% 173.49/173.40 [4481]~P22(f312(f312(f227(a852),f312(a126,x44811)),x44811))
% 173.49/173.40 [3227]E(f312(a118,f312(f88(a1),f312(f114(a1),x32271))),f2(a852))
% 173.49/173.40 [3229]E(f312(f312(f89(a1),f312(f88(a1),x32291)),x32291),f2(a1))
% 173.49/173.40 [3234]E(f312(f53(a1),f312(f282(a1,f2(a1)),x32341)),f312(a118,x32341))
% 173.49/173.40 [3246]E(f312(f312(f240(a852),f312(a126,f2(a852))),x32461),f312(a126,f2(a852)))
% 173.49/173.40 [3346]E(f312(f263(x33461),f189(f860(f859(x33461,x33461),a845))),f189(f860(x33461,a845)))
% 173.49/173.40 [3354]E(f48(f860(x33541,a845),f189(f860(f860(x33541,a845),a845))),f189(f860(x33541,a845)))
% 173.49/173.40 [3355]E(f48(f860(x33551,a845),f235(f860(f860(x33551,a845),a845))),f235(f860(x33551,a845)))
% 173.49/173.40 [3356]E(f49(f860(x33561,a845),f189(f860(f860(x33561,a845),a845))),f235(f860(x33561,a845)))
% 173.49/173.40 [3357]E(f49(f860(x33571,a845),f235(f860(f860(x33571,a845),a845))),f189(f860(x33571,a845)))
% 173.49/173.40 [3405]E(f312(f312(f289(f853(x34051)),f127(x34051)),f189(f860(f853(x34051),a845))),f157(x34051,f189(f860(x34051,a845))))
% 173.49/173.40 [3406]E(f312(f312(f289(f853(x34061)),f127(x34061)),f189(f860(f853(x34061),a845))),f158(x34061,f127(f860(x34061,a845))))
% 173.49/173.40 [3443]E(f312(f312(f89(a852),f4(x34431)),f312(a126,f2(a852))),f4(f312(a3,f312(a126,f312(a19,x34431)))))
% 173.49/173.40 [3475]E(f312(f53(a1),f312(f290(a852,a1,f114(a1)),x34751)),f312(f53(a852),x34751))
% 173.49/173.40 [3478]P22(f312(f312(f227(a852),x34781),f312(f312(f90(a852),x34781),x34781)))
% 173.49/173.40 [3501]E(f312(f47(a852,f312(a126,f2(a852))),f312(f117(a852),x35011)),f312(a118,f312(f47(a1,f87(a1)),f312(f117(a1),x35011))))
% 173.49/173.40 [3511]E(f312(f290(a1,a852,a118),f283(a1,f2(a1),f312(f114(a1),x35111))),f312(f281(a852),x35111))
% 173.49/173.40 [3526]E(f312(f168(a852),f135(a852,f312(f282(a852,f2(a852)),f312(a126,x35261)))),f312(f281(a852),x35261))
% 173.49/173.40 [3527]E(f312(f312(f89(a852),f312(f190(a113),x35271)),f312(a126,f2(a852))),f312(f190(a113),f312(a3,f312(a126,f312(a19,x35271)))))
% 173.49/173.40 [3546]E(f312(f290(a1,a852,a118),f312(f290(a852,a1,f114(a1)),x35461)),x35461)
% 173.49/173.40 [3574]E(f312(f312(f289(a852),f2(a852)),f312(f290(a852,a852,a126),f312(f279(a852),x35741))),f312(f279(a852),f312(a126,x35741)))
% 173.49/173.40 [3583]P54(x35831,x35831,f287(x35831,f189(f860(f859(x35831,x35831),a845))))
% 173.49/173.40 [3589]P22(f312(a194,f312(f88(a1),f312(f114(a1),f312(a126,x35891)))))
% 173.49/173.40 [3600]E(f312(f312(f21(f860(a852,a845)),f312(f234(a852),x36001)),f312(f312(f289(a852),x36001),f189(f860(a852,a845)))),f312(f234(a852),f312(a126,x36001)))
% 173.49/173.40 [3615]E(f312(f312(f89(a1),f312(f312(f21(a1),a92),x36151)),f312(f312(f21(a1),a92),x36151)),f312(f312(f21(a1),a92),f312(f312(f89(a1),x36151),x36151)))
% 173.49/173.40 [3629]E(f312(f312(f289(f860(x36291,a845)),f189(f860(x36291,a845))),f189(f860(f860(x36291,a845),a845))),f312(f288(x36291),f189(f860(x36291,a845))))
% 173.49/173.40 [3657]E(f312(f312(f21(f860(a852,a845)),f312(f280(a852),x36571)),f312(f312(f289(a852),f312(a126,x36571)),f189(f860(a852,a845)))),f312(f280(a852),f312(a126,x36571)))
% 173.49/173.40 [3665]E(f312(f312(f289(f856(x36651)),f192(x36651)),f312(f290(x36651,f856(x36651),f219(x36651)),f235(f860(x36651,a845)))),f235(f860(f856(x36651),a845)))
% 173.49/173.40 [3763]E(f312(f117(a852),f312(f312(f89(a1),x37631),x37631)),f312(f312(f95(a852,a852),f312(f117(a852),x37631)),f312(f312(f18(a852,a852,a852),f89(a852)),f5(a852))))
% 173.49/173.40 [4152]P11(x41521,f860(x41521,a845),f312(f312(f8(f860(x41521,a845),f860(f860(x41521,a845),f860(x41521,a845)),x41521),f312(f7(f860(x41521,a845),f860(x41521,a845),f860(x41521,a845)),f21(f860(x41521,a845)))),f312(f312(f7(x41521,f860(x41521,a845),f860(x41521,a845)),f289(x41521)),f189(f860(x41521,a845)))))
% 173.49/173.40 [4242]E(f312(f233(f859(a1,a1)),f312(f249(a1,a1,a845),f312(f312(f8(f860(a1,a845),f860(a1,a845),a1),f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),x42421)))),f228(a1)))),f119(x42421))
% 173.49/173.40 [4274]E(f312(f233(f859(a1,a1)),f312(f249(a1,a1,a845),f312(f312(f18(a1,f860(a1,a845),f860(a1,a845)),f312(f312(f8(f860(a845,a845),f860(f860(a1,a845),f860(a1,a845)),a1),f8(a845,a845,a1)),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),x42741)))),f228(a1)))),f120(x42741))
% 173.49/173.40 [4323]E(f312(f233(f859(f860(x43231,a845),f860(x43231,a845))),f312(f249(f860(x43231,a845),f860(x43231,a845),a845),f312(f312(f7(f860(x43231,a845),f860(f860(x43231,a845),a845),f860(f860(x43231,a845),a845)),f312(f312(f8(f860(f860(x43231,a845),f860(a845,a845)),f860(f860(f860(x43231,a845),a845),f860(f860(x43231,a845),a845)),f860(x43231,a845)),f18(f860(x43231,a845),a845,a845)),f312(f312(f8(f860(f860(x43231,a845),a845),f860(f860(x43231,a845),f860(a845,a845)),f860(x43231,a845)),f312(f8(a845,f860(a845,a845),f860(x43231,a845)),a310)),f228(f860(x43231,a845))))),f70(x43231)))),f286(x43231))
% 173.49/173.40 [4485]~P22(f312(f70(f853(x44851)),f235(f860(f853(x44851),a845))))
% 173.49/173.40 [4498]~P22(f312(f312(f227(a1),f2(a1)),f312(f88(a1),f312(f114(a1),f312(a126,x44981)))))
% 173.49/173.40 [3381]E(f312(f312(f21(a1),f312(f312(f89(a1),x33811),a111)),a111),x33811)
% 173.49/173.40 [3399]E(f312(f168(a852),f135(a852,f312(f282(a852,f2(a852)),x33991))),f312(f279(a852),x33991))
% 173.49/173.40 [3634]E(f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x36341)),x36341),f312(f312(f21(a1),f312(f312(f89(a1),x36341),x36341)),a111))
% 173.49/173.40 [3682]E(f312(f265(x36821,x36821),f287(x36821,f189(f860(f859(x36821,x36821),a845)))),f287(x36821,f189(f860(f859(x36821,x36821),a845))))
% 173.49/173.40 [3729]P22(f312(f312(f227(a852),x37291),f312(f312(f90(a852),x37291),f312(f312(f90(a852),x37291),x37291))))
% 173.49/173.40 [4011]P22(f312(f70(a852),f312(f233(a852),f312(f312(f7(a852,a852,a845),f228(a852)),x40111))))
% 173.49/173.40 [4012]P22(f312(f70(a852),f312(f233(a852),f312(f312(f7(a852,a852,a845),f227(a852)),x40121))))
% 173.49/173.40 [4293]E(f312(f233(f859(x42931,x42931)),f312(f312(f8(f860(x42931,a845),a845,f859(x42931,x42931)),f96(x42931)),f312(f312(f7(f859(x42931,x42931),f860(x42931,f859(x42931,x42931)),f860(x42931,a845)),f312(f312(f8(f860(f859(x42931,x42931),a845),f860(f860(x42931,f859(x42931,x42931)),f860(x42931,a845)),f859(x42931,x42931)),f8(f859(x42931,x42931),a845,x42931)),a309)),f312(f312(f18(x42931,x42931,f859(x42931,x42931)),f239(x42931,x42931)),f5(x42931))))),f287(x42931,f189(f860(f859(x42931,x42931),a845))))
% 173.49/173.40 [4487]~E(f312(f312(f21(a1),f312(f312(f89(a1),x44871),x44871)),a111),a92)
% 173.49/173.40 [4489]~E(f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x44891)),x44891),f2(a1))
% 173.49/173.40 [3779]E(f312(f312(f89(a1),f312(f312(f21(a1),a111),x37791)),f312(f312(f21(a1),a111),x37791)),f312(f312(f21(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x37791),x37791)),a111)))
% 173.49/173.40 [3899]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),a111),x38991)),f312(f312(f21(a1),a111),x38991))),a111),f312(f312(f21(a1),a111),f312(f312(f89(a1),x38991),x38991)))
% 173.49/173.40 [3933]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x39331),a111)),f312(f312(f89(a1),x39331),a111))),a111),f312(f312(f89(a1),f312(f312(f89(a1),x39331),x39331)),a111))
% 173.49/173.40 [3969]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),a111),x39691)),f312(f312(f21(a1),a111),x39691))),a111),f312(f312(f21(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x39691),x39691)),a111)))
% 173.49/173.40 [4074]E(f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x40741),f2(a852))),f189(f860(f859(a852,a852),a845))))),f312(f114(a1),x40741))
% 173.49/173.40 [4083]E(f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),f317(x40831)),f362(x40831))),f189(f860(f859(a852,a852),a845))))),x40831)
% 173.49/173.40 [4117]E(f312(f233(a1),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),f2(a1)))),x41171)),f312(f290(a852,a1,f114(a1)),f312(f233(a852),f312(f312(f8(a1,a845,a852),x41171),f114(a1)))))
% 173.49/173.40 [4160]P43(f312(f233(a1),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),f2(a1)))),x41601)))
% 173.49/173.40 [4183]P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x41831),f189(f860(f859(a852,a852),a845)))),a80))
% 173.49/173.40 [4189]E(f312(f290(a1,a852,a118),f312(f233(a1),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),f2(a1)))),f312(f312(f8(a852,a845,a1),x41891),a118)))),f312(f233(a852),x41891))
% 173.49/173.40 [4337]E(f292(a852,f312(f312(f50(f859(a852,a852),f860(a852,a845)),f312(a121,x43371)),f312(f249(a852,a852,f860(a852,a845)),f312(f312(f7(a852,f860(a852,a845),f860(a852,f860(a852,a845))),f312(f312(f8(f860(a852,f860(f860(a852,a845),f860(a852,a845))),f860(f860(a852,a845),f860(a852,f860(a852,a845))),a852),f7(a852,f860(a852,a845),f860(a852,a845))),f312(f312(f8(f860(a852,a852),f860(a852,f860(f860(a852,a845),f860(a852,a845))),a852),f312(f8(a852,f860(f860(a852,a845),f860(a852,a845)),a852),f289(a852))),f21(a852)))),f189(f860(a852,a845)))))),f312(a118,x43371))
% 173.49/173.40 [3822]E(f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x38221),x38221)),a111)),a111),f312(f312(f89(a1),x38221),x38221))
% 173.49/173.40 [3874]E(f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x38741),x38741)),a111)),a111),f312(f312(f89(a1),f312(f312(f21(a1),x38741),a111)),f312(f312(f21(a1),x38741),a111)))
% 173.49/173.40 [4091]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),f312(f88(a1),x40911)),a111)),f312(f312(f89(a1),f312(f88(a1),x40911)),a111))),a111),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40911),x40911)),a111)))
% 173.49/173.40 [4132]E(f312(f312(f89(a852),x41321),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(a126,f312(a126,x41321)))
% 173.49/173.40 [4133]E(f312(f312(f90(a852),x41331),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f89(a852),x41331),x41331))
% 173.49/173.40 [4134]E(f312(f47(a852,f312(f312(f89(a852),x41341),x41341)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x41341)
% 173.49/173.40 [4218]E(f54(a852,f312(a126,f312(a126,x42181)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a852,x42181,f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.49/173.40 [4354]E(f312(a98,f312(f312(f50(f859(a852,a852),f860(f859(a852,a852),a845)),f312(a121,x43541)),f312(f249(a852,a852,f860(f859(a852,a852),a845)),f312(f312(f8(f860(a852,f860(f859(a852,a852),a845)),f860(a852,f860(f859(a852,a852),a845)),a852),f312(f8(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845),a852),f264(f859(a852,a852),f859(a852,a852),a122))),f312(f312(f7(a852,f860(f859(a852,a852),a845),f860(a852,f860(f859(a852,a852),a845))),f312(f312(f8(f860(a852,f860(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f860(f860(f859(a852,a852),a845),f860(a852,f860(f859(a852,a852),a845))),a852),f7(a852,f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f8(f860(a852,f859(a852,a852)),f860(a852,f860(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),a852),f312(f8(f859(a852,a852),f860(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),a852),f289(f859(a852,a852)))),f312(f7(a852,a852,f859(a852,a852)),f239(a852,a852))))),f189(f860(f859(a852,a852),a845))))))),f312(f88(a1),x43541))
% 173.49/173.40 [4213]E(f312(f312(f89(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x42131),f312(a126,f312(a126,x42131)))
% 173.49/173.40 [4214]E(f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x42141),f312(f312(f89(a852),x42141),x42141))
% 173.49/173.40 [4247]E(f312(f47(a852,f312(a126,f312(a126,x42471))),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(a126,f312(f47(a852,x42471),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.49/173.40 [4299]E(f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x42991),f312(a126,f312(a126,f312(a126,x42991))))
% 173.49/173.40 [4374]E(f312(f249(a1,a1,f859(a1,a1)),f312(f312(f18(a1,f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f860(f859(a1,a1),f859(a1,a1))),f860(f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),a1),f18(a1,f859(a1,a1),f859(a1,a1))),f312(f312(f8(f860(a1,f859(a1,a1)),f860(a1,f860(f859(a1,a1),f859(a1,a1))),a1),f312(f18(a1,f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),f312(f312(f8(a845,f860(f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),a1),f108(f859(a1,a1))),f312(f312(f8(a1,a845,a1),f312(f227(a1),f2(a1))),f312(f312(f7(a1,a1,a1),f21(a1)),x43741))))),f312(f312(f7(a1,f860(a1,a1),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f859(a1,a1)),f860(f860(a1,a1),f860(a1,f859(a1,a1))),a1),f8(a1,f859(a1,a1),a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f860(a1,a1),a1),f89(a1)),f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f87(a1))))),f312(f312(f7(a1,a1,a1),f21(a1)),x43741))))),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))),f52(x43741))
% 173.49/173.40 [3055]P92(f858(x30551,x30552))
% 173.49/173.40 [3056]P92(f857(x30561,x30562))
% 173.49/173.40 [3057]P92(f859(x30571,x30572))
% 173.49/173.40 [3075]P33(a1,f174(x30751,x30752))
% 173.49/173.40 [3076]P41(x30761,f149(x30761,x30762))
% 173.49/173.40 [3172]P50(x31721,x31722,f237(x31721,x31722))
% 173.49/173.40 [3173]P54(x31731,x31731,f237(x31731,x31732))
% 173.49/173.40 [3446]P19(x34461,x34461,f5(x34461),x34462)
% 173.49/173.40 [3447]P19(x34471,x34471,f39(x34471),x34472)
% 173.49/173.40 [3453]P37(x34531,x34532,f127(x34531),f127(x34531))
% 173.49/173.40 [3454]P19(x34541,f856(x34541),f219(x34541),x34542)
% 173.49/173.40 [3463]P19(f853(x34631),f853(x34631),f165(x34631),x34632)
% 173.49/173.40 [4382]~E(f41(x43821),f40(x43822))
% 173.49/173.40 [4390]~E(f36(x43901,x43902),a23)
% 173.49/173.40 [4391]~E(f35(x43911,x43912),a23)
% 173.49/173.40 [4392]~E(f28(x43921,x43922),a23)
% 173.49/173.40 [4430]~P38(x44301,x44302,f127(x44301))
% 173.49/173.40 [3037]E(f312(f5(x30371),x30372),x30372)
% 173.49/173.40 [3038]E(f312(f233(x30381),x30382),x30382)
% 173.49/173.40 [3040]E(f312(f39(x30401),x30402),x30402)
% 173.49/173.40 [3062]E(f34(f28(x30621,x30622)),f2(a852))
% 173.49/173.40 [3073]E(f94(x30731,f312(a309,x30732)),x30732)
% 173.49/173.40 [3074]E(f99(x30741,f312(a309,x30742)),x30742)
% 173.49/173.40 [3093]E(f312(f190(a846),f28(x30931,x30932)),f2(a852))
% 173.49/173.40 [3099]E(f312(f132(x30991,x30992),f127(x30991)),f127(x30991))
% 173.49/173.40 [3117]E(f148(x31171,f148(x31171,x31172)),f148(x31171,x31172))
% 173.49/173.40 [3118]E(f287(x31181,f287(x31181,x31182)),f287(x31181,x31182))
% 173.49/173.40 [3136]E(f312(f312(f129(x31361),x31362),f127(x31361)),x31362)
% 173.49/173.40 [3145]E(f312(f312(f169(x31451),x31452),f127(x31451)),f127(x31451))
% 173.49/173.40 [3146]E(f312(f312(f134(x31461),x31462),f127(x31461)),f127(x31461))
% 173.49/173.40 [3148]E(f220(x31481,x31482,f192(x31481)),f2(a852))
% 173.49/173.40 [3149]E(f151(x31491,x31492,f127(x31491)),f2(a852))
% 173.49/173.40 [3151]E(f166(x31511,x31512,f127(x31511)),f127(x31511))
% 173.49/173.40 [3152]E(f172(x31521,x31522,f127(x31521)),f127(x31521))
% 173.49/173.40 [3153]E(f170(x31531,f127(x31531),x31532),f127(x31531))
% 173.49/173.40 [3157]E(f312(f168(x31571),f148(x31571,x31572)),f312(f168(x31571),x31572))
% 173.49/173.40 [3160]E(f312(f236(x31601,x31601),f237(x31601,x31602)),x31602)
% 173.49/173.40 [3161]E(f312(f238(x31611,x31611),f237(x31611,x31612)),x31612)
% 173.49/173.40 [3170]P22(f312(a24,f28(x31701,x31702)))
% 173.49/173.40 [3171]E(f312(f265(x31711,x31711),f237(x31711,x31712)),f237(x31711,x31712))
% 173.49/173.40 [3185]E(f287(f853(x31851),f153(x31851,x31852)),f154(x31851,f287(x31851,x31852)))
% 173.49/173.40 [3187]P22(f312(f133(a1),f174(x31871,x31872)))
% 173.49/173.40 [3193]E(f312(f236(x31931,x31931),f287(x31931,x31932)),f235(f860(x31931,a845)))
% 173.49/173.40 [3194]E(f312(f238(x31941,x31941),f287(x31941,x31942)),f235(f860(x31941,a845)))
% 173.49/173.40 [3198]P22(f312(f133(x31981),f148(x31981,x31982)))
% 173.49/173.40 [3200]P22(f312(f156(x32001,x32002),f127(x32001)))
% 173.49/173.40 [3207]E(f312(f168(a1),f174(x32071,x32072)),f283(a1,x32071,x32072))
% 173.49/173.40 [3210]E(f312(f312(f197(x32101,x32101),x32102),f219(x32101)),x32102)
% 173.49/173.40 [3222]P55(x32221,f189(f860(x32221,a845)),x32222)
% 173.49/173.40 [3228]E(f312(f282(a852,x32281),f312(a126,x32282)),f283(a852,x32281,x32282))
% 173.49/173.40 [3245]E(f312(f312(f147(x32451),x32452),f127(x32451)),f136(x32451,x32452,f127(x32451)))
% 173.49/173.40 [3258]E(f283(a852,f312(a126,x32581),x32582),f284(a852,x32581,x32582))
% 173.49/173.40 [3261]P50(x32611,f235(f860(x32611,a845)),f287(x32611,x32612))
% 173.49/173.40 [3324]E(f312(f312(f21(a852),x33241),f312(a126,x33242)),f312(f53(a852),f285(a852,x33242,x33241)))
% 173.49/173.40 [3382]E(f163(x33821,x33822,f127(x33821)),f312(f312(f239(f853(x33821),f853(x33821)),f127(x33821)),f127(x33821)))
% 173.49/173.40 [3403]E(f312(f249(x34031,x34032,f859(x34031,x34032)),f239(x34031,x34032)),f39(f859(x34031,x34032)))
% 173.49/173.40 [3408]P22(f312(f312(f314(f853(x34081)),f127(x34081)),f157(x34081,x34082)))
% 173.49/173.40 [3409]E(f312(f190(f853(x34091)),f128(x34091,x34092)),f312(f312(f21(a852),f312(f190(f853(x34091)),x34092)),f87(a852)))
% 173.49/173.40 [3416]P22(f312(f70(a852),f285(a852,x34161,x34162)))
% 173.49/173.40 [3417]P22(f312(f70(a852),f284(a852,x34171,x34172)))
% 173.49/173.40 [3418]P22(f312(f70(a852),f283(a852,x34181,x34182)))
% 173.49/173.40 [3419]P22(f312(f70(a1),f285(a1,x34191,x34192)))
% 173.49/173.40 [3420]P22(f312(f70(a1),f284(a1,x34201,x34202)))
% 173.49/173.40 [3421]P22(f312(f70(a1),f283(a1,x34211,x34212)))
% 173.49/173.40 [3524]E(f312(f290(a852,a852,a126),f283(a852,x35241,x35242)),f283(a852,f312(a126,x35241),f312(a126,x35242)))
% 173.49/173.40 [3543]E(f312(f312(f267(x35431,x35431,x35431),f287(x35431,x35432)),f287(x35431,x35432)),f287(x35431,x35432))
% 173.49/173.40 [3582]E(f312(f312(f239(a852,a852),f312(f47(a852,x35821),x35822)),f54(a852,x35821,x35822)),f94(f859(a852,a852),f56(x35821,x35822)))
% 173.49/173.40 [3653]P22(f312(f312(f228(a852),f312(f312(f21(a852),x36531),x36532)),f312(a126,x36531)))
% 173.49/173.40 [3722]E(f312(f312(f89(a1),f312(f312(f90(a1),x37221),f312(f47(a1,x37222),x37221))),f54(a1,x37222,x37221)),x37222)
% 173.49/173.40 [3753]E(f312(f312(f50(a852,f860(f859(f853(x37531),f853(x37531)),a845)),f235(f860(a852,a845))),f139(x37531,x37532)),f141(x37531,x37532))
% 173.49/173.40 [3984]P22(f312(f312(f314(f859(f853(x39841),f853(x39841))),f312(f312(f239(f853(x39841),f853(x39841)),f127(x39841)),f127(x39841))),f154(x39841,x39842)))
% 173.49/173.40 [4145]E(f250(x41451,x41451,x41452,x41452,f5(x41451),f5(x41452)),f39(f859(x41451,x41452)))
% 173.49/173.40 [4147]E(f250(x41471,x41471,x41472,x41472,f39(x41471),f39(x41472)),f39(f859(x41471,x41472)))
% 173.49/173.40 [4400]~E(f312(f219(x44001),x44002),f192(x44001))
% 173.49/173.40 [4418]~P42(x44181,f312(f219(x44181),x44182))
% 173.49/173.40 [3134]E(f312(f223(x31341),f312(f219(x31341),x31342)),x31342)
% 173.49/173.40 [3135]E(f312(f165(x31351),f312(f165(x31351),x31352)),x31352)
% 173.49/173.40 [3137]E(f312(f312(f134(x31371),f2(a852)),x31372),x31372)
% 173.49/173.40 [3147]E(f312(f312(f169(x31471),f2(a852)),x31472),f127(x31471))
% 173.49/173.40 [3155]E(f312(f312(f129(x31551),f127(x31551)),x31552),x31552)
% 173.49/173.40 [3164]E(f312(f190(f856(x31641)),f312(f219(x31641),x31642)),f2(a852))
% 173.49/173.40 [3166]E(f48(f860(x31661,a845),f312(f288(x31661),x31662)),x31662)
% 173.49/173.40 [3167]E(f312(f168(x31671),f312(f164(x31671),x31672)),f312(f168(x31671),x31672))
% 173.49/173.40 [3168]E(f312(f168(x31681),f312(f165(x31681),x31682)),f312(f168(x31681),x31682))
% 173.49/173.40 [3175]E(f312(f312(f21(a113),x31751),x31752),f312(f312(a22,x31751),x31752))
% 173.49/173.40 [3188]E(f312(f312(f89(a852),x31881),x31882),f312(f312(f89(a852),x31882),x31881))
% 173.49/173.40 [3189]E(f312(f312(f89(a1),x31891),x31892),f312(f312(f89(a1),x31892),x31891))
% 173.49/173.40 [3190]E(f312(f312(f90(a852),x31901),x31902),f312(f312(f90(a852),x31902),x31901))
% 173.49/173.40 [3191]E(f312(f312(f90(a1),x31911),x31912),f312(f312(f90(a1),x31912),x31911))
% 173.49/173.40 [3215]E(f312(f312(f184(x32151,x32151),f2(a852)),x32152),f39(x32151))
% 173.49/173.40 [3216]E(f312(f190(f853(x32161)),f312(f164(x32161),x32162)),f312(f190(f853(x32161)),x32162))
% 173.49/173.40 [3217]E(f312(f190(f853(x32171)),f312(f165(x32171),x32172)),f312(f190(f853(x32171)),x32172))
% 173.49/173.40 [3218]E(f170(x32181,x32182,f189(f860(a852,a845))),f127(x32181))
% 173.49/173.40 [3219]E(f312(f312(f150(x32191,x32191),f5(x32191)),x32192),x32192)
% 173.49/173.40 [3238]E(f312(f190(f853(x32381)),f148(x32381,x32382)),f312(f53(x32381),f312(f168(x32381),x32382)))
% 173.49/173.40 [3239]E(f34(f35(x32391,x32392)),f312(f312(f89(a852),f34(x32392)),f312(a126,f2(a852))))
% 173.49/173.40 [3240]E(f312(f263(x32401),f312(f265(x32401,x32401),x32402)),f312(f263(x32401),x32402))
% 173.49/173.40 [3244]P22(f312(f70(x32441),f312(f168(x32441),x32442)))
% 173.49/173.40 [3252]E(f312(f312(f89(a1),x32521),f312(f88(a1),x32522)),f312(f312(f21(a1),x32521),x32522))
% 173.49/173.40 [3260]P18(x32601,x32602,f189(f860(f851(x32601),a845)))
% 173.49/173.40 [3262]E(f312(f290(x32621,x32621,f5(x32621)),x32622),x32622)
% 173.49/173.40 [3263]E(f312(f290(x32631,x32631,f39(x32631)),x32632),x32632)
% 173.49/173.40 [3264]E(f312(f291(x32641,x32641,f5(x32641)),x32642),x32642)
% 173.49/173.40 [3265]E(f312(f291(x32651,x32651,f39(x32651)),x32652),x32652)
% 173.49/173.40 [3266]P22(f312(f235(f860(x32661,a845)),x32662))
% 173.49/173.40 [3268]E(f312(f53(a852),f312(f282(a852,x32681),x32682)),f312(f312(f21(a852),x32682),x32681))
% 173.49/173.40 [3269]E(f312(f282(a852,f312(a126,x32691)),x32692),f285(a852,x32691,x32692))
% 173.49/173.40 [3281]E(f312(f312(f289(x32811),x32812),f189(f860(x32811,a845))),f312(f233(x32811),f312(a309,x32812)))
% 173.49/173.40 [3285]E(f312(f312(f289(x32851),x32852),f189(f860(x32851,a845))),f218(x32851,f312(f219(x32851),x32852)))
% 173.49/173.40 [3288]E(f287(x32881,f312(f265(x32881,x32881),x32882)),f312(f265(x32881,x32881),f287(x32881,x32882)))
% 173.49/173.40 [3292]E(f312(f312(f89(a852),f312(a126,x32921)),x32922),f312(f312(f89(a852),x32921),f312(a126,x32922)))
% 173.49/173.40 [3293]E(f312(f312(f21(a852),f312(a126,x32931)),f312(a126,x32932)),f312(f312(f21(a852),x32931),x32932))
% 173.49/173.40 [3298]E(f63(x32981,f2(a852),x32982),f312(f312(f147(f853(x32981)),f127(x32981)),f127(f853(x32981))))
% 173.49/173.40 [3299]E(f312(f53(a852),f284(a852,x32991,x32992)),f312(f312(f21(a852),x32992),x32991))
% 173.49/173.40 [3302]E(f312(f47(a1,f312(f88(a1),x33021)),f312(f88(a1),x33022)),f312(f47(a1,x33021),x33022))
% 173.49/173.40 [3310]P41(x33101,f312(f312(f266(a852,x33101),a232),x33102))
% 173.49/173.40 [3312]P33(a852,f135(a852,f312(f282(a852,x33121),x33122)))
% 173.49/173.40 [3314]P22(f312(f70(a852),f312(f282(a852,x33141),x33142)))
% 173.49/173.40 [3315]P22(f312(f70(a1),f312(f282(a1,x33151),x33152)))
% 173.49/173.40 [3318]E(f312(f265(f853(x33181),f853(x33181)),f153(x33181,x33182)),f153(x33181,f312(f265(x33181,x33181),x33182)))
% 173.49/173.40 [3319]E(f312(f190(a846),f35(x33191,x33192)),f312(f312(f89(a852),f312(f190(a846),x33192)),f312(a126,f2(a852))))
% 173.49/173.40 [3321]E(f312(f282(a1,x33211),f312(f312(f89(a1),x33212),f87(a1))),f283(a1,x33211,x33212))
% 173.49/173.40 [3323]E(f312(f246(a852,a852),f94(f859(a852,a852),f56(x33231,x33232))),f312(f47(a852,x33231),x33232))
% 173.49/173.40 [3331]E(f181(x33311,x33312,f312(f16(f856(x33312),x33311),f192(x33312))),f189(f860(x33312,a845)))
% 173.49/173.40 [3332]E(f179(x33321,x33322,f312(f16(f856(x33322),x33321),f192(x33322))),f189(f860(x33321,a845)))
% 173.49/173.40 [3333]E(f312(f312(f184(f859(x33331,x33331),a845),f87(a852)),x33332),x33332)
% 173.49/173.40 [3335]E(f312(f312(f21(f860(x33351,a845)),x33352),f189(f860(x33351,a845))),x33352)
% 173.49/173.40 [3336]E(f312(f312(f124(f860(x33361,a845)),x33362),f189(f860(x33361,a845))),x33362)
% 173.49/173.40 [3337]E(f312(f312(f115(f860(x33371,a845)),x33372),f235(f860(x33371,a845))),x33372)
% 173.49/173.40 [3344]E(f293(x33441,f312(a20,x33442),f312(f88(a1),f312(a20,x33442))),f312(f312(f296(a1),x33441),x33442))
% 173.49/173.40 [3345]E(f283(a1,f312(f312(f89(a1),x33451),f87(a1)),x33452),f284(a1,x33451,x33452))
% 173.49/173.40 [3350]E(f312(f248(a852,a852),f94(f859(a852,a852),f56(x33501,x33502))),f54(a852,x33501,x33502))
% 173.49/173.40 [3358]E(f294(x33581,f312(a20,x33582),f312(f88(a1),f312(a20,x33582))),f295(a1,x33581,x33582))
% 173.49/173.40 [3361]P22(f312(f312(f314(x33611),x33612),f235(f860(x33611,a845))))
% 173.49/173.40 [3367]E(f312(f312(f21(a852),f312(a126,x33671)),x33672),f312(f53(a852),f283(a852,x33672,x33671)))
% 173.49/173.40 [3389]E(f312(f47(a1,f312(f114(a1),x33891)),f312(f114(a1),x33892)),f312(f114(a1),f312(f47(a852,x33891),x33892)))
% 173.49/173.40 [3395]E(f312(f312(f21(f860(x33951,a845)),x33952),f235(f860(x33951,a845))),f189(f860(x33951,a845)))
% 173.49/173.40 [3396]E(f312(f312(f124(f860(x33961,a845)),x33962),f235(f860(x33961,a845))),f235(f860(x33961,a845)))
% 173.49/173.40 [3397]E(f312(f312(f115(f860(x33971,a845)),x33972),f189(f860(x33971,a845))),f189(f860(x33971,a845)))
% 173.49/173.40 [3411]E(f54(a1,f312(f88(a1),x34111),f312(f88(a1),x34112)),f312(f88(a1),f54(a1,x34111,x34112)))
% 173.49/173.40 [3412]E(f54(a1,f312(f114(a1),x34121),f312(f114(a1),x34122)),f312(f114(a1),f54(a852,x34121,x34122)))
% 173.49/173.40 [3423]E(f312(f190(f853(x34231)),f312(f167(x34231),x34232)),f312(f312(f21(a852),f312(f190(f853(x34231)),x34232)),f87(a852)))
% 173.49/173.40 [3426]E(f312(f47(a1,f54(a1,x34261,x34262)),x34262),f2(a1))
% 173.49/173.40 [3451]E(f312(a3,f312(f47(a852,f312(a19,x34511)),f312(a19,x34512))),f312(f47(a113,x34511),x34512))
% 173.49/173.40 [3456]E(f312(a3,f54(a852,f312(a19,x34561),f312(a19,x34562))),f54(a113,x34561,x34562))
% 173.49/173.40 [3468]E(f312(f312(f90(a852),x34681),f312(f47(a852,x34682),x34681)),f312(f312(f21(a852),x34682),f54(a852,x34682,x34681)))
% 173.49/173.40 [3469]E(f312(f312(f90(a1),x34691),f312(f47(a1,x34692),x34691)),f312(f312(f21(a1),x34692),f54(a1,x34692,x34691)))
% 173.49/173.40 [3495]E(f312(a3,f312(f312(f89(a852),f312(a19,x34951)),f312(a19,x34952))),f312(f312(f89(a113),x34951),x34952))
% 173.49/173.40 [3496]E(f312(a3,f312(f312(f21(a852),f312(a19,x34961)),f312(a19,x34962))),f312(f312(f21(a113),x34961),x34962))
% 173.49/173.40 [3497]E(f312(a3,f312(f312(f90(a852),f312(a19,x34971)),f312(a19,x34972))),f312(f312(f90(a113),x34971),x34972))
% 173.49/173.40 [3505]E(f312(f290(a852,a852,a126),f312(f282(a852,x35051),x35052)),f312(f282(a852,f312(a126,x35051)),f312(a126,x35052)))
% 173.49/173.40 [3528]P22(f312(f56(x35281,x35282),f94(f859(a852,a852),f56(x35281,x35282))))
% 173.49/173.40 [3549]E(f312(f312(f89(a852),f312(f312(f89(a852),f34(x35491)),f34(x35492))),f312(a126,f2(a852))),f34(f36(x35491,x35492)))
% 173.49/173.40 [3550]E(f54(a852,f312(a126,f54(a852,x35501,x35502)),x35502),f54(a852,f312(a126,x35501),x35502))
% 173.49/173.40 [3564]E(f312(f312(f50(f860(x35641,a845),f860(x35641,a845)),x35642),f5(f860(x35641,a845))),f48(f860(x35641,a845),x35642))
% 173.49/173.40 [3565]E(f312(f312(f51(f860(x35651,a845),f860(x35651,a845)),x35652),f5(f860(x35651,a845))),f49(f860(x35651,a845),x35652))
% 173.49/173.40 [3566]E(f312(f290(f853(x35661),f860(x35661,a845),f168(x35661)),f312(f168(f853(x35661)),f62(x35661,x35662))),f312(f288(x35661),f312(f168(x35661),x35662)))
% 173.49/173.40 [3569]P22(f312(f312(f314(f860(x35691,a845)),x35692),f312(f288(x35691),x35692)))
% 173.49/173.40 [3573]E(f54(a1,f312(f88(a1),f54(a1,x35731,x35732)),x35732),f54(a1,f312(f88(a1),x35731),x35732))
% 173.49/173.40 [3585]P22(f312(f312(f227(f860(x35851,a845)),x35852),f235(f860(x35851,a845))))
% 173.49/173.40 [3587]E(f312(f312(f267(x35871,x35871,x35871),f287(x35871,x35872)),f287(x35871,f287(x35871,x35872))),f287(x35871,x35872))
% 173.49/173.40 [3588]E(f312(f312(f124(f860(x35881,a845)),f312(f238(x35881,x35881),x35882)),f312(f236(x35881,x35881),x35882)),f312(f263(x35881),x35882))
% 173.49/173.40 [3608]E(f298(x36081,x36082,f235(f860(x36081,a845)),f235(f860(x36082,a845))),f235(f860(f858(x36081,x36082),a845)))
% 173.49/173.40 [3658]P22(f312(f312(f227(a852),f54(a852,x36581,x36582)),x36581))
% 173.49/173.40 [3680]P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x36801))),f312(f114(a1),x36802)))
% 173.49/173.40 [3705]P22(f312(f312(f314(f860(x37051,a845)),f189(f860(x37051,a845))),f312(f288(x37051),x37052)))
% 173.49/173.40 [3710]E(f287(x37101,f312(f312(f267(x37101,x37101,x37101),x37102),f287(x37101,x37102))),f287(x37101,x37102))
% 173.49/173.40 [3713]E(f312(f312(f267(x37131,x37131,x37131),f287(x37131,x37132)),x37132),f312(f312(f267(x37131,x37131,x37131),x37132),f287(x37131,x37132)))
% 173.49/173.40 [3715]E(f312(a118,f312(f312(f89(a1),f312(f312(f21(a1),x37151),x37152)),f87(a1))),f312(f53(a1),f283(a1,x37152,x37151)))
% 173.49/173.40 [3730]E(f312(f236(x37301,x37301),f312(f312(f267(x37301,x37301,x37301),x37302),f287(x37301,x37302))),f312(f236(x37301,x37301),x37302))
% 173.49/173.40 [3731]E(f312(f238(x37311,x37311),f312(f312(f267(x37311,x37311,x37311),x37312),f287(x37311,x37312))),f312(f238(x37311,x37311),x37312))
% 173.49/173.40 [3747]E(f312(f312(f89(a852),f312(f312(f89(a852),f312(f190(a846),x37471)),f312(f190(a846),x37472))),f312(a126,f2(a852))),f312(f190(a846),f36(x37471,x37472)))
% 173.49/173.40 [3758]P19(a852,a852,f312(f312(f7(a852,a852,a852),f89(a852)),x37581),x37582)
% 173.49/173.40 [3760]P33(a852,f312(f165(a852),f312(f312(f150(f853(x37601),a852),f190(f853(x37601))),f175(x37601,x37602))))
% 173.49/173.40 [3810]P22(f312(f312(f228(a1),f312(f88(a1),f312(f114(a1),f312(a126,x38101)))),f312(f114(a1),x38102)))
% 173.49/173.40 [3854]E(f312(f138(f853(x38541),x38541,f312(f7(x38541,f853(x38541),f853(x38541)),f147(x38541)),f127(x38541)),x38542),f312(f165(x38541),x38542))
% 173.49/173.40 [3906]P22(f312(f312(f227(f860(f859(f853(x39061),f853(x39061)),a845)),f154(x39061,x39062)),f287(f853(x39061),f153(x39061,x39062))))
% 173.49/173.40 [3907]P22(f312(f56(x39071,x39072),f312(f312(f239(a852,a852),f312(f47(a852,x39071),x39072)),f54(a852,x39071,x39072))))
% 173.49/173.40 [3947]P22(f312(f312(f227(f860(f859(f853(x39471),f853(x39471)),a845)),f153(x39471,f287(x39471,x39472))),f287(f853(x39471),f153(x39471,x39472))))
% 173.49/173.40 [4172]E(f312(f312(f251(f859(a113,a113),a113,f859(a113,a113),f859(x41721,f859(a113,a113))),f255(f312(f162(a113),f312(f312(f150(f859(a113,x41721),a113),f246(a113,x41721)),x41722)))),f312(f312(f8(x41721,f860(f859(a113,a113),f859(x41721,f859(a113,a113))),a113),f239(x41721,f859(a113,a113))),f256(x41721,x41722))),f254(x41721,x41722))
% 173.49/173.40 [4353]E(f312(f249(f860(f859(x43531,x43531),a845),f860(f859(x43531,x43531),a845),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f312(f312(f7(f860(f859(x43531,x43531),a845),f860(f860(f859(x43531,x43531),a845),f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845))),f860(f860(f859(x43531,x43531),a845),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845))))),f312(f312(f8(f860(f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845)),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f860(f860(f860(f859(x43531,x43531),a845),f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845))),f860(f860(f859(x43531,x43531),a845),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845))))),f860(f859(x43531,x43531),a845)),f8(f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845)),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845))),f860(f859(x43531,x43531),a845))),f312(f312(f8(f860(f860(x43532,x43531),f860(f860(f859(x43532,x43532),a845),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f860(f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845)),f860(f860(x43532,x43531),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f860(f859(x43531,x43531),a845)),f18(f860(x43532,x43531),f860(f859(x43532,x43532),a845),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f312(f312(f8(f860(f860(x43532,x43531),f860(f859(x43532,x43532),a845)),f860(f860(x43532,x43531),f860(f860(f859(x43532,x43532),a845),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f860(f859(x43531,x43531),a845)),f312(f8(f860(f859(x43532,x43532),a845),f860(f860(f859(x43532,x43532),a845),f859(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845))),f860(x43532,x43531)),f239(f860(f859(x43532,x43532),a845),f860(f859(x43532,x43532),a845)))),f266(x43531,x43532))))),f266(x43531,x43532))),f83(x43531,x43532))
% 173.49/173.40 [4466]~E(f312(f288(x44661),x44662),f189(f860(f860(x44661,a845),a845)))
% 173.49/173.40 [4484]~P22(f312(f312(f314(x44841),x44842),f189(f860(x44841,a845))))
% 173.49/173.40 [4493]~P22(f312(f312(f228(f860(x44931,a845)),x44932),f189(f860(x44931,a845))))
% 173.49/173.40 [3271]E(f312(f312(f21(a852),x32711),f312(f312(f89(a852),x32711),x32712)),f2(a852))
% 173.49/173.40 [3273]E(f312(f312(f124(f860(x32731,a845)),x32732),x32732),x32732)
% 173.49/173.40 [3274]E(f312(f312(f115(f860(x32741,a845)),x32742),x32742),x32742)
% 173.49/173.40 [3301]E(f312(f47(a1,f312(f88(a1),x33011)),x33012),f312(f47(a1,x33011),f312(f88(a1),x33012)))
% 173.49/173.40 [3303]E(f312(f312(f21(f860(x33031,a845)),x33032),x33032),f189(f860(x33031,a845)))
% 173.49/173.40 [3306]E(f312(f139(x33061,x33062),f2(a852)),f189(f860(f859(f853(x33061),f853(x33061)),a845)))
% 173.49/173.40 [3307]E(f312(f312(f89(a852),x33071),f312(a126,x33072)),f312(a126,f312(f312(f89(a852),x33071),x33072)))
% 173.49/173.40 [3320]E(f196(f312(f114(a1),x33201),f312(f114(a1),x33202)),f312(f114(a1),f312(f312(f21(a852),x33201),x33202)))
% 173.49/173.40 [3326]E(f312(f53(a1),f312(f282(a1,x33261),x33262)),f312(a118,f312(f312(f21(a1),x33262),x33261)))
% 173.49/173.40 [3329]E(f312(f312(f89(a852),f312(a126,x33291)),x33292),f312(a126,f312(f312(f89(a852),x33291),x33292)))
% 173.49/173.40 [3334]E(f312(f88(f860(x33341,a845)),f312(f88(f860(x33341,a845)),x33342)),x33342)
% 173.49/173.40 [3347]E(f175(x33471,f312(f312(f147(f853(x33471)),f127(x33471)),x33472)),f175(x33471,x33472))
% 173.49/173.40 [3351]E(f312(f312(f89(a852),x33511),f312(f312(f90(a852),x33511),x33512)),f312(f312(f90(a852),x33511),f312(a126,x33512)))
% 173.49/173.40 [3359]E(f312(f312(a22,f312(a3,x33591)),f312(a3,x33592)),f312(a3,f312(f312(f21(a852),x33591),x33592)))
% 173.49/173.40 [3373]E(f312(f312(f90(a1),f312(f88(a1),x33731)),x33732),f312(f88(a1),f312(f312(f90(a1),x33731),x33732)))
% 173.49/173.40 [3375]E(f312(f312(f240(a1),f312(f114(a1),x33751)),x33752),f312(f114(a1),f312(f312(f240(a852),x33751),x33752)))
% 173.49/173.40 [3376]E(f312(f312(f89(a113),f312(a3,x33761)),f312(a3,x33762)),f312(a3,f312(f312(f89(a852),x33761),x33762)))
% 173.49/173.40 [3377]E(f312(f312(f90(a113),f312(a3,x33771)),f312(a3,x33772)),f312(a3,f312(f312(f90(a852),x33771),x33772)))
% 173.49/173.40 [3378]E(f312(f312(f225(a852),f312(a126,x33781)),f312(a126,x33782)),f312(a126,f312(f312(f225(a852),x33781),x33782)))
% 173.49/173.40 [3379]E(f312(f312(f226(a852),f312(a126,x33791)),f312(a126,x33792)),f312(a126,f312(f312(f226(a852),x33791),x33792)))
% 173.49/173.40 [3385]E(f312(f168(a852),f135(a852,f312(f282(a852,x33851),x33852))),f312(f282(a852,x33851),x33852))
% 173.49/173.40 [3386]E(f292(x33861,f312(f312(f289(x33861),x33862),f189(f860(x33861,a845)))),x33862)
% 173.49/173.40 [3393]E(f312(f236(x33931,x33932),f189(f860(f859(x33931,x33932),a845))),f189(f860(x33932,a845)))
% 173.49/173.40 [3394]E(f312(f238(x33941,x33942),f189(f860(f859(x33941,x33942),a845))),f189(f860(x33941,a845)))
% 173.49/173.40 [3398]E(f312(a118,f312(f312(f21(a1),x33981),x33982)),f312(f53(a1),f284(a1,x33982,x33981)))
% 173.49/173.40 [3402]E(f312(f312(f89(a852),x34021),f312(f312(f90(a852),x34022),x34021)),f312(f312(f90(a852),f312(a126,x34022)),x34021))
% 173.49/173.40 [3404]E(f312(f312(f69(x34041),f189(f860(x34041,a845))),x34042),f189(f860(f860(x34041,a845),a845)))
% 173.49/173.40 [3413]E(f312(f190(f853(a852)),f135(a852,f312(f282(a852,x34131),x34132))),f312(f312(f21(a852),x34132),x34131))
% 173.49/173.40 [3430]E(f312(f312(f124(f860(x34301,a845)),f189(f860(x34301,a845))),x34302),x34302)
% 173.49/173.40 [3431]E(f312(f312(f115(f860(x34311,a845)),f235(f860(x34311,a845))),x34312),x34312)
% 173.49/173.40 [3432]E(f312(f312(f89(a1),f312(f88(a1),x34321)),f312(f88(a1),x34322)),f312(f88(a1),f312(f312(f89(a1),x34321),x34322)))
% 173.49/173.40 [3436]E(f312(f312(f89(a1),f312(f114(a1),x34361)),f312(f114(a1),x34362)),f312(f114(a1),f312(f312(f89(a852),x34361),x34362)))
% 173.49/173.40 [3437]E(f312(f312(f89(a1),f312(f117(a1),x34371)),f312(f117(a1),x34372)),f312(f117(a1),f312(f312(f89(a1),x34371),x34372)))
% 173.49/173.40 [3439]E(f312(f312(f90(a1),f312(f114(a1),x34391)),f312(f114(a1),x34392)),f312(f114(a1),f312(f312(f90(a852),x34391),x34392)))
% 173.49/173.40 [3440]E(f312(f312(f90(a1),f312(f117(a1),x34401)),f312(f117(a1),x34402)),f312(f117(a1),f312(f312(f90(a1),x34401),x34402)))
% 173.49/173.40 [3457]E(f312(f312(f6(x34571,a852),f312(f16(a852,x34571),f87(a852))),x34572),f312(f53(x34571),x34572))
% 173.49/173.40 [3470]E(f312(f88(a1),f54(a1,f312(f88(a1),x34701),x34702)),f54(a1,x34701,f312(f88(a1),x34702)))
% 173.49/173.40 [3472]E(f312(f168(a1),f174(x34721,f312(f312(f21(a1),x34722),f87(a1)))),f312(f282(a1,x34721),x34722))
% 173.49/173.40 [3476]P22(f312(f312(f227(a852),x34761),f312(f312(f89(a852),x34762),x34761)))
% 173.49/173.40 [3477]P22(f312(f312(f227(a852),x34771),f312(f312(f89(a852),x34771),x34772)))
% 173.49/173.40 [3480]E(f312(f312(f21(f860(x34801,a845)),f189(f860(x34801,a845))),x34802),f189(f860(x34801,a845)))
% 173.49/173.40 [3481]E(f312(f312(f124(f860(x34811,a845)),f235(f860(x34811,a845))),x34812),f235(f860(x34811,a845)))
% 173.49/173.40 [3482]E(f312(f312(f115(f860(x34821,a845)),f189(f860(x34821,a845))),x34822),f189(f860(x34821,a845)))
% 173.49/173.40 [3487]E(f312(f312(f239(a1,a1),x34871),f312(f88(a1),x34872)),f312(a59,f312(f312(f239(a1,a1),x34871),x34872)))
% 173.49/173.40 [3488]E(f312(f282(a1,f312(f312(f89(a1),x34881),f87(a1))),x34882),f285(a1,x34881,x34882))
% 173.49/173.40 [3502]E(f312(f168(a1),f174(f312(f312(f89(a1),x35021),f87(a1)),x35022)),f284(a1,x35021,x35022))
% 173.49/173.40 [3506]P22(f312(f312(f227(f860(x35061,a845)),x35062),x35062))
% 173.49/173.40 [3509]E(f312(f312(f124(f860(x35091,a845)),x35092),f312(f88(f860(x35091,a845)),x35092)),f235(f860(x35091,a845)))
% 173.49/173.40 [3510]E(f312(f312(f115(f860(x35101,a845)),x35102),f312(f88(f860(x35101,a845)),x35102)),f189(f860(x35101,a845)))
% 173.49/173.40 [3517]E(f312(f312(f21(a852),f312(f312(f21(a852),x35171),f87(a852))),x35172),f312(f312(f21(a852),x35171),f312(a126,x35172)))
% 173.49/173.40 [3521]E(f312(f312(f21(f860(x35211,a845)),f235(f860(x35211,a845))),x35212),f312(f88(f860(x35211,a845)),x35212))
% 173.49/173.40 [3522]E(f312(f312(f21(a1),f312(f117(a1),x35221)),f312(f117(a1),x35222)),f312(f117(a1),f312(f312(f89(a1),x35221),f312(f88(a1),x35222))))
% 173.49/173.40 [3533]E(f312(f168(a852),f135(a852,f312(f282(a852,x35331),f312(a126,x35332)))),f283(a852,x35331,x35332))
% 173.49/173.40 [3539]E(f312(f312(f90(a852),f312(f47(a852,x35391),x35392)),x35392),f312(f312(f21(a852),x35391),f54(a852,x35391,x35392)))
% 173.49/173.40 [3541]P22(f312(f312(f312(f312(a198,a23),x35411),x35412),x35411))
% 173.49/173.40 [3547]E(f312(f190(f853(f853(x35471))),f62(x35471,x35472)),f312(f312(f240(a852),f312(a126,f312(a126,f2(a852)))),f312(f190(f853(x35471)),x35472)))
% 173.49/173.40 [3567]E(f312(f312(f184(f859(x35671,x35671),a845),f2(a852)),x35672),f287(x35671,f189(f860(f859(x35671,x35671),a845))))
% 173.49/173.40 [3571]P22(f312(f133(a852),f135(a852,f312(f282(a852,x35711),x35712))))
% 173.49/173.40 [3578]P22(f312(f312(f227(a852),f312(f47(a852,x35781),x35782)),x35781))
% 173.49/173.40 [3586]E(f312(f290(a1,a852,a118),f283(a1,f312(f114(a1),x35861),f312(f114(a1),x35862))),f283(a852,x35861,x35862))
% 173.49/173.40 [3596]E(f186(a852,f2(a852),f5(a852),f312(f312(f21(a852),x35961),x35962)),f312(f312(f21(a852),x35961),f312(a126,x35962)))
% 173.49/173.40 [3597]E(f312(a118,f312(f312(f21(a1),x35971),f312(f312(f89(a1),x35972),f87(a1)))),f312(f53(a1),f285(a1,x35972,x35971)))
% 173.49/173.40 [3630]E(f312(f312(f150(a852,a852),a126),f135(a852,f312(f282(a852,x36301),x36302))),f135(a852,f312(f282(a852,f312(a126,x36301)),f312(a126,x36302))))
% 173.49/173.40 [3638]E(f312(f168(a1),f174(f312(f312(f89(a1),x36381),f87(a1)),f312(f312(f21(a1),x36382),f87(a1)))),f285(a1,x36381,x36382))
% 173.49/173.40 [3649]P22(f312(f312(f227(f860(x36491,a845)),f189(f860(x36491,a845))),x36492))
% 173.49/173.40 [3654]E(f94(x36541,f312(f312(f7(x36541,x36541,a845),a309),x36542)),x36542)
% 173.49/173.40 [3655]E(f99(x36551,f312(f312(f7(x36551,x36551,a845),a309),x36552)),x36552)
% 173.49/173.40 [3659]E(f312(f168(a852),f135(a852,f312(f282(a852,f312(a126,x36591)),f312(a126,x36592)))),f284(a852,x36591,x36592))
% 173.49/173.40 [3683]E(f312(f312(f247(x36831,x36832),f235(f860(x36831,a845))),f312(f16(f860(x36832,a845),x36831),f235(f860(x36832,a845)))),f235(f860(f859(x36831,x36832),a845)))
% 173.49/173.40 [3717]E(f312(f233(x37171),f312(f312(f8(a845,a845,x37171),a307),x37172)),f312(f88(f860(x37171,a845)),f312(f233(x37171),x37172)))
% 173.49/173.40 [3720]E(f312(f233(x37201),f312(f312(f7(x37201,x37201,a845),a309),x37202)),f312(f312(f289(x37201),x37202),f189(f860(x37201,a845))))
% 173.49/173.40 [3727]E(f312(f312(f89(a1),f312(f312(f89(a1),x37271),x37271)),f312(f312(f89(a1),x37272),x37272)),f312(f312(f89(a1),f312(f312(f89(a1),x37271),x37272)),f312(f312(f89(a1),x37271),x37272)))
% 173.49/173.40 [3728]E(f312(f312(f21(a1),f312(f312(f89(a1),x37281),x37281)),f312(f312(f89(a1),x37282),x37282)),f312(f312(f89(a1),f312(f312(f21(a1),x37281),x37282)),f312(f312(f21(a1),x37281),x37282)))
% 173.49/173.40 [3744]P22(f312(f312(f227(a852),f312(f53(x37441),f312(f168(x37441),x37442))),f312(f190(f853(x37441)),x37442)))
% 173.49/173.40 [3745]P22(f312(f312(f227(a852),f312(f190(f853(x37451)),f148(x37451,x37452))),f312(f190(f853(x37451)),x37452)))
% 173.49/173.40 [3754]E(f312(f233(x37541),f312(f312(f7(x37541,f860(x37541,a845),a845),f314(x37541)),x37542)),x37542)
% 173.49/173.40 [3775]E(f312(f312(f169(x37751),f312(f312(f21(a852),f312(f190(f853(x37751)),x37752)),f87(a852))),x37752),f128(x37751,x37752))
% 173.49/173.40 [3791]E(f312(f312(f239(a1,a1),f312(f47(a1,f312(f84(a1),x37911)),f312(f84(a1),x37912))),f54(a1,f312(f84(a1),x37911),f312(f84(a1),x37912))),f61(x37911,x37912))
% 173.49/173.40 [3798]E(f186(a852,f2(a852),f312(f312(f8(a852,a852,a852),a126),f312(f225(a852),x37981)),x37982),f312(f312(f225(a852),f312(a126,x37981)),x37982))
% 173.49/173.40 [3802]E(f48(f860(x38021,a845),f312(f290(f860(f859(x38021,x38021),a845),f860(x38021,a845),f263(x38021)),x38022)),f312(f263(x38021),f48(f860(f859(x38021,x38021),a845),x38022)))
% 173.49/173.40 [3803]E(f186(a852,f312(a126,x38031),f312(f312(f8(a852,a852,a852),a126),f312(f226(a852),x38031)),x38032),f312(f312(f226(a852),f312(a126,x38031)),x38032))
% 173.49/173.40 [3825]P22(f312(f312(f227(f860(f860(x38251,a845),a845)),x38252),f312(f288(x38251),f48(f860(x38251,a845),x38252))))
% 173.49/173.40 [3859]E(f312(f312(f50(x38591,f860(x38591,a845)),x38592),f312(f312(f7(x38591,f860(x38591,a845),f860(x38591,a845)),f289(x38591)),f189(f860(x38591,a845)))),x38592)
% 173.49/173.40 [3860]E(f312(f312(f267(x38601,x38601,x38601),f312(f265(x38601,x38601),x38602)),f287(x38601,f312(f265(x38601,x38601),x38602))),f312(f265(x38601,x38601),f312(f312(f267(x38601,x38601,x38601),x38602),f287(x38601,x38602))))
% 173.49/173.40 [3928]E(f312(f168(x39281),f312(f138(f853(x39281),f853(x39281),f129(x39281),f127(x39281)),x39282)),f312(f312(f50(f853(x39281),f860(x39281,a845)),f312(f168(f853(x39281)),x39282)),f168(x39281)))
% 173.49/173.40 [3958]E(f312(f312(f124(f860(f859(x39581,x39581),a845)),f287(x39581,f189(f860(f859(x39581,x39581),a845)))),f312(f312(f267(x39581,x39581,x39581),f287(x39581,x39582)),x39582)),f287(x39581,x39582))
% 173.49/173.40 [3994]E(f312(f312(f177(x39941,x39941),x39942),x39942),f312(f312(f150(x39941,f859(x39941,x39941)),f312(f312(f18(x39941,x39941,f859(x39941,x39941)),f239(x39941,x39941)),f5(x39941))),x39942))
% 173.49/173.40 [4110]E(f312(f138(a852,f853(x41101),f312(f7(f853(x41101),a852,a852),f312(f312(f8(a852,f860(a852,a852),f853(x41101)),f226(a852)),f190(f853(x41101)))),f2(a852)),f312(f165(f853(x41101)),x41102)),f312(f190(f853(f853(x41101))),f175(x41101,x41102)))
% 173.49/173.40 [4188]E(f312(f312(f266(f859(a852,f853(x41881)),f853(x41881)),f304(a852,f853(x41881),a232,f141(x41881,x41882))),f312(f312(f18(f853(x41881),f853(x41881),f859(a852,f853(x41881))),f312(f312(f8(a852,f860(f853(x41881),f859(a852,f853(x41881))),f853(x41881)),f239(a852,f853(x41881))),f190(f853(x41881)))),f5(f853(x41881)))),f142(x41881,x41882))
% 173.49/173.40 [4313]E(f312(f233(x43131),f312(f312(f8(f860(f860(x43131,a845),a845),a845,x43131),f97(f860(x43131,a845))),f312(f312(f8(f860(f860(x43131,a845),a845),f860(f860(x43131,a845),a845),x43131),f312(f18(f860(x43131,a845),a845,a845),f312(f312(f8(a845,f860(a845,a845),f860(x43131,a845)),a315),f312(f312(f7(f860(x43131,a845),f860(f860(x43131,a845),a845),a845),f314(f860(x43131,a845))),x43132)))),f314(x43131)))),f49(f860(x43131,a845),x43132))
% 173.49/173.40 [4494]~P22(f312(f312(f228(a1),f312(f114(a1),x44941)),f312(f88(a1),f312(f114(a1),x44942))))
% 173.49/173.40 [3400]E(f312(f312(f21(a852),f312(f312(f89(a852),x34001),x34002)),x34002),x34001)
% 173.49/173.40 [3401]E(f312(f312(f21(a852),f312(f312(f89(a852),x34011),x34012)),x34011),x34012)
% 173.49/173.40 [3471]E(f312(f312(f89(a852),f312(f312(f21(a852),x34711),x34712)),x34712),f312(f312(f226(a852),x34711),x34712))
% 173.49/173.40 [3601]E(f312(f168(a852),f135(a852,f312(f282(a852,f312(a126,x36011)),x36012))),f285(a852,x36011,x36012))
% 173.49/173.40 [3607]E(f312(f114(a1),f199(f312(a118,f312(f84(a1),x36071)),f312(a118,f312(f84(a1),x36072)))),f312(f312(a200,x36071),x36072))
% 173.49/173.40 [3609]E(f312(f312(f124(f860(x36091,a845)),f312(f88(f860(x36091,a845)),x36092)),x36092),f235(f860(x36091,a845)))
% 173.49/173.40 [3610]E(f312(f312(f115(f860(x36101,a845)),f312(f88(f860(x36101,a845)),x36102)),x36102),f189(f860(x36101,a845)))
% 173.49/173.40 [3627]P22(f312(f312(f227(a852),f312(f312(f21(a852),x36271),x36272)),x36271))
% 173.49/173.40 [3635]E(f312(f312(f21(a852),x36351),f312(f312(f90(a852),f312(f47(a852,x36351),x36352)),x36352)),f54(a852,x36351,x36352))
% 173.49/173.40 [3636]E(f312(f312(f21(a1),x36361),f312(f312(f90(a1),f312(f47(a1,x36361),x36362)),x36362)),f54(a1,x36361,x36362))
% 173.49/173.40 [3651]P22(f312(f312(f228(a852),x36511),f312(a126,f312(f312(f89(a852),x36512),x36511))))
% 173.49/173.40 [3652]P22(f312(f312(f228(a852),x36521),f312(a126,f312(f312(f89(a852),x36521),x36522))))
% 173.49/173.40 [3669]E(f312(f312(f90(a852),f312(a118,f312(f84(a1),x36691))),f312(a118,f312(f84(a1),x36692))),f312(a118,f312(f84(a1),f312(f312(f90(a1),x36691),x36692))))
% 173.49/173.40 [3679]P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x36791)),x36792)))
% 173.49/173.40 [3749]E(f312(f264(f853(x37491),f853(x37491),f154(x37491,x37492)),f312(f312(f289(f853(x37491)),f127(x37491)),f189(f860(f853(x37491),a845)))),f312(f312(f289(f853(x37491)),f127(x37491)),f189(f860(f853(x37491),a845))))
% 173.49/173.40 [3771]E(f312(f312(f124(f860(f859(x37711,x37711),a845)),f287(x37711,x37712)),f287(x37711,f189(f860(f859(x37711,x37711),a845)))),f287(x37711,x37712))
% 173.49/173.40 [3786]E(f312(f47(a1,f312(f117(a1),f312(f312(f89(a1),x37861),x37861))),f312(f117(a1),f312(f312(f89(a1),x37862),x37862))),f312(f47(a1,f312(f117(a1),x37861)),f312(f117(a1),x37862)))
% 173.49/173.40 [3849]E(f312(f312(f240(a1),x38491),f312(f117(a852),f312(f312(f89(a1),x38492),x38492))),f312(f312(f95(a1,a1),f312(f312(f240(a1),x38491),f312(f117(a852),x38492))),f312(f312(f18(a1,a1,a1),f90(a1)),f5(a1))))
% 173.49/173.40 [3855]E(f312(f233(f860(x38551,a845)),f312(f312(f7(f860(x38551,a845),f860(x38551,a845),a845),f227(f860(x38551,a845))),x38552)),f312(f288(x38551),x38552))
% 173.49/173.40 [3871]E(f312(f312(f150(a1,a852),a118),f312(f312(f129(a1),f312(f312(f150(a852,a1),f114(a1)),x38711)),f312(f312(f150(a852,a1),f114(a1)),x38712))),f312(f312(f129(a852),x38711),x38712))
% 173.49/173.40 [3905]E(f312(f290(a1,a1,f312(f312(f7(a1,a1,a1),f89(a1)),x39051)),f312(f282(a1,f2(a1)),f312(f312(f21(a1),x39052),x39051))),f312(f282(a1,x39051),x39052))
% 173.49/173.40 [3908]P51(x39081,f312(f312(f21(f860(f859(x39081,x39081),a845)),x39082),f287(x39081,f189(f860(f859(x39081,x39081),a845)))))
% 173.49/173.40 [3925]E(f312(f190(f853(x39251)),f312(f138(f853(x39251),f853(x39251),f129(x39251),f127(x39251)),x39252)),f312(f162(a852),f312(f312(f150(f853(x39251),a852),f190(f853(x39251))),x39252)))
% 173.49/173.40 [3931]P50(x39311,f235(f860(x39311,a845)),f312(f312(f124(f860(f859(x39311,x39311),a845)),x39312),f287(x39311,f189(f860(f859(x39311,x39311),a845)))))
% 173.49/173.40 [3974]E(f186(a852,f2(a852),f312(f312(f8(a852,a852,a852),a126),f312(f312(f7(a852,a852,a852),f225(a852)),x39741)),x39742),f312(f312(f225(a852),x39742),f312(a126,x39741)))
% 173.49/173.40 [3977]E(f186(a852,f312(a126,x39771),f312(f312(f8(a852,a852,a852),a126),f312(f312(f7(a852,a852,a852),f226(a852)),x39771)),x39772),f312(f312(f226(a852),x39772),f312(a126,x39771)))
% 173.49/173.40 [3980]E(f312(f290(x39801,f853(x39801),f312(f312(f7(x39801,f853(x39801),f853(x39801)),f147(x39801)),f127(x39801))),x39802),f171(x39801,x39802,f312(f312(f289(f853(x39801)),f127(x39801)),f189(f860(f853(x39801),a845)))))
% 173.49/173.40 [3981]E(f312(f312(f124(f860(f859(x39811,x39811),a845)),f312(f312(f267(x39811,x39811,x39811),x39812),f287(x39811,x39812))),f287(x39811,f189(f860(f859(x39811,x39811),a845)))),f287(x39811,x39812))
% 173.49/173.40 [3989]P22(f312(f312(f227(f860(f859(x39891,x39891),a845)),f237(x39891,x39892)),f312(f312(f247(x39891,x39891),x39892),f312(f16(f860(x39891,a845),x39891),x39892))))
% 173.49/173.40 [3992]E(f312(f290(a1,a852,a118),f312(f312(f124(f860(a1,a845)),f312(f290(a852,a1,f114(a1)),x39921)),f312(f290(a852,a1,f114(a1)),x39922))),f312(f312(f124(f860(a852,a845)),x39921),x39922))
% 173.49/173.40 [3993]E(f312(f290(a1,a852,a118),f312(f312(f115(f860(a1,a845)),f312(f290(a852,a1,f114(a1)),x39931)),f312(f290(a852,a1,f114(a1)),x39932))),f312(f312(f115(f860(a852,a845)),x39931),x39932))
% 173.49/173.40 [3997]E(f312(f233(x39971),f312(f312(f8(a845,a845,x39971),a307),f312(f312(f7(x39971,f860(x39971,a845),a845),f314(x39971)),x39972))),f312(f88(f860(x39971,a845)),x39972))
% 173.49/173.40 [4024]E(f312(f138(f853(x40241),f853(x40241),f129(x40241),f127(x40241)),f312(f312(f150(f853(x40241),f853(x40241)),f165(x40241)),f312(f165(f853(x40241)),x40242))),f312(f165(x40241),f312(f138(f853(x40241),f853(x40241),f129(x40241),f127(x40241)),x40242)))
% 173.49/173.40 [4053]E(f312(f312(f50(a852,f860(f859(x40531,x40531),a845)),f235(f860(a852,a845))),f312(f312(f7(a852,f860(f859(x40531,x40531),a845),f860(f859(x40531,x40531),a845)),f184(f859(x40531,x40531),a845)),x40532)),f287(x40531,x40532))
% 173.49/173.40 [4075]E(f94(x40751,f312(f312(f8(f860(x40751,a845),a845,x40751),f312(a309,x40752)),f312(f312(f7(x40751,f860(x40751,a845),f860(x40751,a845)),f289(x40751)),f189(f860(x40751,a845))))),f292(x40751,x40752))
% 173.49/173.40 [4082]E(f312(f190(f853(x40821)),f148(x40821,f312(f138(f853(x40821),f853(x40821),f129(x40821),f127(x40821)),x40822))),f312(f53(x40821),f312(f312(f50(f853(x40821),f860(x40821,a845)),f312(f168(f853(x40821)),x40822)),f168(x40821))))
% 173.49/173.40 [4098]E(f312(f312(f124(f860(f859(x40981,x40981),a845)),x40982),f312(f312(f267(x40981,x40981,x40981),f312(f312(f267(x40981,x40981,x40981),x40982),f287(x40981,x40982))),x40982)),f312(f312(f267(x40981,x40981,x40981),x40982),f287(x40981,x40982)))
% 173.49/173.40 [4119]P22(f312(f312(f227(f860(f859(x41191,x41191),a845)),f312(f312(f267(x41191,x41191,x41191),x41192),f287(x41191,x41192))),f312(f312(f247(x41191,x41191),f312(f263(x41191),x41192)),f312(f16(f860(x41191,a845),x41191),f312(f263(x41191),x41192)))))
% 173.49/173.40 [4161]E(f312(f233(f853(x41611)),f312(f312(f7(f853(x41611),f860(x41611,a845),a845),f312(f312(f8(f860(x41611,a845),f860(f860(x41611,a845),a845),f853(x41611)),f227(f860(x41611,a845))),f168(x41611))),x41612)),f157(x41611,x41612))
% 173.49/173.40 [4174]E(f312(f152(f853(x41741),x41741,f127(x41741),f312(f312(f8(f853(x41741),f860(f853(x41741),f853(x41741)),x41741),f312(f7(f853(x41741),f853(x41741),f853(x41741)),f129(x41741))),f312(f312(f7(x41741,f853(x41741),f853(x41741)),f147(x41741)),f127(x41741)))),x41742),f312(f164(x41741),x41742))
% 173.49/173.40 [4217]P19(f860(x42171,x42172),f860(f859(x42171,x42172),a845),f312(f312(f8(f860(f859(x42171,x42172),a845),f860(f859(x42171,x42172),a845),f860(x42171,x42172)),f233(f859(x42171,x42172))),f312(f312(f8(f860(x42171,f860(x42172,a845)),f860(f859(x42171,x42172),a845),f860(x42171,x42172)),f249(x42171,x42172,a845)),f312(f8(x42172,f860(x42172,a845),x42171),f312(f7(x42172,x42172,a845),a309)))),f235(f860(f860(x42171,x42172),a845)))
% 173.49/173.40 [4222]E(f54(a1,f312(f117(a1),f312(f312(f89(a1),x42221),x42221)),f312(f117(a1),f312(f312(f89(a1),x42222),x42222))),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a1,f312(f117(a1),x42221),f312(f117(a1),x42222))))
% 173.49/173.40 [4264]E(f312(f312(f50(x42641,f860(f859(x42641,x42641),a845)),x42642),f312(f312(f7(x42641,f860(f859(x42641,x42641),a845),f860(f859(x42641,x42641),a845)),f312(f312(f8(f859(x42641,x42641),f860(f860(f859(x42641,x42641),a845),f860(f859(x42641,x42641),a845)),x42641),f289(f859(x42641,x42641))),f312(f312(f18(x42641,x42641,f859(x42641,x42641)),f239(x42641,x42641)),f5(x42641)))),f189(f860(f859(x42641,x42641),a845)))),f237(x42641,x42642))
% 173.49/173.40 [4348]E(f312(f233(f860(x43481,a845)),f312(f312(f8(f860(f860(x43481,a845),a845),a845,f860(x43481,a845)),f96(f860(x43481,a845))),f312(f312(f7(f860(x43481,a845),f860(f860(x43481,a845),a845),f860(f860(x43481,a845),a845)),f312(f312(f8(f860(f860(x43481,a845),f860(a845,a845)),f860(f860(f860(x43481,a845),a845),f860(f860(x43481,a845),a845)),f860(x43481,a845)),f18(f860(x43481,a845),a845,a845)),f312(f312(f8(f860(f860(x43481,a845),a845),f860(f860(x43481,a845),f860(a845,a845)),f860(x43481,a845)),f312(f8(a845,f860(a845,a845),f860(x43481,a845)),a310)),f312(f312(f7(f860(x43481,a845),f860(f860(x43481,a845),f860(x43481,a845)),f860(f860(x43481,a845),a845)),f312(f312(f8(f860(f860(x43481,a845),a845),f860(f860(f860(x43481,a845),f860(x43481,a845)),f860(f860(x43481,a845),a845)),f860(x43481,a845)),f8(f860(x43481,a845),a845,f860(x43481,a845))),a309)),f88(f860(x43481,a845)))))),f312(f312(f8(f860(f860(x43481,a845),a845),a845,f860(x43481,a845)),f312(f314(f860(x43481,a845)),x43482)),f288(x43481))))),f312(f288(x43481),f312(f88(f860(x43481,a845)),x43482)))
% 173.49/173.40 [4491]~E(f312(f312(f89(a1),x44911),x44911),f312(f312(f21(a1),f312(f312(f89(a1),x44912),x44912)),a111))
% 173.49/173.40 [4496]~P22(f312(f312(f228(a852),f312(f312(f89(a852),x44961),x44962)),x44962))
% 173.49/173.40 [4497]~P22(f312(f312(f228(a852),f312(f312(f89(a852),x44971),x44972)),x44971))
% 173.49/173.40 [3718]E(f312(f312(f150(a852,x37181),f312(f161(x37181),x37182)),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(x37181)),x37182)))),x37182)
% 173.49/173.40 [3783]E(f312(f264(x37831,x37831,f287(x37831,f189(f860(f859(x37831,x37831),a845)))),x37832),x37832)
% 173.49/173.40 [3909]E(f287(x39091,f312(f312(f21(f860(f859(x39091,x39091),a845)),x39092),f287(x39091,f189(f860(f859(x39091,x39091),a845))))),f287(x39091,x39092))
% 173.49/173.40 [3910]E(f287(x39101,f312(f312(f124(f860(f859(x39101,x39101),a845)),x39102),f287(x39101,f189(f860(f859(x39101,x39101),a845))))),f287(x39101,x39102))
% 173.49/173.40 [3961]E(f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x39611),x39611)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x39612),x39612)),a111)),f312(f312(f89(a1),f312(f312(f21(a1),x39611),x39612)),f312(f312(f21(a1),x39611),x39612)))
% 173.49/173.40 [4002]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x40021),x40022)),f312(f312(f89(a1),x40021),x40022))),a111),f312(f312(f89(a1),f312(f312(f89(a1),x40021),x40021)),f312(f312(f21(a1),f312(f312(f89(a1),x40022),x40022)),a111)))
% 173.49/173.40 [4028]E(f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40281),x40281)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x40282),x40282)),a111)),f312(f312(f89(a1),f312(f312(f89(a1),x40281),f312(f312(f21(a1),x40282),a111))),f312(f312(f89(a1),x40281),f312(f312(f21(a1),x40282),a111))))
% 173.49/173.40 [4039]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x40391),x40392)),f312(f312(f89(a1),x40391),x40392))),a111),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40391),x40391)),a111)),f312(f312(f89(a1),x40392),x40392)))
% 173.49/173.40 [4040]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),x40401),x40402)),f312(f312(f21(a1),x40401),x40402))),a111),f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40401),x40401)),a111)),f312(f312(f89(a1),x40402),x40402)))
% 173.49/173.40 [4093]E(f312(f114(a1),f312(f47(a852,f312(f312(f90(a852),f312(a118,f312(f84(a1),x40931))),f312(a118,f312(f84(a1),x40932)))),f199(f312(a118,f312(f84(a1),x40931)),f312(a118,f312(f84(a1),x40932))))),f208(x40931,x40932))
% 173.49/173.40 [4138]E(f312(f312(f251(f859(a113,a113),a113,f859(a113,a113),f859(x41381,f859(a113,a113))),f255(f312(a3,f312(f190(f853(x41381)),x41382)))),f312(f312(f8(x41381,f860(f859(a113,a113),f859(x41381,f859(a113,a113))),a113),f239(x41381,f859(a113,a113))),f312(f312(f8(a852,x41381,a113),f312(f161(x41381),x41382)),a19))),f261(x41381,x41382))
% 173.49/173.40 [4223]E(f312(f138(a852,f853(x42231),f312(f7(f853(x42231),a852,a852),f312(f312(f8(a852,f860(a852,a852),f853(x42231)),f226(a852)),f190(f853(x42231)))),f2(a852)),f312(f165(f853(x42231)),f175(x42231,x42232))),f312(f190(f853(f853(x42231))),f312(f132(f853(x42231),f312(f312(f8(a845,a845,f853(x42231)),a307),f312(f312(f7(f853(x42231),f853(x42231),a845),a309),f127(x42231)))),x42232)))
% 173.49/173.40 [4229]E(f312(f312(f50(a852,f860(x42291,a845)),f235(f860(a852,a845))),f312(f312(f7(a852,f860(a852,f860(x42291,a845)),f860(x42291,a845)),f312(f312(f8(f860(a852,a845),f860(f860(a852,f860(x42291,a845)),f860(x42291,a845)),a852),f50(a852,f860(x42291,a845))),f282(a852,f2(a852)))),x42292)),f312(f312(f50(a852,f860(x42291,a845)),f235(f860(a852,a845))),x42292))
% 173.49/173.40 [4248]P22(f312(f70(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),x42481)),f312(f312(f7(a852,a852,a845),f228(a852)),x42482)))))
% 173.49/173.40 [4357]E(f312(f233(f859(f853(x43571),f853(x43571))),f312(f249(f853(x43571),f853(x43571),a845),f312(f312(f18(f853(x43571),f860(f853(x43571),a845),f860(f853(x43571),a845)),f312(f312(f8(f860(f853(x43571),f860(a845,a845)),f860(f860(f853(x43571),a845),f860(f853(x43571),a845)),f853(x43571)),f18(f853(x43571),a845,a845)),f312(f312(f8(f860(f853(x43571),a845),f860(f853(x43571),f860(a845,a845)),f853(x43571)),f312(f8(a845,f860(a845,a845),f853(x43571)),a311)),f312(f312(f7(f853(x43571),f860(f853(x43571),a852),f860(f853(x43571),a845)),f312(f312(f8(f860(a852,a845),f860(f860(f853(x43571),a852),f860(f853(x43571),a845)),f853(x43571)),f8(a852,a845,f853(x43571))),f312(f312(f8(a852,f860(a852,a845),f853(x43571)),f228(a852)),f190(f853(x43571))))),f190(f853(x43571)))))),f312(f312(f18(f853(x43571),f860(f853(x43571),a845),f860(f853(x43571),a845)),f312(f312(f8(f860(f853(x43571),f860(a845,a845)),f860(f860(f853(x43571),a845),f860(f853(x43571),a845)),f853(x43571)),f18(f853(x43571),a845,a845)),f312(f312(f8(f860(f853(x43571),a845),f860(f853(x43571),f860(a845,a845)),f853(x43571)),f312(f8(a845,f860(a845,a845),f853(x43571)),a310)),f312(f312(f7(f853(x43571),f860(f853(x43571),a852),f860(f853(x43571),a845)),f312(f312(f8(f860(a852,a845),f860(f860(f853(x43571),a852),f860(f853(x43571),a845)),f853(x43571)),f8(a852,a845,f853(x43571))),f312(f312(f8(a852,f860(a852,a845),f853(x43571)),a309),f190(f853(x43571))))),f190(f853(x43571)))))),f312(f312(f7(f853(x43571),f860(f859(f853(x43571),f853(x43571)),a845),f860(f853(x43571),a845)),f312(f312(f8(f860(f853(x43571),f860(f860(f859(f853(x43571),f853(x43571)),a845),a845)),f860(f860(f859(f853(x43571),f853(x43571)),a845),f860(f853(x43571),a845)),f853(x43571)),f7(f853(x43571),f860(f859(f853(x43571),f853(x43571)),a845),a845)),f312(f312(f8(f860(f853(x43571),f859(f853(x43571),f853(x43571))),f860(f853(x43571),f860(f860(f859(f853(x43571),f853(x43571)),a845),a845)),f853(x43571)),f312(f8(f859(f853(x43571),f853(x43571)),f860(f860(f859(f853(x43571),f853(x43571)),a845),a845),f853(x43571)),f314(f859(f853(x43571),f853(x43571))))),f239(f853(x43571),f853(x43571))))),f141(x43571,x43572)))))),f142(x43571,x43572))
% 173.49/173.40 [4031]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),x40311),x40312)),f312(f312(f90(a1),x40311),x40312))),x40312),f312(f312(f90(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40311),x40311)),a111)),x40312))
% 173.49/173.40 [4136]E(f312(a118,f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x41361),x41362)),f189(f860(f859(a852,a852),a845)))))),f312(f312(f21(a852),x41361),x41362))
% 173.49/173.40 [4141]E(f312(f312(f267(x41411,x41411,x41411),f312(f312(f124(f860(f859(x41411,x41411),a845)),x41412),f287(x41411,f189(f860(f859(x41411,x41411),a845))))),f287(x41411,f312(f312(f124(f860(f859(x41411,x41411),a845)),x41412),f287(x41411,f189(f860(f859(x41411,x41411),a845)))))),f287(x41411,x41412))
% 173.49/173.40 [4181]E(f254(x41811,f312(f132(f859(a113,x41811),f312(f249(a113,x41811,a845),f312(f312(f8(a845,f860(x41811,a845),a113),f16(a845,x41811)),f312(f228(a113),f2(a113))))),x41812)),f254(x41811,x41812))
% 173.49/173.40 [4182]E(f256(x41821,f312(f132(f859(a113,x41821),f312(f249(a113,x41821,a845),f312(f312(f8(a845,f860(x41821,a845),a113),f16(a845,x41821)),f312(f228(a113),f2(a113))))),x41822)),f256(x41821,x41822))
% 173.49/173.40 [4184]E(f312(f88(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x41841),x41842)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x41842),x41841)),f189(f860(f859(a852,a852),a845))))))
% 173.49/173.41 [4240]E(f312(f312(f266(f853(a852),x42401),f141(a852,a232)),f312(f312(f7(x42401,f853(f860(x42401,a852)),f853(a852)),f312(f312(f8(f860(f860(x42401,a852),a852),f860(f853(f860(x42401,a852)),f853(a852)),x42401),f150(f860(x42401,a852),a852)),f312(f7(f860(x42401,a852),x42401,a852),f5(f860(x42401,a852))))),x42402)),f149(x42401,x42402))
% 173.49/173.41 [4261]E(f312(f312(f95(a1,a852),f312(f117(a1),f312(f312(f89(a1),x42611),a111))),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f2(a852))),f312(f312(f8(a852,a852,a1),a126),f312(f312(f8(a852,a852,a1),f312(f225(a852),x42612)),a118)))),f312(f312(f225(a852),f312(a126,x42612)),f312(f117(a852),x42611)))
% 173.49/173.41 [4262]E(f312(f312(f95(a1,a852),f312(f117(a1),f312(f312(f89(a1),x42621),a111))),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f312(a126,x42622))),f312(f312(f8(a852,a852,a1),a126),f312(f312(f8(a852,a852,a1),f312(f226(a852),x42622)),a118)))),f312(f312(f226(a852),f312(a126,x42622)),f312(f117(a852),x42621)))
% 173.49/173.41 [4281]E(f312(f138(f853(x42811),f853(x42811),f129(x42811),f127(x42811)),f312(f312(f150(f853(x42811),f853(x42811)),f152(f853(x42811),x42811,f127(x42811),f312(f312(f8(f853(x42811),f860(f853(x42811),f853(x42811)),x42811),f16(f853(x42811),f853(x42811))),f312(f312(f7(x42811,f853(x42811),f853(x42811)),f147(x42811)),f127(x42811))))),x42812)),f312(f312(f150(f853(x42811),x42811),f137(x42811)),f312(f132(f853(x42811),f312(f312(f8(a845,a845,f853(x42811)),a307),f312(f312(f7(f853(x42811),f853(x42811),a845),a309),f127(x42811)))),x42812)))
% 173.49/173.41 [4338]E(f312(f249(a1,a1,a845),f312(f312(f7(a1,f860(a1,a845),f860(a1,a845)),f312(f312(f8(f860(a1,f860(a845,a845)),f860(f860(a1,a845),f860(a1,a845)),a1),f18(a1,a845,a845)),f312(f312(f8(f860(a1,a845),f860(a1,f860(a845,a845)),a1),f312(f8(a845,f860(a845,a845),a1),a310)),f312(f312(f8(f860(a1,a1),f860(a1,a845),a1),f312(f8(a1,a845,a1),f312(a309,x43381))),f312(f312(f8(a1,f860(a1,a1),a1),f89(a1)),f312(f90(a1),x43382)))))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),f312(a315,f312(f312(f228(a1),f2(a1)),x43382))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f227(a1),f2(a1)))),f312(f312(f7(a1,a1,a845),f228(a1)),x43382))))),f312(f312(f8(a845,a845,a1),f312(a315,f312(a307,f312(f312(f228(a1),f2(a1)),x43382)))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f228(a1),x43382))),f312(f312(f7(a1,a1,a845),f227(a1)),f2(a1))))))),f57(x43381,x43382))
% 173.49/173.41 [4340]E(f312(f233(x43401),f312(f312(f8(f860(a852,a845),a845,x43401),f96(a852)),f312(f312(f7(x43401,f860(a852,a845),f860(a852,a845)),f312(f312(f8(f860(a852,f860(a845,a845)),f860(f860(a852,a845),f860(a852,a845)),x43401),f18(a852,a845,a845)),f312(f312(f8(f860(a852,a845),f860(a852,f860(a845,a845)),x43401),f312(f8(a845,f860(a845,a845),a852),a310)),f312(f312(f7(x43401,f860(a852,x43401),f860(a852,a845)),f312(f312(f8(f860(x43401,a845),f860(f860(a852,x43401),f860(a852,a845)),x43401),f8(x43401,a845,a852)),a309)),f312(f161(x43401),x43402))))),f312(f312(f7(a852,a852,a845),f228(a852)),f312(f190(f853(x43401)),x43402))))),f312(f168(x43401),x43402))
% 173.49/173.41 [4151]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x41511),a111)),x41512)),f312(f312(f21(a1),f312(f312(f89(a1),x41511),a111)),x41512))),a111),f312(f312(f21(a1),f312(f312(f89(a1),x41511),x41511)),f312(f312(f21(a1),f312(f312(f89(a1),x41512),x41512)),a111)))
% 173.49/173.41 [4276]E(f312(f138(f853(f853(x42761)),f853(f853(x42761)),f129(f853(x42761)),f127(f853(x42761))),f312(f312(f150(f853(x42761),f853(f853(x42761))),f152(f853(f853(x42761)),x42761,f127(f853(x42761)),f312(f16(f860(f853(x42761),f853(f853(x42761))),x42761),f312(f312(f7(f853(x42761),f853(f853(x42761)),f853(f853(x42761))),f147(f853(x42761))),f127(f853(x42761)))))),x42762)),f312(f312(f150(f853(x42761),f853(x42761)),f167(x42761)),f312(f132(f853(x42761),f312(f312(f8(a845,a845,f853(x42761)),a307),f312(f312(f7(f853(x42761),f853(x42761),a845),a309),f127(x42761)))),x42762)))
% 173.49/173.41 [4286]E(f312(f312(f95(a1,a852),f312(f117(a1),f312(f312(f89(a1),x42861),a111))),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f2(a852))),f312(f312(f8(a852,a852,a1),a126),f312(f312(f7(a1,a852,a852),f312(f312(f8(a852,f860(a852,a852),a1),f225(a852)),a118)),x42862)))),f312(f312(f225(a852),f312(f117(a852),x42861)),f312(a126,x42862)))
% 173.49/173.41 [4287]E(f312(f312(f95(a1,a852),f312(f117(a1),f312(f312(f89(a1),x42871),a111))),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f312(a126,x42872))),f312(f312(f8(a852,a852,a1),a126),f312(f312(f7(a1,a852,a852),f312(f312(f8(a852,f860(a852,a852),a1),f226(a852)),a118)),x42872)))),f312(f312(f226(a852),f312(f117(a852),x42871)),f312(a126,x42872)))
% 173.49/173.41 [4275]E(f312(f249(x42751,x42751,a845),f312(f312(f18(x42751,a845,f860(x42751,a845)),f312(f312(f8(f860(x42751,f860(a845,a845)),f860(a845,f860(x42751,a845)),x42751),f7(x42751,a845,a845)),f312(f312(f8(f860(x42751,a845),f860(x42751,f860(a845,a845)),x42751),f312(f8(a845,f860(a845,a845),x42751),a310)),a309))),x42752)),f237(x42751,x42752))
% 173.49/173.41 [4318]E(f312(f47(a852,x43181),f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x43182)),f312(f47(a852,x43181),f312(a126,f312(a126,f312(a126,x43182)))))
% 173.49/173.41 [4319]E(f54(a852,x43191,f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x43192)),f54(a852,x43191,f312(a126,f312(a126,f312(a126,x43192)))))
% 173.49/173.41 [4320]E(f54(a852,f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x43201),x43202),f54(a852,f312(a126,f312(a126,f312(a126,x43201))),x43202))
% 173.49/173.41 [4331]E(f130(f312(x43311,f312(f312(f90(a113),f312(f117(a113),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x43312))),f312(f206(x43311),x43312))
% 173.49/173.41 [4332]E(f312(f47(a852,f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),x43321)),x43322),f312(f47(a852,f312(a126,f312(a126,f312(a126,x43321)))),x43322))
% 173.49/173.41 [3428]P36(x34281,x34282,x34283,x34283)
% 173.49/173.41 [4401]~E(f36(x44011,x44012),f312(a27,x44013))
% 173.49/173.41 [4402]~E(f35(x44021,x44022),f312(a27,x44023))
% 173.49/173.41 [4403]~E(f28(x44031,x44032),f312(a27,x44033))
% 173.49/173.41 [4404]~E(f312(a27,x44041),f36(x44042,x44043))
% 173.49/173.41 [4405]~E(f312(a27,x44051),f35(x44052,x44053))
% 173.49/173.41 [4406]~E(f312(a27,x44061),f28(x44062,x44063))
% 173.49/173.41 [4425]~E(f33(x44251,x44252,x44253),a23)
% 173.49/173.41 [4426]~E(f32(x44261,x44262,x44263),a23)
% 173.49/173.41 [4427]~E(f31(x44271,x44272,x44273),a23)
% 173.49/173.41 [3213]E(f312(f312(f193(x32131,x32132),x32133),f192(x32131)),f192(x32132))
% 173.49/173.41 [3214]E(f312(f312(f150(x32141,x32142),x32143),f127(x32141)),f127(x32142))
% 173.49/173.41 [3233]E(f34(f31(x32331,x32332,x32333)),f2(a852))
% 173.49/173.41 [3254]E(f312(f185(x32541,x32542,x32543),f2(a852)),x32542)
% 173.49/173.41 [3255]E(f312(f190(a846),f31(x32551,x32552,x32553)),f2(a852))
% 173.49/173.41 [3257]E(f312(f312(f177(x32571,x32572),x32573),f127(x32572)),f127(f859(x32571,x32572)))
% 173.49/173.41 [3291]E(f94(x32911,f71(x32911,x32912,x32913)),f312(f72(x32911,x32912),x32913))
% 173.49/173.41 [3343]E(f136(x33431,x33432,f148(x33431,x33433)),f148(x33431,f136(x33431,x33432,x33433)))
% 173.49/173.41 [3363]E(f312(f246(f853(x33631),f853(x33631)),f163(x33631,x33632,x33633)),f312(f132(x33631,x33632),x33633))
% 173.49/173.41 [3441]E(f186(x34411,x34412,x34413,f2(a852)),x34412)
% 173.49/173.41 [3442]E(f17(x34421,x34422,x34423,f2(a113)),x34422)
% 173.49/173.41 [3448]E(f159(x34481,x34482,x34483,f127(x34481)),f127(x34482))
% 173.49/173.41 [3449]E(f160(x34491,x34492,x34493,f127(x34491)),f127(x34492))
% 173.49/173.41 [3455]E(f312(f312(f161(x34551),f312(f312(f147(x34551),x34552),x34553)),f2(a852)),x34552)
% 173.49/173.41 [3489]E(f68(x34891,x34892,f127(x34891),x34893),f127(f859(x34891,x34892)))
% 173.49/173.41 [3508]P19(x35081,x35082,x35083,f189(f860(x35081,a845)))
% 173.49/173.41 [3553]P36(x35531,x35532,f312(f16(f856(x35532),x35531),f192(x35532)),x35533)
% 173.49/173.41 [3661]E(f312(f82(x36611,x36612,x36611,x36613),f39(x36611)),x36613)
% 173.49/173.41 [3840]P22(f312(f312(f314(f859(x38401,x38401)),f312(f312(f239(x38401,x38401),x38402),x38402)),f287(x38401,x38403)))
% 173.49/173.41 [4501]~P22(f312(f312(f314(f859(f853(x45011),f853(x45011))),f312(f312(f239(f853(x45011),f853(x45011)),x45012),f127(x45011))),f141(x45011,x45013)))
% 173.49/173.41 [4502]~P22(f312(f312(f314(f859(f853(x45021),f853(x45021))),f312(f312(f239(f853(x45021),f853(x45021)),x45022),f127(x45021))),f143(x45021,x45023)))
% 173.49/173.41 [4503]~P22(f312(f312(f314(f859(f853(x45031),f853(x45031))),f312(f312(f239(f853(x45031),f853(x45031)),x45032),f127(x45031))),f153(x45031,x45033)))
% 173.49/173.41 [4504]~P22(f312(f312(f314(f859(f853(x45041),f853(x45041))),f312(f312(f239(f853(x45041),f853(x45041)),f127(x45041)),x45042)),f141(x45041,x45043)))
% 173.49/173.41 [4505]~P22(f312(f312(f314(f859(f853(x45051),f853(x45051))),f312(f312(f239(f853(x45051),f853(x45051)),f127(x45051)),x45052)),f153(x45051,x45053)))
% 173.49/173.41 [3226]E(f312(f312(f197(x32261,x32262),f192(x32261)),x32263),f192(x32262))
% 173.49/173.41 [3243]E(f312(f265(x32431,x32432),f312(f265(x32432,x32431),x32433)),x32433)
% 173.49/173.41 [3267]E(f312(f312(f177(x32671,x32672),f127(x32671)),x32673),f127(f859(x32671,x32672)))
% 173.49/173.41 [3270]E(f170(x32701,x32702,f312(f279(a852),x32703)),f312(f312(f169(x32701),x32703),x32702))
% 173.49/173.41 [3287]E(f148(x32871,f312(f132(x32871,x32872),x32873)),f312(f132(x32871,x32872),f148(x32871,x32873)))
% 173.49/173.41 [3289]E(f312(f236(x32891,x32892),f312(f265(x32892,x32891),x32893)),f312(f238(x32892,x32891),x32893))
% 173.49/173.41 [3290]E(f312(f238(x32901,x32902),f312(f265(x32902,x32901),x32903)),f312(f236(x32902,x32901),x32903))
% 173.49/173.41 [3308]E(f312(f132(x33081,x33082),f312(f165(x33081),x33083)),f312(f165(x33081),f312(f132(x33081,x33082),x33083)))
% 173.49/173.41 [3322]E(f312(f312(f134(x33221),x33222),f312(f167(x33221),x33223)),f312(f312(f134(x33221),f312(a126,x33222)),x33223))
% 173.49/173.41 [3338]E(f34(f32(x33381,x33382,x33383)),f312(f312(f89(a852),f34(x33383)),f312(a126,f2(a852))))
% 173.49/173.41 [3339]E(f312(f290(x33391,x33392,x33393),f189(f860(x33391,a845))),f189(f860(x33392,a845)))
% 173.49/173.41 [3340]E(f312(f291(x33401,x33402,x33403),f189(f860(x33402,a845))),f189(f860(x33401,a845)))
% 173.49/173.41 [3341]E(f312(f291(x33411,x33412,x33413),f235(f860(x33412,a845))),f235(f860(x33411,a845)))
% 173.49/173.41 [3342]E(f312(f264(x33421,x33422,x33423),f189(f860(x33421,a845))),f189(f860(x33422,a845)))
% 173.49/173.41 [3362]E(f312(f312(f197(x33621,x33622),x33623),f312(f16(f856(x33622),x33621),f192(x33622))),f192(x33622))
% 173.49/173.41 [3371]E(f312(f312(f289(x33711),x33712),f312(f168(x33711),x33713)),f312(f168(x33711),f136(x33711,x33712,x33713)))
% 173.49/173.41 [3383]E(f220(x33831,x33832,f312(f219(x33831),x33833)),f312(f312(f89(a852),f312(x33832,x33833)),f312(a126,f2(a852))))
% 173.49/173.41 [3459]E(f312(f190(a846),f32(x34591,x34592,x34593)),f312(f312(f89(a852),f312(f190(a846),x34593)),f312(a126,f2(a852))))
% 173.49/173.41 [3460]E(f312(f290(f859(x34601,x34602),x34602,f248(x34601,x34602)),x34603),f312(f236(x34601,x34602),x34603))
% 173.49/173.41 [3461]E(f312(f290(f859(x34611,x34612),x34611,f246(x34611,x34612)),x34613),f312(f238(x34611,x34612),x34613))
% 173.49/173.41 [3532]E(f312(f312(f239(x35321,x35322),f312(f246(x35321,x35322),x35323)),f312(f248(x35321,x35322),x35323)),x35323)
% 173.49/173.41 [3542]E(f312(f312(f249(x35421,x35422,x35421),f16(x35421,x35422)),x35423),f312(f246(x35421,x35422),x35423))
% 173.49/173.41 [3562]E(f180(x35621,x35622,x35623,f312(f16(f856(x35622),x35621),f192(x35622))),x35623)
% 173.49/173.41 [3563]E(f180(x35631,x35632,f312(f16(f856(x35632),x35631),f192(x35632)),x35633),x35633)
% 173.49/173.41 [3616]E(f34(f33(x36161,x36162,x36163)),f312(f312(f89(a852),f312(f312(f89(a852),f34(x36162)),f34(x36163))),f312(a126,f2(a852))))
% 173.49/173.41 [3664]E(f312(f82(x36641,x36641,x36642,f39(x36641)),x36643),x36643)
% 173.49/173.41 [3774]P22(f312(f312(f195(f28(x37741,x37742)),x37743),f312(f312(f312(a201,x37743),x37741),f312(x37742,x37743))))
% 173.49/173.41 [3776]E(f312(f190(a846),f33(x37761,x37762,x37763)),f312(f312(f89(a852),f312(f312(f89(a852),f312(f190(a846),x37762)),f312(f190(a846),x37763))),f312(a126,f2(a852))))
% 173.49/173.41 [3850]P22(f312(f312(f227(f860(x38501,a845)),f312(f168(x38501),f312(f132(x38501,x38502),x38503))),f312(f168(x38501),x38503)))
% 173.49/173.41 [3896]P22(f312(f312(f227(f860(x38961,a845)),f312(f168(x38961),f312(f312(f169(x38961),x38962),x38963))),f312(f168(x38961),x38963)))
% 173.49/173.41 [3897]P22(f312(f312(f227(f860(x38971,a845)),f312(f168(x38971),f312(f312(f134(x38971),x38972),x38973))),f312(f168(x38971),x38973)))
% 173.49/173.41 [3901]P22(f312(f312(f227(f860(x39011,a845)),f312(f168(x39011),f166(x39011,x39012,x39013))),f312(f168(x39011),x39013)))
% 173.49/173.41 [3902]P22(f312(f312(f227(f860(x39021,a845)),f312(f168(x39021),f170(x39021,x39022,x39023))),f312(f168(x39021),x39022)))
% 173.49/173.41 [3923]P19(f859(x39231,x39232),f859(x39232,x39231),f312(f249(x39231,x39232,f859(x39232,x39231)),f312(f7(x39232,x39231,f859(x39232,x39231)),f239(x39232,x39231))),x39233)
% 173.49/173.41 [3936]E(f312(f312(f312(f184(f853(x39361),f853(x39361)),f54(a852,x39362,f312(f190(f853(x39361)),x39363))),f164(x39361)),x39363),f312(f312(f312(f184(f853(x39361),f853(x39361)),x39362),f164(x39361)),x39363))
% 173.49/173.41 [3978]P22(f312(f312(f314(f859(f853(x39781),f853(x39781))),f312(f312(f239(f853(x39781),f853(x39781)),x39782),x39782)),f154(x39781,f287(x39781,x39783))))
% 173.49/173.41 [4121]E(f94(f859(x41211,x41212),f312(f312(f18(f859(x41211,x41212),x41212,a845),f312(f312(f8(x41211,f860(x41212,a845),f859(x41211,x41212)),x41213),f246(x41211,x41212))),f248(x41211,x41212))),f94(f859(x41211,x41212),f312(f249(x41211,x41212,a845),x41213)))
% 173.49/173.41 [4122]E(f99(f859(x41221,x41222),f312(f312(f18(f859(x41221,x41222),x41222,a845),f312(f312(f8(x41221,f860(x41222,a845),f859(x41221,x41222)),x41223),f246(x41221,x41222))),f248(x41221,x41222))),f99(f859(x41221,x41222),f312(f249(x41221,x41222,a845),x41223)))
% 173.49/173.41 [4158]E(f312(f312(f266(f859(a852,x41581),x41581),f304(a852,x41581,a232,x41582)),f312(f312(f18(x41581,x41581,f859(a852,x41581)),f312(f312(f8(a852,f860(x41581,f859(a852,x41581)),x41581),f239(a852,x41581)),x41583)),f5(x41581))),f306(x41581,x41583,x41582))
% 173.49/173.41 [4225]E(f312(f250(x42251,x42251,x42252,x42252,f5(x42251),f5(x42252)),x42253),x42253)
% 173.49/173.41 [4297]E(f312(f138(f853(f853(x42971)),f853(f853(x42971)),f129(f853(x42971)),f127(f853(x42971))),f312(f312(f150(f853(x42971),f853(f853(x42971))),f312(f312(f7(f853(x42971),f853(x42971),f853(f853(x42971))),f312(f312(f8(f860(x42971,f853(x42971)),f860(f853(x42971),f853(f853(x42971))),f853(x42971)),f150(x42971,f853(x42971))),f312(f7(x42971,f853(x42971),f853(x42971)),f147(x42971)))),x42972)),f63(x42971,x42973,x42972))),f63(x42971,f312(a126,x42973),x42972))
% 173.49/173.41 [4420]~E(f312(f312(f147(x44201),x44202),x44203),x44203)
% 173.49/173.41 [4429]~E(f312(f312(f147(x44291),x44292),x44293),f127(x44291))
% 173.49/173.41 [4456]~E(f312(f312(f289(x44561),x44562),x44563),f189(f860(x44561,a845)))
% 173.49/173.41 [4482]~E(f312(f290(x44821,f860(x44821,a845),x44822),x44823),f312(f288(x44821),x44823))
% 173.49/173.41 [3248]E(f312(f312(f155(x32481,f127(x32481)),x32482),x32483),f127(x32481))
% 173.49/173.41 [3249]E(f312(f137(x32491),f312(f312(f147(x32491),x32492),x32493)),x32492)
% 173.49/173.41 [3250]E(f312(f167(x32501),f312(f312(f147(x32501),x32502),x32503)),x32503)
% 173.49/173.41 [3294]E(f312(f312(f134(x32941),f87(a852)),f312(f312(f147(x32941),x32942),x32943)),x32943)
% 173.49/173.41 [3328]E(f128(x33281,f312(f312(f134(x33281),x33282),x33283)),f312(f312(f134(x33281),x33282),f128(x33281,x33283)))
% 173.49/173.41 [3330]E(f312(f312(f155(x33301,x33302),x33303),f312(f312(f161(x33301),x33302),x33303)),x33302)
% 173.49/173.41 [3353]E(f312(f312(f289(x33531),x33532),f312(f312(f289(x33531),x33532),x33533)),f312(f312(f289(x33531),x33532),x33533))
% 173.49/173.41 [3365]E(f312(f312(f173(x33651,x33652),f127(f859(x33651,x33652))),x33653),f192(x33652))
% 173.49/173.41 [3368]E(f312(f312(f289(x33681),x33682),f312(f168(x33681),x33683)),f312(f168(x33681),f312(f312(f147(x33681),x33682),x33683)))
% 173.49/173.41 [3370]E(f312(f312(f134(x33701),x33702),f312(f167(x33701),x33703)),f312(f167(x33701),f312(f312(f134(x33701),x33702),x33703)))
% 173.49/173.41 [3380]E(f312(f312(f169(x33801),f87(a852)),f312(f312(f147(x33801),x33802),x33803)),f312(f312(f147(x33801),x33802),f127(x33801)))
% 173.49/173.41 [3427]E(f312(f72(x34271,x34272),f312(f312(f289(x34271),x34273),f189(f860(x34271,a845)))),x34273)
% 173.49/173.41 [3473]E(f312(f312(f89(a852),x34731),f312(f312(f89(a852),x34732),x34733)),f312(f312(f89(a852),x34732),f312(f312(f89(a852),x34731),x34733)))
% 173.49/173.41 [3474]E(f312(f312(f89(a1),x34741),f312(f312(f89(a1),x34742),x34743)),f312(f312(f89(a1),x34742),f312(f312(f89(a1),x34741),x34743)))
% 173.49/173.41 [3479]E(f312(f312(f247(x34791,x34792),f189(f860(x34791,a845))),x34793),f189(f860(f859(x34791,x34792),a845)))
% 173.49/173.41 [3499]E(f312(f312(f124(f860(x34991,a845)),x34992),x34993),f312(f312(f124(f860(x34991,a845)),x34993),x34992))
% 173.49/173.41 [3500]E(f312(f312(f115(f860(x35001,a845)),x35002),x35003),f312(f312(f115(f860(x35001,a845)),x35003),x35002))
% 173.49/173.41 [3503]E(f312(f312(f129(x35031),x35032),f312(f312(f147(x35031),x35033),f127(x35031))),f312(f164(x35031),f312(f312(f147(x35031),x35033),x35032)))
% 173.49/173.41 [3504]E(f312(f312(f129(x35041),f312(f165(x35041),x35042)),f312(f165(x35041),x35043)),f312(f165(x35041),f312(f312(f129(x35041),x35043),x35042)))
% 173.49/173.41 [3512]E(f312(f167(x35121),f312(f312(f169(x35121),f312(a126,x35122)),x35123)),f312(f312(f169(x35121),x35122),f312(f167(x35121),x35123)))
% 173.49/173.41 [3516]E(f312(f47(a852,x35161),f312(f312(f90(a852),x35162),x35163)),f312(f47(a852,f312(f47(a852,x35161),x35162)),x35163))
% 173.49/173.41 [3519]P22(f312(f312(f314(x35191),x35192),f312(f312(f289(x35191),x35192),x35193)))
% 173.49/173.41 [3523]E(f312(f312(f51(x35231,f860(x35232,a845)),f189(f860(x35231,a845))),x35233),f235(f860(x35232,a845)))
% 173.49/173.41 [3525]E(f312(f264(x35251,x35251,f237(x35251,x35252)),x35253),f312(f312(f115(f860(x35251,a845)),x35252),x35253))
% 173.49/173.41 [3538]E(f312(f190(f853(x35381)),f312(f312(f147(x35381),x35382),x35383)),f312(f312(f89(a852),f312(f190(f853(x35381)),x35383)),f312(a126,f2(a852))))
% 173.49/173.41 [3544]E(f128(x35441,f312(f312(f129(x35441),x35442),f312(f312(f147(x35441),x35443),f127(x35441)))),x35442)
% 173.49/173.41 [3545]E(f140(x35451,f312(f312(f129(x35451),x35452),f312(f312(f147(x35451),x35453),f127(x35451)))),x35453)
% 173.49/173.41 [3551]E(f312(f312(f129(x35511),f312(f312(f169(x35511),x35512),x35513)),f312(f312(f134(x35511),x35512),x35513)),x35513)
% 173.49/173.41 [3560]E(f312(f312(f21(a852),f312(f312(f89(a852),x35601),x35602)),f312(f312(f89(a852),x35603),x35602)),f312(f312(f21(a852),x35601),x35603))
% 173.49/173.41 [3561]E(f312(f312(f21(a852),f312(f312(f89(a852),x35611),x35612)),f312(f312(f89(a852),x35611),x35613)),f312(f312(f21(a852),x35612),x35613))
% 173.49/173.41 [3568]E(f312(f312(f129(x35681),f312(f165(x35681),x35682)),f312(f312(f147(x35681),x35683),f127(x35681))),f312(f165(x35681),f312(f312(f147(x35681),x35683),x35682)))
% 173.49/173.41 [3570]E(f312(f312(f89(a852),f312(f190(f853(x35701)),x35702)),f312(f190(f853(x35701)),x35703)),f312(f190(f853(x35701)),f312(f312(f129(x35701),x35702),x35703)))
% 173.49/173.41 [3577]E(f312(f312(f124(f860(x35771,a845)),f312(f168(x35771),x35772)),f312(f168(x35771),x35773)),f312(f168(x35771),f312(f312(f129(x35771),x35772),x35773)))
% 173.49/173.41 [3579]E(f54(a852,f312(f312(f90(a852),x35791),x35792),f312(f312(f90(a852),x35791),x35793)),f312(f312(f90(a852),x35791),f54(a852,x35792,x35793)))
% 173.49/173.41 [3593]E(f312(f312(f169(x35931),f312(f312(f21(a852),x35932),f87(a852))),f312(f167(x35931),x35933)),f312(f167(x35931),f312(f312(f169(x35931),x35932),x35933)))
% 173.49/173.41 [3598]E(f312(f312(f115(f860(x35981,a845)),x35982),f312(f88(f860(x35981,a845)),x35983)),f312(f312(f21(f860(x35981,a845)),x35982),x35983))
% 173.49/173.41 [3599]E(f312(f312(f21(f860(x35991,a845)),x35992),f312(f88(f860(x35991,a845)),x35993)),f312(f312(f115(f860(x35991,a845)),x35992),x35993))
% 173.49/173.41 [3620]E(f312(f312(f247(x36201,x36202),x36203),f312(f16(f860(x36202,a845),x36201),f189(f860(x36202,a845)))),f189(f860(f859(x36201,x36202),a845)))
% 173.49/173.41 [3622]E(f312(f312(f89(a852),f312(f312(f90(a852),x36221),x36222)),f312(f312(f90(a852),x36221),x36223)),f312(f312(f90(a852),x36221),f312(f312(f89(a852),x36222),x36223)))
% 173.49/173.41 [3623]E(f312(f312(f21(a852),f312(f312(f90(a852),x36231),x36232)),f312(f312(f90(a852),x36231),x36233)),f312(f312(f90(a852),x36231),f312(f312(f21(a852),x36232),x36233)))
% 173.49/173.41 [3624]E(f312(f312(f89(a1),f312(f312(f90(a1),x36241),x36242)),f312(f312(f90(a1),x36241),x36243)),f312(f312(f90(a1),x36241),f312(f312(f89(a1),x36242),x36243)))
% 173.49/173.41 [3625]E(f312(f312(f21(a1),f312(f312(f90(a1),x36251),x36252)),f312(f312(f90(a1),x36251),x36253)),f312(f312(f90(a1),x36251),f312(f312(f21(a1),x36252),x36253)))
% 173.49/173.41 [3626]E(f312(f312(f90(a1),f312(f312(f240(a1),x36261),x36262)),f312(f312(f240(a1),x36261),x36263)),f312(f312(f240(a1),x36261),f312(f312(f89(a852),x36262),x36263)))
% 173.49/173.41 [3639]E(f312(f312(f50(x36391,f860(x36392,a845)),x36393),f312(f16(f860(x36392,a845),x36391),f189(f860(x36392,a845)))),f189(f860(x36392,a845)))
% 173.49/173.41 [3641]E(f54(a852,f312(f312(f90(a852),x36411),x36412),f312(f312(f90(a852),x36413),x36412)),f312(f312(f90(a852),f54(a852,x36411,x36413)),x36412))
% 173.49/173.41 [3645]E(f54(a1,f312(f312(f21(a1),x36451),f54(a1,x36452,x36453)),x36453),f54(a1,f312(f312(f21(a1),x36451),x36452),x36453))
% 173.49/173.41 [3646]E(f54(a1,f312(f312(f90(a1),x36461),f54(a1,x36462,x36463)),x36463),f54(a1,f312(f312(f90(a1),x36461),x36462),x36463))
% 173.49/173.41 [3647]P22(f312(f312(f227(f860(x36471,a845)),x36472),f312(f312(f289(x36471),x36473),x36472)))
% 173.49/173.41 [3650]E(f312(f290(f859(x36501,x36502),x36501,f246(x36501,x36502)),f312(f168(f859(x36501,x36502)),x36503)),f179(x36501,x36502,f312(f173(x36501,x36502),x36503)))
% 173.49/173.41 [3697]P22(f312(f70(x36971),f179(x36971,x36972,f312(f173(x36971,x36972),x36973))))
% 173.49/173.41 [3723]E(f312(f312(f51(f860(x37231,a845),f860(x37231,a845)),x37232),f312(f124(f860(x37231,a845)),x37233)),f312(f312(f124(f860(x37231,a845)),x37233),f49(f860(x37231,a845),x37232)))
% 173.49/173.41 [3724]E(f312(f312(f50(f860(x37241,a845),f860(x37241,a845)),x37242),f312(f115(f860(x37241,a845)),x37243)),f312(f312(f115(f860(x37241,a845)),x37243),f48(f860(x37241,a845),x37242)))
% 173.49/173.41 [3734]E(f312(f168(x37341),f312(f312(f312(f184(f853(x37341),f853(x37341)),x37342),f164(x37341)),x37343)),f312(f168(x37341),x37343))
% 173.49/173.41 [3738]E(f312(f312(f169(x37381),f312(f190(f853(x37381)),f172(x37381,x37382,x37383))),x37383),f172(x37381,x37382,x37383))
% 173.49/173.41 [3739]E(f179(x37391,x37392,f312(f312(f8(x37392,f856(x37392),x37391),f219(x37392)),x37393)),f235(f860(x37391,a845)))
% 173.49/173.41 [3743]E(f312(f190(f853(x37431)),f312(f312(f312(f184(f853(x37431),f853(x37431)),x37432),f164(x37431)),x37433)),f312(f190(f853(x37431)),x37433))
% 173.49/173.41 [3746]E(f312(f312(f249(x37461,x37462,x37462),f312(f16(f860(x37462,x37462),x37461),f5(x37462))),x37463),f312(f248(x37461,x37462),x37463))
% 173.49/173.41 [3751]E(f54(a1,f312(f312(f21(a1),f54(a1,x37511,x37512)),x37513),x37512),f54(a1,f312(f312(f21(a1),x37511),x37513),x37512))
% 173.49/173.41 [3752]E(f54(a1,f312(f312(f240(a1),f54(a1,x37521,x37522)),x37523),x37522),f54(a1,f312(f312(f240(a1),x37521),x37523),x37522))
% 173.49/173.41 [3756]E(f312(f312(f50(f860(f859(x37561,x37562),a845),f860(x37562,a845)),x37563),f236(x37561,x37562)),f312(f236(x37561,x37562),f48(f860(f859(x37561,x37562),a845),x37563)))
% 173.49/173.41 [3757]E(f312(f312(f50(f860(f859(x37571,x37572),a845),f860(x37571,a845)),x37573),f238(x37571,x37572)),f312(f238(x37571,x37572),f48(f860(f859(x37571,x37572),a845),x37573)))
% 173.49/173.41 [3788]E(f312(f82(x37881,x37881,x37881,x37882),f312(f312(f184(x37881,x37881),x37883),x37882)),f312(f312(f184(x37881,x37881),f312(a126,x37883)),x37882))
% 173.49/173.41 [3799]E(f221(f856(x37991),x37992,f192(x37991),f312(f312(f8(x37991,f856(x37991),x37992),f219(x37991)),x37993)),f312(f193(x37992,x37991),x37993))
% 173.49/173.41 [3805]E(f312(f312(f134(x38051),f312(f312(f21(a852),f312(f190(f853(x38051)),x38052)),x38053)),f312(f165(x38051),x38052)),f312(f165(x38051),f312(f312(f169(x38051),x38053),x38052)))
% 173.49/173.41 [3806]E(f312(f312(f169(x38061),f312(f312(f21(a852),f312(f190(f853(x38061)),x38062)),x38063)),f312(f165(x38061),x38062)),f312(f165(x38061),f312(f312(f134(x38061),x38063),x38062)))
% 173.49/173.41 [3809]E(f312(f312(f89(a852),f312(f162(a852),f312(f312(f150(x38091,a852),x38092),x38093))),f312(f190(f853(x38091)),x38093)),f151(x38091,x38092,x38093))
% 173.49/173.41 [3826]E(f312(f164(x38261),f312(f312(f312(f184(f853(x38261),f853(x38261)),x38262),f164(x38261)),x38263)),f312(f312(f312(f184(f853(x38261),f853(x38261)),f312(a126,x38262)),f164(x38261)),x38263))
% 173.49/173.41 [3841]P22(f312(f312(f227(a852),f312(f190(f853(x38411)),f312(f132(x38411,x38412),x38413))),f312(f190(f853(x38411)),x38413)))
% 173.49/173.41 [3858]E(f312(f312(f124(f860(f860(x38581,a845),a845)),f312(f288(x38581),x38582)),f312(f290(f860(x38581,a845),f860(x38581,a845),f312(f289(x38581),x38583)),f312(f288(x38581),x38582))),f312(f288(x38581),f312(f312(f289(x38581),x38583),x38582)))
% 173.49/173.41 [3878]P18(x38781,x38782,f312(f312(f289(f851(x38781)),f312(f312(f312(f100(x38781),x38783),a23),x38783)),f189(f860(f851(x38781),a845))))
% 173.49/173.41 [3893]P22(f312(f312(f227(a852),f312(f190(f853(x38931)),f172(x38931,x38932,x38933))),f312(f190(f853(x38931)),x38933)))
% 173.49/173.41 [3900]E(f312(f238(x39001,x39002),f312(f233(f859(x39001,x39002)),f312(f249(x39001,x39002,a845),x39003))),f312(f233(x39001),f312(f312(f8(f860(x39002,a845),a845,x39001),f96(x39002)),x39003)))
% 173.49/173.41 [3911]E(f312(f290(a852,a852,f312(f312(f7(a852,a852,a852),f89(a852)),x39111)),f283(a852,x39112,x39113)),f283(a852,f312(f312(f89(a852),x39112),x39111),f312(f312(f89(a852),x39113),x39111)))
% 173.49/173.41 [3913]P22(f312(f70(f856(x39131)),f312(f290(x39132,f856(x39131),f312(f173(x39132,x39131),x39133)),f235(f860(x39132,a845)))))
% 173.49/173.41 [3926]E(f312(f290(a852,a852,f312(f312(f7(a852,a852,a852),f89(a852)),x39261)),f312(f282(a852,x39262),x39263)),f312(f282(a852,f312(f312(f89(a852),x39262),x39261)),f312(f312(f89(a852),x39263),x39261)))
% 173.49/173.41 [3927]E(f312(f312(f89(a852),f312(f312(f90(a852),x39271),f54(a852,f312(f47(a852,x39272),x39271),x39273))),f54(a852,x39272,x39271)),f54(a852,x39272,f312(f312(f90(a852),x39271),x39273)))
% 173.49/173.41 [3944]E(f312(f312(f177(x39441,x39442),f312(f312(f150(f859(x39441,x39442),x39441),f246(x39441,x39442)),x39443)),f312(f312(f150(f859(x39441,x39442),x39442),f248(x39441,x39442)),x39443)),x39443)
% 173.49/173.41 [3962]E(f312(f312(f129(x39621),x39622),f312(f138(f853(x39621),f853(x39621),f129(x39621),f127(x39621)),x39623)),f312(f138(f853(x39621),f853(x39621),f129(x39621),x39622),x39623))
% 173.49/173.41 [3982]P22(f312(f312(f314(f859(x39821,x39821)),f312(f312(f239(x39821,x39821),x39822),x39822)),f312(f312(f184(f859(x39821,x39821),a845),f2(a852)),x39823)))
% 173.49/173.41 [3988]E(f312(f233(x39881),f312(f312(f8(f860(x39882,a845),a845,x39881),f96(x39882)),f312(f7(x39882,x39881,a845),x39883))),f312(f236(x39882,x39881),f312(f233(f859(x39882,x39881)),f312(f249(x39882,x39881,a845),x39883))))
% 173.49/173.41 [4008]E(f312(f312(f124(f860(x40081,a845)),f312(f312(f50(a852,f860(x40081,a845)),f283(a852,f87(a852),x40082)),x40083)),f312(x40083,f2(a852))),f312(f312(f50(a852,f860(x40081,a845)),f312(f281(a852),x40082)),x40083))
% 173.49/173.41 [4023]E(f312(f138(f853(x40231),f853(x40231),f129(x40231),f127(x40231)),f312(f312(f150(f853(x40231),f853(x40231)),f132(x40231,x40232)),x40233)),f312(f132(x40231,x40232),f312(f138(f853(x40231),f853(x40231),f129(x40231),f127(x40231)),x40233)))
% 173.49/173.41 [4026]E(f312(f248(f853(x40261),f853(x40261)),f163(x40261,x40262,x40263)),f312(f132(x40261,f312(f82(a845,a845,x40261,a307),x40262)),x40263))
% 173.49/173.41 [4044]E(f312(f312(f51(x40441,f860(x40442,a845)),f235(f860(x40441,a845))),f312(f312(f8(f860(x40442,a845),f860(x40442,a845),x40441),f233(x40442)),f312(f7(x40442,x40441,a845),x40443))),f312(f233(x40442),f312(f312(f8(f860(x40441,a845),a845,x40442),f97(x40441)),x40443)))
% 173.49/173.41 [4058]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),x40581),f312(f47(a1,x40582),x40581))),f54(a1,x40582,x40581))),x40583),f312(f312(f89(a1),x40582),x40583))
% 173.49/173.41 [4105]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),f312(f47(a1,x41051),x41052)),x41052)),f54(a1,x41051,x41052))),x41053),f312(f312(f89(a1),x41051),x41053))
% 173.49/173.41 [4139]E(f94(f859(x41391,x41392),f312(f249(x41391,x41392,a845),f312(f312(f8(f860(x41392,f859(x41391,x41392)),f860(x41392,a845),x41391),f312(f8(f859(x41391,x41392),a845,x41392),x41393)),f239(x41391,x41392)))),f94(f859(x41391,x41392),x41393))
% 173.49/173.41 [4140]E(f99(f859(x41401,x41402),f312(f249(x41401,x41402,a845),f312(f312(f8(f860(x41402,f859(x41401,x41402)),f860(x41402,a845),x41401),f312(f8(f859(x41401,x41402),a845,x41402),x41403)),f239(x41401,x41402)))),f99(f859(x41401,x41402),x41403))
% 173.49/173.41 [4169]P22(f312(f312(f227(f860(x41691,a845)),f48(f860(x41691,a845),f312(f312(f115(f860(f860(x41691,a845),a845)),x41692),x41693))),f312(f312(f115(f860(x41691,a845)),f48(f860(x41691,a845),x41692)),f48(f860(x41691,a845),x41693))))
% 173.49/173.41 [4170]E(f312(f165(x41701),f312(f312(f312(f184(f853(x41701),f853(x41701)),f312(f312(f21(a852),f312(f190(f853(x41701)),x41702)),f54(a852,x41703,f312(f190(f853(x41701)),x41702)))),f164(x41701)),x41702)),f312(f312(f312(f184(f853(x41701),f853(x41701)),x41703),f164(x41701)),f312(f165(x41701),x41702)))
% 173.49/173.41 [4185]E(f312(f233(x41851),f312(f312(f8(a845,a845,x41851),a307),f312(f312(f7(x41851,f856(x41852),a845),f312(f312(f8(f856(x41852),f860(f856(x41852),a845),x41851),a309),x41853)),f192(x41852)))),f179(x41851,x41852,x41853))
% 173.49/173.41 [4210]P22(f312(f312(f227(a852),f312(f190(f853(x42101)),f312(f312(f134(x42101),f312(f190(f853(x42101)),f172(x42101,x42102,x42103))),x42103))),f312(f190(f853(x42101)),x42103)))
% 173.49/173.41 [4250]E(f312(f233(x42501),f312(f312(f8(f860(x42502,a845),a845,x42501),f96(x42502)),f312(f312(f8(f856(x42501),f860(x42502,a845),x42501),f312(f7(x42502,f856(x42501),a845),f312(f312(f8(f856(x42501),f860(f856(x42501),a845),x42502),a309),x42503))),f219(x42501)))),f181(x42502,x42501,x42503))
% 173.49/173.41 [4495]~P22(f312(f71(x44951,x44952,f189(f860(x44951,a845))),x44953))
% 173.49/173.41 [4500]~P22(f312(f312(f314(f859(x45001,x45001)),f312(f312(f239(x45001,x45001),x45002),x45003)),f149(x45001,f127(f860(x45001,a852)))))
% 173.49/173.41 [3513]E(f312(f190(f853(x35131)),f312(f312(f169(x35131),x35132),x35133)),f312(f312(f225(a852),f312(f190(f853(x35131)),x35133)),x35132))
% 173.49/173.41 [3514]E(f312(f190(f853(x35141)),f312(f312(f134(x35141),x35142),x35143)),f312(f312(f21(a852),f312(f190(f853(x35141)),x35143)),x35142))
% 173.49/173.41 [3537]E(f312(f190(f853(f853(x35371))),f63(x35371,x35372,x35373)),f312(f312(f240(a852),f312(f190(f853(x35371)),x35373)),x35372))
% 173.49/173.41 [3554]E(f312(f312(f89(a852),f312(f312(f89(a852),x35541),x35542)),x35543),f312(f312(f89(a852),x35541),f312(f312(f89(a852),x35542),x35543)))
% 173.49/173.41 [3555]E(f312(f312(f89(a1),f312(f312(f89(a1),x35551),x35552)),x35553),f312(f312(f89(a1),x35551),f312(f312(f89(a1),x35552),x35553)))
% 173.49/173.41 [3556]E(f312(f312(f21(a852),f312(f312(f21(a852),x35561),x35562)),x35563),f312(f312(f21(a852),x35561),f312(f312(f89(a852),x35562),x35563)))
% 173.49/173.41 [3557]E(f312(f312(f90(a852),f312(f312(f90(a852),x35571),x35572)),x35573),f312(f312(f90(a852),x35571),f312(f312(f90(a852),x35572),x35573)))
% 173.49/173.41 [3558]E(f312(f312(f90(a1),f312(f312(f90(a1),x35581),x35582)),x35583),f312(f312(f90(a1),x35581),f312(f312(f90(a1),x35582),x35583)))
% 173.49/173.41 [3559]E(f312(f312(f240(a1),f312(f312(f240(a1),x35591),x35592)),x35593),f312(f312(f240(a1),x35591),f312(f312(f90(a852),x35592),x35593)))
% 173.49/173.41 [3575]E(f158(x35751,f312(f312(f147(f860(x35751,a845)),x35752),x35753)),f171(x35751,x35752,f158(x35751,x35753)))
% 173.49/173.41 [3621]E(f312(f312(f21(a852),f312(f312(f21(a852),x36211),x36212)),x36213),f312(f312(f21(a852),f312(f312(f21(a852),x36211),x36213)),x36212))
% 173.49/173.41 [3628]E(f312(f312(f115(f860(x36281,a845)),x36282),f312(f312(f21(f860(x36281,a845)),x36283),x36282)),f189(f860(x36281,a845)))
% 173.49/173.41 [3670]E(f48(f860(x36701,a845),f312(f312(f289(f860(x36701,a845)),x36702),x36703)),f312(f312(f124(f860(x36701,a845)),x36702),f48(f860(x36701,a845),x36703)))
% 173.49/173.41 [3671]E(f49(f860(x36711,a845),f312(f312(f289(f860(x36711,a845)),x36712),x36713)),f312(f312(f115(f860(x36711,a845)),x36712),f49(f860(x36711,a845),x36713)))
% 173.49/173.41 [3673]E(f312(f312(f89(a852),f312(f312(f90(a852),x36731),x36732)),f312(f312(f90(a852),x36733),x36732)),f312(f312(f90(a852),f312(f312(f89(a852),x36731),x36733)),x36732))
% 173.49/173.41 [3674]E(f312(f312(f21(a852),f312(f312(f90(a852),x36741),x36742)),f312(f312(f90(a852),x36743),x36742)),f312(f312(f90(a852),f312(f312(f21(a852),x36741),x36743)),x36742))
% 173.49/173.41 [3675]E(f312(f312(f89(a1),f312(f312(f90(a1),x36751),x36752)),f312(f312(f90(a1),x36753),x36752)),f312(f312(f90(a1),f312(f312(f89(a1),x36751),x36753)),x36752))
% 173.49/173.41 [3677]E(f312(f312(f21(a1),f312(f312(f90(a1),x36771),x36772)),f312(f312(f90(a1),x36773),x36772)),f312(f312(f90(a1),f312(f312(f21(a1),x36771),x36773)),x36772))
% 173.49/173.41 [3678]E(f312(f312(f225(a852),f312(f312(f21(a852),x36781),x36782)),f312(f312(f21(a852),x36783),x36782)),f312(f312(f21(a852),f312(f312(f225(a852),x36781),x36783)),x36782))
% 173.49/173.41 [3700]E(f312(f312(f115(f860(f853(x37001),a845)),f156(x37001,x37002)),f156(x37001,x37003)),f156(x37001,f312(f312(f115(f860(x37001,a845)),x37002),x37003)))
% 173.49/173.41 [3702]E(f312(f312(f124(f860(x37021,a845)),x37022),f312(f312(f21(f860(x37021,a845)),x37023),x37022)),f312(f312(f124(f860(x37021,a845)),x37022),x37023))
% 173.49/173.41 [3703]E(f312(f312(f124(f860(x37031,a845)),x37032),f312(f312(f124(f860(x37031,a845)),x37032),x37033)),f312(f312(f124(f860(x37031,a845)),x37032),x37033))
% 173.49/173.41 [3704]E(f312(f312(f115(f860(x37041,a845)),x37042),f312(f312(f115(f860(x37041,a845)),x37042),x37043)),f312(f312(f115(f860(x37041,a845)),x37042),x37043))
% 173.49/173.41 [3716]E(f312(f312(f267(x37161,x37162,x37162),x37163),f287(x37162,f189(f860(f859(x37162,x37162),a845)))),x37163)
% 173.49/173.41 [3719]E(f312(f312(f124(f860(x37191,a845)),f312(f312(f289(x37191),x37192),f189(f860(x37191,a845)))),x37193),f312(f312(f289(x37191),x37192),x37193))
% 173.49/173.41 [3737]E(f312(f312(f21(a852),f312(f312(f21(a852),f312(a126,x37371)),x37372)),f312(a126,x37373)),f312(f312(f21(a852),f312(f312(f21(a852),x37371),x37372)),x37373))
% 173.49/173.41 [3768]E(f312(f312(f115(f860(f860(x37681,a845),a845)),f312(f288(x37681),x37682)),f312(f288(x37681),x37683)),f312(f288(x37681),f312(f312(f115(f860(x37681,a845)),x37682),x37683)))
% 173.49/173.41 [3772]E(f312(f312(f124(f860(x37721,a845)),f312(f88(f860(x37721,a845)),x37722)),x37723),f312(f88(f860(x37721,a845)),f312(f312(f21(f860(x37721,a845)),x37722),x37723)))
% 173.49/173.41 [3785]E(f312(f312(f289(x37851),x37852),f312(f312(f21(f860(x37851,a845)),x37853),f312(f312(f289(x37851),x37852),f189(f860(x37851,a845))))),f312(f312(f289(x37851),x37852),x37853))
% 173.49/173.41 [3796]P22(f312(f312(f227(f860(x37961,a845)),x37962),f312(f312(f124(f860(x37961,a845)),x37963),x37962)))
% 173.49/173.41 [3797]P22(f312(f312(f227(f860(x37971,a845)),x37972),f312(f312(f124(f860(x37971,a845)),x37972),x37973)))
% 173.49/173.41 [3800]E(f312(f312(f115(f860(x38001,a845)),f312(f88(f860(x38001,a845)),x38002)),f312(f88(f860(x38001,a845)),x38003)),f312(f88(f860(x38001,a845)),f312(f312(f124(f860(x38001,a845)),x38002),x38003)))
% 173.49/173.41 [3801]E(f312(f312(f124(f860(x38011,a845)),f312(f88(f860(x38011,a845)),x38012)),f312(f88(f860(x38011,a845)),x38013)),f312(f88(f860(x38011,a845)),f312(f312(f115(f860(x38011,a845)),x38012),x38013)))
% 173.49/173.41 [3813]P22(f312(f312(f227(f860(x38131,a845)),f312(f168(x38131),x38132)),f312(f168(x38131),f312(f312(f147(x38131),x38133),x38132))))
% 173.49/173.41 [3823]E(f312(f312(f124(f860(x38231,a845)),f312(f312(f21(f860(x38231,a845)),x38232),x38233)),f312(f312(f115(f860(x38231,a845)),x38232),x38233)),x38232)
% 173.49/173.41 [3880]E(f312(f312(f9(x38801,a1),f312(f312(f8(a852,a1,x38801),f114(a1)),x38802)),x38803),f312(f114(a1),f312(f312(f9(x38801,a852),x38802),x38803)))
% 173.49/173.41 [3881]E(f312(f312(f6(x38811,a1),f312(f312(f8(a852,a1,x38811),f114(a1)),x38812)),x38813),f312(f114(a1),f312(f312(f6(x38811,a852),x38812),x38813)))
% 173.49/173.41 [3929]E(f312(f312(f129(x39291),f172(x39291,x39292,x39293)),f312(f312(f134(x39291),f312(f190(f853(x39291)),f172(x39291,x39292,x39293))),x39293)),x39293)
% 173.49/173.41 [3934]E(f312(f88(f860(f859(x39341,x39342),a845)),f312(f312(f247(x39341,x39342),x39343),f312(f16(f860(x39342,a845),x39341),f235(f860(x39342,a845))))),f312(f312(f247(x39341,x39342),f312(f88(f860(x39341,a845)),x39343)),f312(f16(f860(x39342,a845),x39341),f235(f860(x39342,a845)))))
% 173.49/173.41 [3935]E(f312(f88(f860(f859(x39351,x39352),a845)),f312(f312(f247(x39351,x39352),f235(f860(x39351,a845))),f312(f16(f860(x39352,a845),x39351),x39353))),f312(f312(f247(x39351,x39352),f235(f860(x39351,a845))),f312(f16(f860(x39352,a845),x39351),f312(f88(f860(x39352,a845)),x39353))))
% 173.49/173.41 [3983]E(f312(f312(f50(f860(x39831,a845),f860(x39831,a845)),x39832),f312(f312(f7(f860(x39831,a845),f860(x39831,a845),f860(x39831,a845)),f115(f860(x39831,a845))),x39833)),f312(f312(f115(f860(x39831,a845)),f48(f860(x39831,a845),x39832)),x39833))
% 173.49/173.41 [3990]E(f312(f138(f853(x39901),f853(x39901),f129(x39901),f127(x39901)),f312(f312(f147(f853(x39901)),x39902),x39903)),f312(f312(f129(x39901),x39902),f312(f138(f853(x39901),f853(x39901),f129(x39901),f127(x39901)),x39903)))
% 173.49/173.41 [4003]E(f312(f312(f89(a852),f312(f312(f90(a852),x40031),f312(f47(a852,x40032),x40033))),f312(f47(a852,f312(f312(f90(a852),x40031),f54(a852,x40032,x40033))),x40033)),f312(f47(a852,f312(f312(f90(a852),x40031),x40032)),x40033))
% 173.49/173.41 [4004]E(f312(f312(f89(a1),f312(f312(f90(a1),x40041),f312(f47(a1,x40042),x40043))),f312(f47(a1,f312(f312(f90(a1),x40041),f54(a1,x40042,x40043))),x40043)),f312(f47(a1,f312(f312(f90(a1),x40041),x40042)),x40043))
% 173.49/173.41 [4014]E(f312(f312(f289(f860(x40141,a845)),f312(f264(x40141,x40141,x40142),f312(f312(f289(x40141),x40143),f189(f860(x40141,a845))))),f189(f860(f860(x40141,a845),a845))),f312(f312(f69(x40141),f312(f312(f289(x40141),x40143),f189(f860(x40141,a845)))),x40142))
% 173.49/173.41 [4061]E(f312(f312(f21(f860(x40611,a845)),f312(f168(x40611),x40612)),f312(f312(f289(x40611),x40613),f189(f860(x40611,a845)))),f312(f168(x40611),f312(f132(x40611,f312(f312(f8(a845,a845,x40611),a307),f312(a309,x40613))),x40612)))
% 173.49/173.41 [4109]E(f312(f312(f129(x41091),f312(f138(f853(x41091),f853(x41091),f129(x41091),f127(x41091)),x41092)),f312(f138(f853(x41091),f853(x41091),f129(x41091),f127(x41091)),x41093)),f312(f138(f853(x41091),f853(x41091),f129(x41091),f127(x41091)),f312(f312(f129(f853(x41091)),x41092),x41093)))
% 173.49/173.41 [4112]E(f312(f312(f89(a852),f312(f312(f89(a852),f312(f47(a852,x41121),x41122)),f312(f47(a852,x41123),x41122))),f312(f47(a852,f312(f312(f89(a852),f54(a852,x41121,x41122)),f54(a852,x41123,x41122))),x41122)),f312(f47(a852,f312(f312(f89(a852),x41121),x41123)),x41122))
% 173.49/173.41 [4113]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f47(a1,x41131),x41132)),f312(f47(a1,x41133),x41132))),f312(f47(a1,f312(f312(f89(a1),f54(a1,x41131,x41132)),f54(a1,x41133,x41132))),x41132)),f312(f47(a1,f312(f312(f89(a1),x41131),x41133)),x41132))
% 173.49/173.41 [4115]E(f312(f312(f239(f853(x41151),f853(x41151)),f312(f132(x41151,x41152),x41153)),f312(f132(x41151,f312(f82(a845,a845,x41151,a307),x41152)),x41153)),f163(x41151,x41152,x41153))
% 173.49/173.41 [4173]E(f312(f312(f115(f860(f853(x41731),a845)),f312(f312(f7(f853(x41731),f860(f853(x41731),a845),a845),f314(f853(x41731))),f157(x41731,x41732))),f312(f312(f7(f853(x41731),f860(f853(x41731),a845),a845),f314(f853(x41731))),f157(x41731,x41733))),f156(x41731,f312(f312(f115(f860(x41731,a845)),f312(f312(f7(x41731,f860(x41731,a845),a845),f314(x41731)),x41732)),f312(f312(f7(x41731,f860(x41731,a845),a845),f314(x41731)),x41733))))
% 173.49/173.41 [4187]E(f312(f233(x41871),f312(f312(f18(x41871,a845,a845),f312(f312(f8(a845,f860(a845,a845),x41871),a311),f312(f312(f7(x41871,x41871,a845),a309),x41872))),f312(f312(f7(x41871,f860(x41871,a845),a845),f314(x41871)),x41873))),f312(f312(f289(x41871),x41872),x41873))
% 173.49/173.41 [4207]E(f312(f312(f95(f853(f853(x42071)),f853(f853(x42071))),f62(x42071,x42072)),f312(f312(f18(f853(f853(x42071)),f853(f853(x42071)),f853(f853(x42071))),f312(f312(f8(f853(f853(x42071)),f860(f853(f853(x42071)),f853(f853(x42071))),f853(f853(x42071))),f129(f853(x42071))),f312(f150(f853(x42071),f853(x42071)),f312(f147(x42071),x42073)))),f5(f853(f853(x42071))))),f62(x42071,f312(f312(f147(x42071),x42073),x42072)))
% 173.49/173.41 [4211]E(f312(f233(x42111),f312(f312(f18(x42111,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42111),a311),f312(f312(f7(x42111,f860(x42111,a845),a845),f314(x42111)),x42112))),f312(f312(f7(x42111,f860(x42111,a845),a845),f314(x42111)),x42113))),f312(f312(f124(f860(x42111,a845)),x42112),x42113))
% 173.49/173.41 [4212]E(f312(f233(x42121),f312(f312(f18(x42121,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42121),a310),f312(f312(f7(x42121,f860(x42121,a845),a845),f314(x42121)),x42122))),f312(f312(f7(x42121,f860(x42121,a845),a845),f314(x42121)),x42123))),f312(f312(f115(f860(x42121,a845)),x42122),x42123))
% 173.49/173.41 [4300]E(f312(f312(f50(x43001,f860(f860(x43001,a845),a845)),x43002),f312(f312(f7(x43001,f860(f860(x43001,a845),a845),f860(f860(x43001,a845),a845)),f312(f312(f8(f860(x43001,a845),f860(f860(f860(x43001,a845),a845),f860(f860(x43001,a845),a845)),x43001),f289(f860(x43001,a845))),f312(f312(f8(f860(x43001,a845),f860(x43001,a845),x43001),f264(x43001,x43001,x43003)),f312(f312(f7(x43001,f860(x43001,a845),f860(x43001,a845)),f289(x43001)),f189(f860(x43001,a845)))))),f189(f860(f860(x43001,a845),a845)))),f312(f312(f69(x43001),x43002),x43003))
% 173.49/173.41 [4304]E(f312(f233(f853(x43041)),f312(f312(f18(f853(x43041),a845,a845),f312(f312(f8(a845,f860(a845,a845),f853(x43041)),a310),f312(f312(f7(f853(x43041),a852,a845),f312(f312(f8(a852,f860(a852,a845),f853(x43041)),a309),f190(f853(x43041)))),x43042))),f312(f312(f7(f853(x43041),f860(x43041,a845),a845),f312(f312(f8(f860(x43041,a845),f860(f860(x43041,a845),a845),f853(x43041)),f227(f860(x43041,a845))),f168(x43041))),f312(f168(x43041),x43043)))),f312(f168(f853(x43041)),f63(x43041,x43042,x43043)))
% 173.49/173.41 [3689]E(f54(a852,f312(f312(f89(a852),f312(f312(f90(a852),x36891),x36892)),x36893),x36892),f54(a852,x36893,x36892))
% 173.49/173.41 [3736]E(f135(a852,f312(f282(a852,f312(f312(f89(a852),x37361),x37362)),x37363)),f312(f312(f134(a852),x37362),f135(a852,f312(f282(a852,x37361),x37363))))
% 173.49/173.41 [3784]E(f312(f312(f89(a1),f312(f114(a1),x37841)),f312(f312(f89(a1),f312(f114(a1),x37842)),x37843)),f312(f312(f89(a1),f312(f114(a1),f312(f312(f89(a852),x37841),x37842))),x37843))
% 173.49/173.41 [3792]E(f312(f312(f21(f860(x37921,a845)),f312(f312(f21(f860(x37921,a845)),x37922),x37923)),x37923),f312(f312(f21(f860(x37921,a845)),x37922),x37923))
% 173.49/173.41 [3793]E(f312(f312(f124(f860(x37931,a845)),f312(f312(f21(f860(x37931,a845)),x37932),x37933)),x37933),f312(f312(f124(f860(x37931,a845)),x37932),x37933))
% 173.49/173.41 [3814]E(f312(f312(f267(x38141,x38141,x38142),f287(x38141,f189(f860(f859(x38141,x38141),a845)))),x38143),x38143)
% 173.49/173.41 [3820]E(f312(f312(f124(f860(x38201,a845)),f312(f263(x38201),x38202)),f312(f263(x38201),x38203)),f312(f263(x38201),f312(f312(f124(f860(f859(x38201,x38201),a845)),x38202),x38203)))
% 173.49/173.41 [3831]E(f254(x38311,f312(f312(f147(f859(a113,x38311)),f312(f312(f239(a113,x38311),f2(a113)),x38312)),x38313)),f254(x38311,x38313))
% 173.49/173.41 [3834]E(f312(f312(f124(f860(x38341,a845)),f48(f860(x38341,a845),x38342)),f48(f860(x38341,a845),x38343)),f48(f860(x38341,a845),f312(f312(f124(f860(f860(x38341,a845),a845)),x38342),x38343)))
% 173.49/173.41 [3835]E(f312(f312(f115(f860(x38351,a845)),f49(f860(x38351,a845),x38352)),f49(f860(x38351,a845),x38353)),f49(f860(x38351,a845),f312(f312(f124(f860(f860(x38351,a845),a845)),x38352),x38353)))
% 173.49/173.41 [3872]E(f312(f312(f267(x38721,x38721,x38721),f312(f312(f184(f859(x38721,x38721),a845),x38722),x38723)),x38723),f312(f312(f184(f859(x38721,x38721),a845),f312(a126,x38722)),x38723))
% 173.49/173.41 [3919]P22(f312(f312(f227(f860(x39191,a845)),f312(f312(f21(f860(x39191,a845)),x39192),x39193)),x39192))
% 173.49/173.41 [3920]P22(f312(f312(f227(f860(x39201,a845)),f312(f312(f115(f860(x39201,a845)),x39202),x39203)),x39203))
% 173.49/173.41 [3921]P22(f312(f312(f227(f860(x39211,a845)),f312(f312(f115(f860(x39211,a845)),x39212),x39213)),x39212))
% 173.49/173.41 [3946]E(f287(x39461,f312(f312(f124(f860(f859(x39461,x39461),a845)),f287(x39461,x39462)),f287(x39461,x39463))),f287(x39461,f312(f312(f124(f860(f859(x39461,x39461),a845)),x39462),x39463)))
% 173.49/173.41 [3949]E(f48(f860(x39491,a845),f312(f312(f289(f860(x39491,a845)),x39492),f312(f312(f289(f860(x39491,a845)),x39493),f189(f860(f860(x39491,a845),a845))))),f312(f312(f124(f860(x39491,a845)),x39492),x39493))
% 173.49/173.41 [3950]E(f49(f860(x39501,a845),f312(f312(f289(f860(x39501,a845)),x39502),f312(f312(f289(f860(x39501,a845)),x39503),f189(f860(f860(x39501,a845),a845))))),f312(f312(f115(f860(x39501,a845)),x39502),x39503))
% 173.49/173.41 [3956]E(f312(f312(f267(x39561,x39561,x39561),f312(f312(f184(f859(x39561,x39561),a845),x39562),x39563)),x39563),f312(f312(f267(x39561,x39561,x39561),x39563),f312(f312(f184(f859(x39561,x39561),a845),x39562),x39563)))
% 173.49/173.41 [4027]E(f312(f312(f124(f860(x40271,a845)),f312(f233(x40271),f312(f312(f7(x40271,x40271,a845),a309),x40272))),x40273),f312(f312(f289(x40271),x40272),x40273))
% 173.49/173.41 [4029]E(f312(a118,f312(f312(f9(x40291,a1),f312(f312(f8(a852,a1,x40291),f114(a1)),x40292)),x40293)),f312(f312(f9(x40291,a852),x40292),x40293))
% 173.49/173.41 [4030]E(f312(a118,f312(f312(f6(x40301,a1),f312(f312(f8(a852,a1,x40301),f114(a1)),x40302)),x40303)),f312(f312(f6(x40301,a852),x40302),x40303))
% 173.49/173.41 [4106]E(f312(f152(f853(x41061),x41061,f312(f167(x41061),x41062),f312(f16(f860(f853(x41061),f853(x41061)),x41061),f312(f312(f7(f853(x41061),f853(x41061),f853(x41061)),f129(x41061)),x41062))),x41063),f312(f167(x41061),f312(f312(f129(x41061),x41063),x41062)))
% 173.49/173.41 [4135]P22(f312(f312(f227(f860(f860(x41351,a845),a845)),f312(f312(f124(f860(f860(x41351,a845),a845)),f312(f288(x41351),x41352)),f312(f288(x41351),x41353))),f312(f288(x41351),f312(f312(f124(f860(x41351,a845)),x41352),x41353))))
% 173.49/173.41 [4230]E(f312(f233(x42301),f312(f312(f18(x42301,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42301),a310),f312(f312(f7(x42301,f860(x42301,a845),a845),f314(x42301)),x42302))),f312(f312(f8(a845,a845,x42301),a307),f312(f312(f7(x42301,f860(x42301,a845),a845),f314(x42301)),x42303)))),f312(f312(f21(f860(x42301,a845)),x42302),x42303))
% 173.49/173.41 [4251]E(f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,a852,a845),f228(a852)),f312(f190(f853(x42511)),x42512)))),f312(f312(f8(x42511,a845,a852),x42513),f312(f161(x42511),x42512))))),f312(f190(f853(x42511)),f312(f132(x42511,x42513),x42512)))
% 173.49/173.41 [4253]E(f312(f190(f853(x42531)),f170(x42531,x42532,x42533)),f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,a852,a845),f228(a852)),f312(f190(f853(x42531)),x42532)))),f312(f312(f7(a852,f860(a852,a845),a845),f314(a852)),x42533)))))
% 173.49/173.41 [4343]E(f312(f312(f115(f860(f859(f853(x43431),f853(x43431)),a845)),f312(f290(f859(f859(x43431,f853(x43431)),f859(x43431,f853(x43431))),f859(f853(x43431),f853(x43431)),f250(f859(x43431,f853(x43431)),f853(x43431),f859(x43431,f853(x43431)),f853(x43431),f312(f249(x43431,f853(x43431),f853(x43431)),f147(x43431)),f312(f249(x43431,f853(x43431),f853(x43431)),f147(x43431)))),f304(x43431,f853(x43431),x43432,f312(f139(x43431,x43432),x43433)))),f312(f233(f859(f853(x43431),f853(x43431))),f312(f249(f853(x43431),f853(x43431),a845),f312(f312(f7(f853(x43431),f860(f853(x43431),a845),f860(f853(x43431),a845)),f312(f312(f8(f860(a845,a845),f860(f860(f853(x43431),a845),f860(f853(x43431),a845)),f853(x43431)),f8(a845,a845,f853(x43431))),f312(f312(f8(a845,f860(a845,a845),f853(x43431)),a310),f312(f312(f7(f853(x43431),a852,a845),f312(f312(f8(a852,f860(a852,a845),f853(x43431)),a309),f190(f853(x43431)))),f312(a126,x43433))))),f312(f312(f7(f853(x43431),a852,a845),f312(f312(f8(a852,f860(a852,a845),f853(x43431)),a309),f190(f853(x43431)))),f312(a126,x43433)))))),f312(f139(x43431,x43432),f312(a126,x43433)))
% 173.49/173.41 [3836]E(f54(a852,f312(a126,f312(f312(f89(a852),f312(f312(f90(a852),x38361),x38362)),x38363)),x38362),f54(a852,f312(a126,x38363),x38362))
% 173.49/173.41 [4096]E(f312(f233(x40961),f312(f312(f18(x40961,a845,a845),f312(f312(f8(a845,f860(a845,a845),x40961),a310),x40962)),x40963)),f312(f312(f115(f860(x40961,a845)),f312(f233(x40961),x40962)),f312(f233(x40961),x40963)))
% 173.49/173.41 [4097]E(f312(f233(x40971),f312(f312(f18(x40971,a845,a845),f312(f312(f8(a845,f860(a845,a845),x40971),a311),x40972)),x40973)),f312(f312(f124(f860(x40971,a845)),f312(f233(x40971),x40972)),f312(f233(x40971),x40973)))
% 173.49/173.41 [4099]E(f312(f312(f129(x40991),f312(f312(f134(x40991),f54(a852,x40992,f312(f190(f853(x40991)),x40993))),x40993)),f312(f312(f169(x40991),f54(a852,x40992,f312(f190(f853(x40991)),x40993))),x40993)),f312(f312(f312(f184(f853(x40991),f853(x40991)),x40992),f164(x40991)),x40993))
% 173.49/173.41 [4104]E(f312(f233(x41041),f312(f312(f18(x41041,a845,a845),f312(f312(f8(a845,f860(a845,a845),x41041),a315),x41042)),x41043)),f312(f312(f124(f860(x41041,a845)),f312(f88(f860(x41041,a845)),f312(f233(x41041),x41042))),f312(f233(x41041),x41043)))
% 173.49/173.41 [4118]E(f312(f312(f89(a852),f312(f190(f853(x41181)),f312(f132(x41181,x41182),x41183))),f312(f190(f853(x41181)),f312(f132(x41181,f312(f312(f8(a845,a845,x41181),a307),x41182)),x41183))),f312(f190(f853(x41181)),x41183))
% 173.49/173.41 [4142]P22(f312(f312(f227(f860(x41421,a845)),f312(f312(f124(f860(x41421,a845)),f49(f860(x41421,a845),x41422)),f49(f860(x41421,a845),x41423))),f49(f860(x41421,a845),f312(f312(f115(f860(f860(x41421,a845),a845)),x41422),x41423))))
% 173.49/173.41 [4156]E(f312(f168(x41561),f312(f132(x41561,f312(f312(f8(a845,a845,x41561),a307),f312(f312(f7(x41561,x41561,a845),a309),x41562))),x41563)),f312(f312(f21(f860(x41561,a845)),f312(f168(x41561),x41563)),f312(f312(f289(x41561),x41562),f189(f860(x41561,a845)))))
% 173.49/173.41 [4165]P22(f312(f312(f227(f860(f859(x41651,x41651),a845)),f312(f312(f124(f860(f859(x41651,x41651),a845)),f287(x41651,x41652)),f287(x41651,x41653))),f287(x41651,f312(f312(f124(f860(f859(x41651,x41651),a845)),x41652),x41653))))
% 173.49/173.41 [4192]E(f312(f312(f90(a852),f312(a126,f312(a126,f2(a852)))),f312(f312(f6(a852,a852),f312(f312(f8(a852,a852,a852),f312(f89(a852),x41921)),f312(f312(f7(a852,a852,a852),f90(a852)),x41922))),f312(f279(a852),x41923))),f312(f312(f90(a852),x41923),f312(f312(f89(a852),x41921),f312(f312(f89(a852),x41921),f312(f312(f90(a852),f312(f312(f21(a852),x41923),f87(a852))),x41922)))))
% 173.49/173.41 [4202]E(f312(f233(x42021),f312(f312(f18(x42021,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42021),a310),f312(f312(f7(x42021,f860(x42021,a845),a845),f314(x42021)),f312(f168(x42021),x42022)))),x42023)),f312(f168(x42021),f312(f132(x42021,x42023),x42022)))
% 173.49/173.41 [4342]E(f312(f233(x43421),f312(f312(f8(f860(a852,a845),a845,x43421),f96(a852)),f312(f312(f7(x43421,f860(a852,a845),f860(a852,a845)),f312(f312(f8(f860(a852,f860(a845,a845)),f860(f860(a852,a845),f860(a852,a845)),x43421),f18(a852,a845,a845)),f312(f312(f8(f860(a852,a845),f860(a852,f860(a845,a845)),x43421),f312(f8(a845,f860(a845,a845),a852),a310)),f312(f312(f7(x43421,f860(a852,x43421),f860(a852,a845)),f312(f312(f8(f860(x43421,a845),f860(f860(a852,x43421),f860(a852,a845)),x43421),f8(x43421,a845,a852)),a309)),f312(f161(x43421),x43422))))),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,a852,a845),f228(a852)),f312(f190(f853(x43421)),x43422)))),f312(f312(f7(a852,f860(a852,a845),a845),f314(a852)),x43423))))),f312(f168(x43421),f170(x43421,x43422,x43423)))
% 173.49/173.41 [4241]E(f312(f233(x42411),f312(f312(f18(x42411,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42411),a315),f312(f312(f8(a845,a845,x42411),a307),f312(f312(f7(x42411,x42411,a845),a309),x42412)))),x42413)),f312(f312(f289(x42411),x42412),f312(f233(x42411),x42413)))
% 173.49/173.41 [4272]E(f312(f312(f150(f859(x42721,a852),x42721),f246(x42721,a852)),f312(f132(f859(x42721,a852),f312(f312(f7(f859(x42721,a852),f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),f859(x42721,a852)),f314(a852)),f248(x42721,a852))),x42722)),f312(f312(f177(x42721,a852),x42723),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(x42721)),x42723)))))),f170(x42721,x42723,x42722))
% 173.49/173.41 [4301]E(f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f6(a852,a1),f312(f312(f8(a1,a1,a852),f312(f89(a1),x43011)),f312(f312(f7(a852,a1,a1),f312(f312(f8(a1,f860(a1,a1),a852),f90(a1)),f114(a1))),x43012))),f312(f279(a852),x43013))),f312(f312(f90(a1),f312(f114(a1),x43013)),f312(f312(f89(a1),x43011),f312(f312(f89(a1),x43011),f312(f312(f90(a1),f312(f114(a1),f312(f312(f21(a852),x43013),f87(a852)))),x43012)))))
% 173.49/173.41 [4336]E(f312(f233(f859(x43361,x43362)),f312(f249(x43361,x43362,a845),f312(f312(f7(x43361,f860(f859(x43362,x43361),a845),f860(x43362,a845)),f312(f312(f8(f860(x43362,f860(f860(f859(x43362,x43361),a845),a845)),f860(f860(f859(x43362,x43361),a845),f860(x43362,a845)),x43361),f7(x43362,f860(f859(x43362,x43361),a845),a845)),f312(f312(f8(f860(x43362,f859(x43362,x43361)),f860(x43362,f860(f860(f859(x43362,x43361),a845),a845)),x43361),f312(f8(f859(x43362,x43361),f860(f860(f859(x43362,x43361),a845),a845),x43362),f314(f859(x43362,x43361)))),f312(f7(x43362,x43361,f859(x43362,x43361)),f239(x43362,x43361))))),x43363))),f312(f265(x43362,x43361),x43363))
% 173.49/173.41 [4370]E(f312(f233(f853(x43701)),f312(f312(f8(f860(x43701,a845),a845,f853(x43701)),f96(x43701)),f312(f312(f8(f860(x43701,f860(f853(x43701),a845)),f860(x43701,a845),f853(x43701)),f312(f8(f860(f853(x43701),a845),a845,x43701),f96(f853(x43701)))),f312(f312(f7(f853(x43701),f860(x43701,f860(f853(x43701),a845)),f860(x43701,f860(f853(x43701),a845))),f312(f312(f8(f860(x43701,f860(f860(f853(x43701),a845),f860(f853(x43701),a845))),f860(f860(x43701,f860(f853(x43701),a845)),f860(x43701,f860(f853(x43701),a845))),f853(x43701)),f18(x43701,f860(f853(x43701),a845),f860(f853(x43701),a845))),f312(f312(f8(f860(x43701,f860(f853(x43701),f860(a845,a845))),f860(x43701,f860(f860(f853(x43701),a845),f860(f853(x43701),a845))),f853(x43701)),f312(f8(f860(f853(x43701),f860(a845,a845)),f860(f860(f853(x43701),a845),f860(f853(x43701),a845)),x43701),f18(f853(x43701),a845,a845))),f312(f312(f8(f860(x43701,f860(f853(x43701),a845)),f860(x43701,f860(f853(x43701),f860(a845,a845))),f853(x43701)),f312(f8(f860(f853(x43701),a845),f860(f853(x43701),f860(a845,a845)),x43701),f312(f8(a845,f860(a845,a845),f853(x43701)),a310))),f312(f312(f7(f853(x43701),f860(x43701,f860(f853(x43701),f853(x43701))),f860(x43701,f860(f853(x43701),a845))),f312(f312(f8(f860(f860(f853(x43701),f853(x43701)),f860(f853(x43701),a845)),f860(f860(x43701,f860(f853(x43701),f853(x43701))),f860(x43701,f860(f853(x43701),a845))),f853(x43701)),f8(f860(f853(x43701),f853(x43701)),f860(f853(x43701),a845),x43701)),f312(f312(f8(f860(f853(x43701),a845),f860(f860(f853(x43701),f853(x43701)),f860(f853(x43701),a845)),f853(x43701)),f8(f853(x43701),a845,f853(x43701))),a309))),f147(x43701)))))),f312(f312(f7(x43701,f860(f853(x43701),a845),f860(f853(x43701),a845)),f312(f312(f8(f860(a845,a845),f860(f860(f853(x43701),a845),f860(f853(x43701),a845)),x43701),f8(a845,a845,f853(x43701))),f312(f312(f8(a845,f860(a845,a845),x43701),a310),f312(f312(f7(x43701,f860(x43701,a845),a845),f314(x43701)),x43702)))),f312(f312(f7(f853(x43701),f860(f853(x43701),a845),a845),f314(f853(x43701))),x43703)))))),f171(x43701,x43702,x43703))
% 173.49/173.41 [4356]E(f312(f312(f95(a1,f859(a1,a1)),f312(f312(f21(a1),x43561),x43562)),f312(f312(f7(a1,f859(a1,a1),f859(a1,a1)),f312(f312(f18(a1,f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),f312(f312(f8(a845,f860(f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),a1),f108(f859(a1,a1))),f312(f227(a1),f2(a1)))),f312(f239(a1,a1),f312(f312(f89(a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x43563)),f87(a1))))),f312(f312(f239(a1,a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x43563)),x43561))),f312(f52(x43562),f312(f312(f239(a1,a1),x43563),x43561)))
% 173.49/173.41 [3766]P36(x37661,x37662,x37663,f180(x37661,x37662,x37664,x37663))
% 173.49/173.41 [4408]~E(f35(x44081,x44082),f36(x44083,x44084))
% 173.49/173.41 [4411]~E(f28(x44111,x44112),f36(x44113,x44114))
% 173.49/173.41 [4412]~E(f28(x44121,x44122),f35(x44123,x44124))
% 173.49/173.41 [4431]~E(f312(a27,x44311),f33(x44312,x44313,x44314))
% 173.49/173.41 [4432]~E(f312(a27,x44321),f32(x44322,x44323,x44324))
% 173.49/173.41 [4433]~E(f312(a27,x44331),f31(x44332,x44333,x44334))
% 173.49/173.41 [4434]~E(f33(x44341,x44342,x44343),f312(a27,x44344))
% 173.49/173.41 [4435]~E(f32(x44351,x44352,x44353),f312(a27,x44354))
% 173.49/173.41 [4436]~E(f31(x44361,x44362,x44363),f312(a27,x44364))
% 173.49/173.41 [3392]E(f312(f312(f312(f81(x33921,x33922),x33923),x33924),f312(x33923,x33924)),x33923)
% 173.49/173.41 [3450]E(f312(f312(f241(x34501,x34502,x34503),x34504),f2(a852)),x34502)
% 173.49/173.41 [3464]E(f43(x34641,x34642,x34643,f40(x34644)),f312(x34643,x34644))
% 173.49/173.41 [3465]E(f43(x34651,x34652,x34653,f41(x34654)),f312(x34652,x34654))
% 173.49/173.41 [3466]E(f44(x34661,x34662,x34663,f40(x34664)),f312(x34663,x34664))
% 173.49/173.41 [3467]E(f44(x34671,x34672,x34673,f41(x34674)),f312(x34672,x34674))
% 173.49/173.41 [3494]E(f186(x34941,x34942,x34943,f312(a126,x34944)),f312(x34943,x34944))
% 173.49/173.41 [3530]E(f166(x35301,x35302,f166(x35301,x35303,x35304)),f166(x35301,x35303,f166(x35301,x35302,x35304)))
% 173.49/173.41 [3660]E(f312(f221(x36601,x36602,x36603,x36604),f192(x36602)),x36603)
% 173.49/173.41 [3662]E(f312(f152(x36621,x36622,x36623,x36624),f127(x36622)),x36623)
% 173.49/173.41 [3663]E(f312(f138(x36631,x36632,x36633,x36634),f127(x36632)),x36634)
% 173.49/173.41 [3696]E(f312(f190(f857(x36961,x36962)),f209(x36961,x36962,x36963,x36964)),f2(a852))
% 173.49/173.41 [3767]P36(x37671,x37672,f312(f312(f312(f81(x37671,f856(x37672)),x37673),x37674),f192(x37672)),x37673)
% 173.49/173.41 [3781]E(f312(f221(f856(x37811),x37812,f192(x37811),f312(f16(f856(x37811),x37812),f192(x37811))),f312(x37813,x37814)),f192(x37811))
% 173.49/173.41 [3824]E(f312(f312(f124(f860(x38241,a845)),f179(x38241,x38242,x38243)),f179(x38241,x38242,x38244)),f179(x38241,x38242,f180(x38241,x38242,x38244,x38243)))
% 173.49/173.41 [3856]E(f312(f312(f251(x38561,x38562,x38563,f859(x38562,x38563)),x38564),f239(x38562,x38563)),x38564)
% 173.49/173.41 [3865]E(f222(x38651,x38652,x38653,x38654,f192(x38652)),x38653)
% 173.49/173.41 [3866]E(f182(x38661,x38662,x38663,x38664,f127(x38662)),x38663)
% 173.49/173.41 [3867]E(f182(x38671,x38672,x38673,f127(x38671),x38674),x38673)
% 173.49/173.41 [4149]P45(x41491,x41492,x41493,x41494,f189(f860(x41491,a845)),x41494)
% 173.49/173.41 [3192]E(f312(f312(f16(x31921,x31922),x31923),x31924),x31923)
% 173.49/173.41 [3309]E(f312(f312(f193(x33091,x33092),x33093),f312(f219(x33091),x33094)),f312(f219(x33092),f312(x33093,x33094)))
% 173.49/173.41 [3485]E(f166(x34851,x34852,f312(f132(x34851,x34853),x34854)),f312(f132(x34851,x34853),f166(x34851,x34852,x34854)))
% 173.49/173.41 [3515]E(f312(f312(f73(x35151,x35152,x35153),x35154),f189(f860(x35151,a845))),x35154)
% 173.49/173.41 [3536]E(f312(f312(f161(x35361),f312(f312(f147(x35361),x35362),x35363)),f312(a126,x35364)),f312(f312(f161(x35361),x35363),x35364))
% 173.49/173.41 [3576]P34(x35761,f2(a852),f312(f312(f312(f100(x35761),x35762),f312(a27,x35763)),x35764))
% 173.49/173.41 [3603]E(f312(f312(x36031,x36032),f312(f185(x36033,x36034,x36031),x36032)),f312(f185(x36033,x36034,x36031),f312(a126,x36032)))
% 173.49/173.41 [3694]E(f312(f312(f155(x36941,f312(f312(f147(x36941),x36942),x36943)),f2(a852)),x36944),f312(f312(f147(x36941),x36944),x36943))
% 173.49/173.41 [3706]E(f312(f312(f50(f860(x37061,a845),f860(x37062,a845)),x37063),f290(x37061,x37062,x37064)),f312(f290(x37061,x37062,x37064),f48(f860(x37061,a845),x37063)))
% 173.49/173.41 [3707]E(f312(f312(f50(f860(x37071,a845),f860(x37072,a845)),x37073),f291(x37072,x37071,x37074)),f312(f291(x37072,x37071,x37074),f48(f860(x37071,a845),x37073)))
% 173.49/173.41 [3808]E(f179(x38081,x38082,f183(x38081,x38082,x38083,x38084)),f312(f312(f115(f860(x38081,a845)),f179(x38081,x38082,x38083)),x38084))
% 173.49/173.41 [3830]E(f312(f138(x38301,x38302,f312(f7(x38302,x38301,x38301),x38303),x38304),f312(f165(x38302),f127(x38302))),x38304)
% 173.49/173.41 [3870]P22(f312(f312(f312(f312(a198,f28(x38701,x38702)),x38703),x38704),f312(f312(f312(a201,x38703),x38701),f312(x38702,x38703))))
% 173.49/173.41 [3879]E(f85(x38791,x38792,x38793,x38794,f189(f860(x38791,a845))),x38793)
% 173.49/173.41 [3922]E(f312(f312(f312(f312(f81(x39221,f856(x39222)),f312(f16(f856(x39222),x39221),f192(x39222))),x39223),f192(x39222)),x39224),f192(x39222))
% 173.49/173.41 [4079]E(f312(f249(x40791,x40792,x40793),f312(f312(f8(f860(x40792,f859(x40791,x40792)),f860(x40792,x40793),x40791),f312(f8(f859(x40791,x40792),x40793,x40792),x40794)),f239(x40791,x40792))),x40794)
% 173.49/173.41 [3317]E(f312(f312(f197(x33171,x33172),f312(f219(x33171),x33173)),x33174),f312(x33174,x33173))
% 173.49/173.41 [3390]E(f312(f248(x33901,x33902),f312(f312(f239(x33901,x33902),x33903),x33904)),x33904)
% 173.49/173.41 [3391]E(f312(f246(x33911,x33912),f312(f312(f239(x33911,x33912),x33913),x33914)),x33913)
% 173.49/173.41 [3424]E(f312(f190(f853(x34241)),f312(f312(f150(x34242,x34241),x34243),x34244)),f312(f190(f853(x34242)),x34244))
% 173.49/173.41 [3425]E(f312(f190(f853(x34251)),f312(f312(f155(x34251,x34252),x34253),x34254)),f312(f190(f853(x34251)),x34252))
% 173.49/173.41 [3445]E(f312(f312(f134(x34451),f312(a126,x34452)),f312(f312(f147(x34451),x34453),x34454)),f312(f312(f134(x34451),x34452),x34454))
% 173.49/173.41 [3518]E(f312(f312(f289(x35181),x35182),f312(f312(f289(x35181),x35183),x35184)),f312(f312(f289(x35181),x35183),f312(f312(f289(x35181),x35182),x35184)))
% 173.49/173.41 [3520]E(f312(f312(f150(x35201,x35202),x35203),f128(x35201,x35204)),f128(x35202,f312(f312(f150(x35201,x35202),x35203),x35204)))
% 173.49/173.41 [3534]E(f312(f165(x35341),f312(f312(f150(x35342,x35341),x35343),x35344)),f312(f312(f150(x35342,x35341),x35343),f312(f165(x35342),x35344)))
% 173.49/173.41 [3535]E(f312(f312(f150(x35351,x35352),x35353),f312(f167(x35351),x35354)),f312(f167(x35352),f312(f312(f150(x35351,x35352),x35353),x35354)))
% 173.49/173.41 [3548]E(f312(f312(f169(x35481),f312(a126,x35482)),f312(f312(f147(x35481),x35483),x35484)),f312(f312(f147(x35481),x35483),f312(f312(f169(x35481),x35482),x35484)))
% 173.49/173.41 [3552]E(f312(f168(x35521),f312(f312(f150(x35522,x35521),x35523),x35524)),f312(f290(x35522,x35521,x35523),f312(f168(x35522),x35524)))
% 173.49/173.41 [3602]E(f17(x36021,x36022,x36023,f312(a3,f312(a126,f312(a19,x36024)))),f312(x36023,x36024))
% 173.49/173.41 [3604]E(f312(f312(f129(x36041),f312(f132(x36041,x36042),x36043)),f312(f132(x36041,x36042),x36044)),f312(f132(x36041,x36042),f312(f312(f129(x36041),x36043),x36044)))
% 173.49/173.41 [3617]E(f148(x36171,f312(f312(f150(x36172,x36171),x36173),f148(x36172,x36174))),f148(x36171,f312(f312(f150(x36172,x36171),x36173),x36174)))
% 173.49/173.41 [3631]E(f312(f265(x36311,x36311),f312(f312(f266(x36312,x36311),x36313),x36314)),f312(f312(f266(x36312,x36311),f312(f265(x36312,x36312),x36313)),x36314))
% 173.49/173.41 [3642]E(f312(f312(f267(x36421,x36422,x36423),x36424),f189(f860(f859(x36422,x36423),a845))),f189(f860(f859(x36421,x36423),a845)))
% 173.49/173.41 [3643]E(f312(f312(f169(x36431),f312(f312(f21(a852),x36432),x36433)),f312(f312(f134(x36431),x36433),x36434)),f312(f312(f134(x36431),x36433),f312(f312(f169(x36431),x36432),x36434)))
% 173.49/173.41 [3686]E(f48(f860(x36861,a845),f312(f290(x36862,f860(x36861,a845),x36863),x36864)),f312(f312(f50(x36862,f860(x36861,a845)),x36864),x36863))
% 173.49/173.41 [3687]E(f49(f860(x36871,a845),f312(f290(x36872,f860(x36871,a845),x36873),x36874)),f312(f312(f51(x36872,f860(x36871,a845)),x36874),x36873))
% 173.49/173.41 [3688]E(f312(f190(f853(f859(x36881,x36882))),f312(f312(f177(x36881,x36882),x36883),x36884)),f312(f312(f225(a852),f312(f190(f853(x36881)),x36883)),f312(f190(f853(x36882)),x36884)))
% 173.49/173.41 [3690]E(f312(f291(x36901,x36902,x36903),f312(f88(f860(x36902,a845)),x36904)),f312(f88(f860(x36901,a845)),f312(f291(x36901,x36902,x36903),x36904)))
% 173.49/173.41 [3721]E(f312(f183(x37211,x37212,x37213,f189(f860(x37211,a845))),x37214),f192(x37212))
% 173.49/173.41 [3742]E(f312(f291(x37421,x37422,x37423),f312(f233(x37422),x37424)),f312(f233(x37421),f312(f312(f8(x37422,a845,x37421),x37424),x37423)))
% 173.49/173.41 [3759]E(f312(f312(f161(x37591),f312(f312(f129(x37591),x37592),f312(f312(f147(x37591),x37593),x37594))),f312(f190(f853(x37591)),x37592)),x37593)
% 173.49/173.41 [3765]E(f312(f183(x37651,x37652,f312(f16(f856(x37652),x37651),f192(x37652)),x37653),x37654),f192(x37652))
% 173.49/173.41 [3789]E(f312(f290(x37891,x37892,x37893),f312(f291(x37891,x37892,x37893),x37894)),f312(f312(f115(f860(x37892,a845)),x37894),f312(f290(x37891,x37892,x37893),f235(f860(x37891,a845)))))
% 173.49/173.41 [3807]P22(f312(f312(f314(x38071),f312(x38072,x38073)),f312(f290(x38074,x38071,x38072),f235(f860(x38074,a845)))))
% 173.49/173.41 [3819]E(f312(f312(f247(x38191,x38192),f312(f168(x38191),x38193)),f312(f16(f860(x38192,a845),x38191),f312(f168(x38192),x38194))),f312(f168(f859(x38191,x38192)),f68(x38191,x38192,x38193,x38194)))
% 173.49/173.41 [3833]E(f151(x38331,x38332,f312(f312(f147(x38331),x38333),x38334)),f312(f312(f89(a852),f312(f312(f89(a852),f312(x38332,x38333)),f151(x38331,x38332,x38334))),f312(a126,f2(a852))))
% 173.49/173.41 [3847]E(f186(f853(x38471),f312(f312(f147(x38471),x38472),x38473),f312(f312(f7(a852,f853(x38471),f853(x38471)),f134(x38471)),x38473),x38474),f312(f312(f134(x38471),x38474),f312(f312(f147(x38471),x38472),x38473)))
% 173.49/173.41 [3848]P19(x38481,f859(x38482,x38481),f316(x38483,x38484,x38482,x38481),f312(f312(f50(x38482,f860(x38481,a845)),x38484),x38483))
% 173.49/173.41 [3857]E(f312(f312(f21(f860(x38571,a845)),f312(f312(f21(f860(x38571,a845)),x38572),x38573)),f312(f312(f289(x38571),x38574),f189(f860(x38571,a845)))),f312(f312(f21(f860(x38571,a845)),x38572),f312(f312(f289(x38571),x38574),x38573)))
% 173.49/173.41 [3868]E(f312(f312(f184(f860(x38681,x38682),f860(x38681,x38682)),x38683),f82(x38682,x38682,x38681,x38684)),f82(x38682,x38682,x38681,f312(f312(f184(x38682,x38682),x38683),x38684)))
% 173.49/173.41 [3945]E(f312(f312(f312(f184(f853(x39451),f853(x39451)),x39452),f164(x39451)),f312(f312(f312(f184(f853(x39451),f853(x39451)),x39453),f164(x39451)),x39454)),f312(f312(f312(f184(f853(x39451),f853(x39451)),f312(f312(f89(a852),x39452),x39453)),f164(x39451)),x39454))
% 173.49/173.41 [4032]P22(f312(f312(f227(f860(x40321,a845)),f312(f168(x40321),f312(f312(f155(x40321,x40322),x40323),x40324))),f312(f312(f289(x40321),x40324),f312(f168(x40321),x40322))))
% 173.49/173.41 [4069]E(f312(f312(f50(f860(x40691,a845),f860(f859(x40691,x40692),a845)),x40693),f312(f312(f7(f860(x40691,a845),f860(x40691,f860(x40692,a845)),f860(f859(x40691,x40692),a845)),f247(x40691,x40692)),x40694)),f312(f312(f247(x40691,x40692),f48(f860(x40691,a845),x40693)),x40694))
% 173.49/173.41 [4125]P22(f312(f75(x41251,x41252,x41253,x41254,f189(f860(x41251,a845))),x41254))
% 173.49/173.41 [4168]E(f312(f312(f50(x41681,f860(x41682,a845)),x41683),f312(f312(f7(x41681,f860(x41682,a845),f860(x41682,a845)),f312(f312(f8(x41682,f860(f860(x41682,a845),f860(x41682,a845)),x41681),f289(x41682)),x41684)),f189(f860(x41682,a845)))),f312(f290(x41681,x41682,x41684),x41683))
% 173.49/173.41 [4176]P22(f312(f312(f227(f860(x41761,a845)),f312(f236(x41762,x41761),f312(f312(f115(f860(f859(x41762,x41761),a845)),x41763),x41764))),f312(f312(f115(f860(x41761,a845)),f312(f236(x41762,x41761),x41763)),f312(f236(x41762,x41761),x41764))))
% 173.49/173.41 [4177]P22(f312(f312(f227(f860(x41771,a845)),f312(f238(x41771,x41772),f312(f312(f115(f860(f859(x41771,x41772),a845)),x41773),x41774))),f312(f312(f115(f860(x41771,a845)),f312(f238(x41771,x41772),x41773)),f312(f238(x41771,x41772),x41774))))
% 173.49/173.41 [4239]P22(f312(f312(f227(f860(f859(x42391,x42392),a845)),f312(f290(x42392,f859(x42391,x42392),f316(x42393,x42394,x42391,x42392)),f312(f312(f50(x42391,f860(x42392,a845)),x42394),x42393))),f312(f312(f247(x42391,x42392),x42394),x42393)))
% 173.49/173.41 [4278]E(f94(f859(x42781,x42782),f312(f249(x42781,x42782,a845),f312(f312(f7(x42781,f860(x42782,a845),f860(x42782,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x42782,a845),f860(x42782,a845)),x42781),f8(a845,a845,x42782)),f312(f312(f8(a845,f860(a845,a845),x42781),a310),f312(a309,x42783)))),f312(a309,x42784)))),f312(f312(f239(x42781,x42782),x42783),x42784))
% 173.49/173.41 [4279]E(f99(f859(x42791,x42792),f312(f249(x42791,x42792,a845),f312(f312(f7(x42791,f860(x42792,a845),f860(x42792,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x42792,a845),f860(x42792,a845)),x42791),f8(a845,a845,x42792)),f312(f312(f8(a845,f860(a845,a845),x42791),a310),f312(a309,x42793)))),f312(a309,x42794)))),f312(f312(f239(x42791,x42792),x42793),x42794))
% 173.49/173.41 [4346]E(f312(f312(f249(f853(x43461),f853(x43461),f859(f853(x43461),f853(x43461))),f312(f312(f18(f853(x43461),f860(f853(x43461),f859(f853(x43461),f853(x43461))),f860(f853(x43461),f859(f853(x43461),f853(x43461)))),f312(f312(f8(f860(f853(x43461),f860(f859(f853(x43461),f853(x43461)),f859(f853(x43461),f853(x43461)))),f860(f860(f853(x43461),f859(f853(x43461),f853(x43461))),f860(f853(x43461),f859(f853(x43461),f853(x43461)))),f853(x43461)),f18(f853(x43461),f859(f853(x43461),f853(x43461)),f859(f853(x43461),f853(x43461)))),f312(f312(f8(f860(f853(x43461),f859(f853(x43461),f853(x43461))),f860(f853(x43461),f860(f859(f853(x43461),f853(x43461)),f859(f853(x43461),f853(x43461)))),f853(x43461)),f312(f8(f859(f853(x43461),f853(x43461)),f860(f859(f853(x43461),f853(x43461)),f859(f853(x43461),f853(x43461))),f853(x43461)),f312(f108(f859(f853(x43461),f853(x43461))),f312(x43462,x43463)))),f312(f312(f8(f853(x43461),f860(f853(x43461),f859(f853(x43461),f853(x43461))),f853(x43461)),f239(f853(x43461),f853(x43461))),f312(f147(x43461),x43463))))),f312(f312(f7(f853(x43461),f860(f853(x43461),f853(x43461)),f860(f853(x43461),f859(f853(x43461),f853(x43461)))),f312(f312(f8(f860(f853(x43461),f859(f853(x43461),f853(x43461))),f860(f860(f853(x43461),f853(x43461)),f860(f853(x43461),f859(f853(x43461),f853(x43461)))),f853(x43461)),f8(f853(x43461),f859(f853(x43461),f853(x43461)),f853(x43461))),f239(f853(x43461),f853(x43461)))),f312(f147(x43461),x43463)))),f163(x43461,x43462,x43464)),f163(x43461,x43462,f312(f312(f147(x43461),x43463),x43464)))
% 173.49/173.41 [4352]E(f312(f138(f860(x43521,f856(x43522)),f859(x43521,x43522),f312(f7(f859(x43521,x43522),f860(x43521,f856(x43522)),f860(x43521,f856(x43522))),f312(f249(x43521,x43522,f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522)))),f312(f312(f7(x43521,f860(x43522,f856(x43522)),f860(x43522,f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522))))),f312(f312(f8(f860(f856(x43522),f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522)))),f860(f860(x43522,f856(x43522)),f860(x43522,f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522))))),x43521),f8(f856(x43522),f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522))),x43522)),f312(f312(f8(f860(f860(x43521,f856(x43522)),f860(f856(x43522),f860(x43521,f856(x43522)))),f860(f856(x43522),f860(f860(x43521,f856(x43522)),f860(x43521,f856(x43522)))),x43521),f7(f860(x43521,f856(x43522)),f856(x43522),f860(x43521,f856(x43522)))),f312(f7(f860(x43521,f856(x43522)),x43521,f860(f856(x43522),f860(x43521,f856(x43522)))),f81(x43521,f856(x43522)))))),f219(x43522)))),x43523),f312(f165(f859(x43521,x43522)),x43524)),f180(x43521,x43522,x43523,f312(f173(x43521,x43522),x43524)))
% 173.49/173.41 [3462]E(f312(f190(f851(x34621)),f312(f312(f312(f100(x34621),x34622),x34623),x34624)),f2(a852))
% 173.49/173.41 [3580]E(f312(f312(f169(x35801),x35802),f312(f312(f169(x35801),x35803),x35804)),f312(f312(f169(x35801),f312(f312(f225(a852),x35802),x35803)),x35804))
% 173.49/173.41 [3581]E(f312(f312(f134(x35811),x35812),f312(f312(f134(x35811),x35813),x35814)),f312(f312(f134(x35811),f312(f312(f89(a852),x35812),x35813)),x35814))
% 173.49/173.41 [3594]E(f312(f312(f129(x35941),f312(f312(f147(x35941),x35942),x35943)),x35944),f312(f312(f147(x35941),x35942),f312(f312(f129(x35941),x35943),x35944)))
% 173.49/173.41 [3595]E(f312(f312(f129(x35951),f312(f312(f129(x35951),x35952),x35953)),x35954),f312(f312(f129(x35951),x35952),f312(f312(f129(x35951),x35953),x35954)))
% 173.49/173.41 [3672]E(f312(f312(f161(x36721),f312(f312(f147(x36721),x36722),x36723)),x36724),f186(x36721,x36722,f312(f161(x36721),x36723),x36724))
% 173.49/173.41 [3681]E(f312(f312(f184(x36811,x36811),x36812),f312(f312(f184(x36811,x36811),x36813),x36814)),f312(f312(f184(x36811,x36811),f312(f312(f90(a852),x36813),x36812)),x36814))
% 173.49/173.41 [3709]E(f312(f312(f124(f860(x37091,a845)),x37092),f312(f312(f289(x37091),x37093),x37094)),f312(f312(f289(x37091),x37093),f312(f312(f124(f860(x37091,a845)),x37092),x37094)))
% 173.49/173.41 [3725]E(f312(f312(f312(f184(x37251,x37251),x37252),x37253),f312(x37253,x37254)),f312(x37253,f312(f312(f312(f184(x37251,x37251),x37252),x37253),x37254)))
% 173.49/173.41 [3732]E(f312(f312(f267(x37321,x37322,x37323),f189(f860(f859(x37321,x37322),a845))),x37324),f189(f860(f859(x37321,x37323),a845)))
% 173.49/173.41 [3748]E(f312(f312(f124(f860(x37481,a845)),f312(f312(f289(x37481),x37482),x37483)),x37484),f312(f312(f289(x37481),x37482),f312(f312(f124(f860(x37481,a845)),x37483),x37484)))
% 173.49/173.41 [3769]E(f180(x37691,x37692,f312(f173(x37691,x37692),x37693),f312(f173(x37691,x37692),x37694)),f312(f173(x37691,x37692),f312(f312(f129(f859(x37691,x37692)),x37694),x37693)))
% 173.49/173.41 [3770]E(f312(f53(f859(x37701,x37702)),f312(f312(f247(x37701,x37702),x37703),f312(f16(f860(x37702,a845),x37701),x37704))),f312(f312(f90(a852),f312(f53(x37701),x37703)),f312(f53(x37702),x37704)))
% 173.49/173.41 [3778]E(f312(f312(f115(f860(x37781,a845)),f312(f312(f289(x37781),x37782),x37783)),f312(f312(f289(x37781),x37782),x37784)),f312(f312(f289(x37781),x37782),f312(f312(f115(f860(x37781,a845)),x37783),x37784)))
% 173.49/173.41 [3794]E(f312(f312(f124(f860(x37941,a845)),x37942),f312(f312(f124(f860(x37941,a845)),x37943),x37944)),f312(f312(f124(f860(x37941,a845)),x37943),f312(f312(f124(f860(x37941,a845)),x37942),x37944)))
% 173.49/173.41 [3795]E(f312(f312(f115(f860(x37951,a845)),x37952),f312(f312(f115(f860(x37951,a845)),x37953),x37954)),f312(f312(f115(f860(x37951,a845)),x37953),f312(f312(f115(f860(x37951,a845)),x37952),x37954)))
% 173.49/173.41 [3804]E(f73(x38041,x38042,f312(f312(f8(x38042,f860(x38042,x38042),x38041),x38043),x38044)),f312(f74(x38042,x38041,x38043),x38044))
% 173.49/173.41 [3812]E(f175(x38121,f312(f312(f150(f853(x38122),f853(x38121)),f312(f150(x38122,x38121),x38123)),x38124)),f312(f312(f150(f853(x38122),f853(x38121)),f312(f150(x38122,x38121),x38123)),f175(x38122,x38124)))
% 173.49/173.41 [3829]E(f312(f138(f853(x38291),f853(x38291),f129(x38291),f127(x38291)),f312(f312(f150(x38292,f853(x38291)),x38293),x38294)),f160(x38292,x38291,x38293,x38294))
% 173.49/173.41 [3832]E(f183(x38321,x38322,x38323,f312(f88(f860(x38321,a845)),f312(f312(f289(x38321),x38324),f189(f860(x38321,a845))))),f312(f312(f312(f81(x38321,f856(x38322)),x38323),x38324),f192(x38322)))
% 173.49/173.41 [3875]E(f312(f312(f312(f81(x38751,f856(x38752)),f312(f173(x38751,x38752),x38753)),f312(f246(x38751,x38752),x38754)),f312(f219(x38752),f312(f248(x38751,x38752),x38754))),f312(f173(x38751,x38752),f312(f312(f147(f859(x38751,x38752)),x38754),x38753)))
% 173.49/173.41 [3892]E(f312(f82(x38921,x38921,x38921,f312(f312(f184(x38921,x38921),x38922),x38923)),f312(f312(f184(x38921,x38921),x38924),x38923)),f312(f312(f184(x38921,x38921),f312(f312(f89(a852),x38922),x38924)),x38923))
% 173.49/173.41 [3914]E(f312(f312(f115(f860(x39141,a845)),f312(f312(f21(f860(x39141,a845)),x39142),x39143)),f312(f312(f21(f860(x39141,a845)),x39142),x39144)),f312(f312(f21(f860(x39141,a845)),x39142),f312(f312(f124(f860(x39141,a845)),x39143),x39144)))
% 173.49/173.41 [3915]E(f312(f312(f124(f860(x39151,a845)),f312(f312(f21(f860(x39151,a845)),x39152),x39153)),f312(f312(f21(f860(x39151,a845)),x39152),x39154)),f312(f312(f21(f860(x39151,a845)),x39152),f312(f312(f115(f860(x39151,a845)),x39153),x39154)))
% 173.49/173.41 [3916]E(f312(f312(f115(f860(x39161,a845)),f312(f312(f124(f860(x39161,a845)),x39162),x39163)),f312(f312(f124(f860(x39161,a845)),x39162),x39164)),f312(f312(f124(f860(x39161,a845)),x39162),f312(f312(f115(f860(x39161,a845)),x39163),x39164)))
% 173.49/173.41 [3917]E(f312(f312(f21(f860(x39171,a845)),f312(f312(f115(f860(x39171,a845)),x39172),x39173)),f312(f312(f115(f860(x39171,a845)),x39172),x39174)),f312(f312(f115(f860(x39171,a845)),x39172),f312(f312(f21(f860(x39171,a845)),x39173),x39174)))
% 173.49/173.41 [3918]E(f312(f312(f124(f860(x39181,a845)),f312(f312(f115(f860(x39181,a845)),x39182),x39183)),f312(f312(f115(f860(x39181,a845)),x39182),x39184)),f312(f312(f115(f860(x39181,a845)),x39182),f312(f312(f124(f860(x39181,a845)),x39183),x39184)))
% 173.49/173.41 [3924]E(f312(f53(f859(x39241,x39242)),f312(f312(f247(x39241,x39242),f312(f312(f289(x39241),x39243),f189(f860(x39241,a845)))),f312(f16(f860(x39242,a845),x39241),x39244))),f312(f53(x39242),x39244))
% 173.49/173.41 [3959]E(f312(f312(f51(x39591,f860(x39592,a845)),x39593),f312(f312(f8(f860(x39592,a845),f860(x39592,a845),x39591),f88(f860(x39592,a845))),x39594)),f312(f88(f860(x39592,a845)),f312(f312(f50(x39591,f860(x39592,a845)),x39593),x39594)))
% 173.49/173.41 [3960]E(f312(f312(f50(x39601,f860(x39602,a845)),x39603),f312(f312(f8(f860(x39602,a845),f860(x39602,a845),x39601),f88(f860(x39602,a845))),x39604)),f312(f88(f860(x39602,a845)),f312(f312(f51(x39601,f860(x39602,a845)),x39603),x39604)))
% 173.49/173.41 [3976]E(f312(f312(f267(x39761,x39761,x39761),f312(f312(f184(f859(x39761,x39761),a845),x39762),x39763)),f312(f312(f184(f859(x39761,x39761),a845),x39764),x39763)),f312(f312(f184(f859(x39761,x39761),a845),f312(f312(f89(a852),x39762),x39764)),x39763))
% 173.49/173.41 [4009]E(f312(f312(f51(x40091,f860(f860(x40092,a845),a845)),x40093),f312(f312(f8(f860(x40092,a845),f860(f860(x40092,a845),a845),x40091),f288(x40092)),x40094)),f312(f288(x40092),f312(f312(f51(x40091,f860(x40092,a845)),x40093),x40094)))
% 173.49/173.41 [4037]E(f312(f312(f50(f860(x40371,a845),f860(x40372,a845)),x40373),f312(f312(f7(f860(x40371,a845),f860(x40371,f860(x40372,a845)),f860(x40372,a845)),f50(x40371,f860(x40372,a845))),x40374)),f312(f312(f50(x40371,f860(x40372,a845)),f48(f860(x40371,a845),x40373)),x40374))
% 173.49/173.41 [4038]E(f312(f312(f51(f860(x40381,a845),f860(x40382,a845)),x40383),f312(f312(f7(f860(x40381,a845),f860(x40381,f860(x40382,a845)),f860(x40382,a845)),f51(x40381,f860(x40382,a845))),x40384)),f312(f312(f51(x40381,f860(x40382,a845)),f48(f860(x40381,a845),x40383)),x40384))
% 173.49/173.41 [4043]E(f312(f312(f150(x40431,x40432),x40433),f312(f138(f853(x40431),f853(x40431),f129(x40431),f127(x40431)),x40434)),f312(f138(f853(x40432),f853(x40432),f129(x40432),f127(x40432)),f312(f312(f150(f853(x40431),f853(x40432)),f312(f150(x40431,x40432),x40433)),x40434)))
% 173.49/173.41 [4046]E(f186(f853(x40461),f127(x40461),f312(f312(f8(f853(x40461),f853(x40461),a852),f312(f147(x40461),x40462)),f312(f312(f7(a852,f853(x40461),f853(x40461)),f169(x40461)),x40463)),x40464),f312(f312(f169(x40461),x40464),f312(f312(f147(x40461),x40462),x40463)))
% 173.49/173.41 [4089]P22(f312(f312(f227(f860(x40891,a845)),f312(f290(x40892,x40891,x40893),f312(f291(x40892,x40891,x40893),x40894))),x40894))
% 173.49/173.41 [4092]E(f312(f290(f859(x40921,x40922),f859(x40922,x40921),f312(f249(x40921,x40922,f859(x40922,x40921)),f312(f7(x40922,x40921,f859(x40922,x40921)),f239(x40922,x40921)))),f312(f312(f247(x40921,x40922),x40923),f312(f16(f860(x40922,a845),x40921),x40924))),f312(f312(f247(x40922,x40921),x40924),f312(f16(f860(x40921,a845),x40922),x40923)))
% 173.49/173.41 [4101]E(f312(f312(f50(x41011,f860(x41012,a845)),x41013),f312(f312(f8(f860(x41011,a845),f860(x41012,a845),x41011),f291(x41012,x41011,x41014)),f312(f312(f7(x41011,f860(x41011,a845),f860(x41011,a845)),f289(x41011)),f189(f860(x41011,a845))))),f312(f291(x41012,x41011,x41014),x41013))
% 173.49/173.41 [4102]E(f312(f312(f50(x41021,f860(x41022,a845)),x41023),f312(f312(f8(f860(x41021,a845),f860(x41022,a845),x41021),f264(x41021,x41022,x41024)),f312(f312(f7(x41021,f860(x41021,a845),f860(x41021,a845)),f289(x41021)),f189(f860(x41021,a845))))),f312(f264(x41021,x41022,x41024),x41023))
% 173.49/173.41 [4191]E(f312(f312(f124(f860(x41911,a845)),f312(f312(f124(f860(x41911,a845)),f312(f312(f115(f860(x41911,a845)),x41912),x41913)),f312(f312(f115(f860(x41911,a845)),x41913),x41914))),f312(f312(f115(f860(x41911,a845)),x41914),x41912)),f312(f312(f115(f860(x41911,a845)),f312(f312(f115(f860(x41911,a845)),f312(f312(f124(f860(x41911,a845)),x41912),x41913)),f312(f312(f124(f860(x41911,a845)),x41913),x41914))),f312(f312(f124(f860(x41911,a845)),x41914),x41912)))
% 173.49/173.41 [4252]E(f312(f138(f853(x42521),f853(x42521),f129(x42521),f127(x42521)),f312(f312(f150(x42522,f853(x42521)),f312(f312(f7(x42522,f853(x42521),f853(x42521)),f312(f312(f8(x42521,f860(f853(x42521),f853(x42521)),x42522),f147(x42521)),x42523)),f127(x42521))),x42524)),f312(f312(f150(x42522,x42521),x42523),x42524))
% 173.49/173.41 [4263]E(f312(f312(f95(a1,x42631),f312(f117(a1),f312(f312(f89(a1),x42632),a111))),f312(f312(f18(a1,x42631,x42631),f312(f312(f7(a1,x42631,f860(x42631,x42631)),f312(f312(f8(a845,f860(x42631,f860(x42631,x42631)),a1),f108(x42631)),a194)),x42633)),f312(f312(f8(a852,x42631,a1),x42634),a118))),f186(x42631,x42633,x42634,f312(f117(a852),x42632)))
% 173.49/173.41 [4499]~P22(f312(f312(f189(f860(x44991,f860(x44992,a845))),x44993),x44994))
% 173.49/173.41 [3735]E(f312(f312(f161(x37351),f312(f312(f129(x37351),x37352),x37353)),f312(f312(f89(a852),f312(f190(f853(x37351)),x37352)),x37354)),f312(f312(f161(x37351),x37353),x37354))
% 173.49/173.41 [3741]E(f312(f312(f134(x37411),x37412),f312(f312(f169(x37411),f312(f312(f89(a852),x37413),x37412)),x37414)),f312(f312(f169(x37411),x37413),f312(f312(f134(x37411),x37412),x37414)))
% 173.49/173.41 [3845]E(f312(f312(f124(f860(x38451,a845)),f312(f236(x38452,x38451),x38453)),f312(f236(x38452,x38451),x38454)),f312(f236(x38452,x38451),f312(f312(f124(f860(f859(x38452,x38451),a845)),x38453),x38454)))
% 173.49/173.41 [3846]E(f312(f312(f124(f860(x38461,a845)),f312(f238(x38461,x38462),x38463)),f312(f238(x38461,x38462),x38464)),f312(f238(x38461,x38462),f312(f312(f124(f860(f859(x38461,x38462),a845)),x38463),x38464)))
% 173.49/173.41 [3851]E(f312(f312(f21(f860(x38511,a845)),f312(f312(f115(f860(x38511,a845)),x38512),x38513)),x38514),f312(f312(f115(f860(x38511,a845)),x38512),f312(f312(f21(f860(x38511,a845)),x38513),x38514)))
% 173.49/173.41 [3852]E(f312(f312(f124(f860(x38521,a845)),f312(f312(f124(f860(x38521,a845)),x38522),x38523)),x38524),f312(f312(f124(f860(x38521,a845)),x38522),f312(f312(f124(f860(x38521,a845)),x38523),x38524)))
% 173.49/173.41 [3853]E(f312(f312(f115(f860(x38531,a845)),f312(f312(f115(f860(x38531,a845)),x38532),x38533)),x38534),f312(f312(f115(f860(x38531,a845)),x38532),f312(f312(f115(f860(x38531,a845)),x38533),x38534)))
% 173.49/173.41 [3894]E(f312(f312(f124(f860(f859(x38941,x38942),a845)),f312(f265(x38942,x38941),x38943)),f312(f265(x38942,x38941),x38944)),f312(f265(x38942,x38941),f312(f312(f124(f860(f859(x38942,x38941),a845)),x38943),x38944)))
% 173.49/173.41 [3895]E(f312(f312(f115(f860(f859(x38951,x38952),a845)),f312(f265(x38952,x38951),x38953)),f312(f265(x38952,x38951),x38954)),f312(f265(x38952,x38951),f312(f312(f115(f860(f859(x38952,x38951),a845)),x38953),x38954)))
% 173.49/173.41 [3963]E(f312(f312(f124(f860(x39631,a845)),f312(f312(f21(f860(x39631,a845)),x39632),x39633)),f312(f312(f21(f860(x39631,a845)),x39634),x39633)),f312(f312(f21(f860(x39631,a845)),f312(f312(f124(f860(x39631,a845)),x39632),x39634)),x39633))
% 173.49/173.41 [3964]E(f312(f312(f115(f860(x39641,a845)),f312(f312(f124(f860(x39641,a845)),x39642),x39643)),f312(f312(f124(f860(x39641,a845)),x39644),x39643)),f312(f312(f124(f860(x39641,a845)),f312(f312(f115(f860(x39641,a845)),x39642),x39644)),x39643))
% 173.49/173.41 [3965]E(f312(f312(f21(f860(x39651,a845)),f312(f312(f115(f860(x39651,a845)),x39652),x39653)),f312(f312(f115(f860(x39651,a845)),x39654),x39653)),f312(f312(f115(f860(x39651,a845)),f312(f312(f21(f860(x39651,a845)),x39652),x39654)),x39653))
% 173.49/173.41 [3966]E(f312(f312(f124(f860(x39661,a845)),f312(f312(f115(f860(x39661,a845)),x39662),x39663)),f312(f312(f115(f860(x39661,a845)),x39664),x39663)),f312(f312(f115(f860(x39661,a845)),f312(f312(f124(f860(x39661,a845)),x39662),x39664)),x39663))
% 173.49/173.41 [3967]E(f312(f312(f21(f860(x39671,a845)),f312(f312(f115(f860(x39671,a845)),x39672),x39673)),f312(f312(f115(f860(x39671,a845)),x39674),x39673)),f312(f312(f21(f860(x39671,a845)),f312(f312(f115(f860(x39671,a845)),x39672),x39673)),x39674))
% 173.49/173.41 [3979]E(f312(f312(f21(f860(x39791,a845)),f312(f312(f21(f860(x39791,a845)),x39792),f312(f312(f289(x39791),x39793),f189(f860(x39791,a845))))),x39794),f312(f312(f21(f860(x39791,a845)),x39792),f312(f312(f289(x39791),x39793),x39794)))
% 173.49/173.41 [4034]E(f312(f312(f124(f860(x40341,a845)),f312(f312(f289(x40341),x40342),f312(f312(f289(x40341),x40343),f189(f860(x40341,a845))))),f312(f263(x40341),x40344)),f312(f263(x40341),f312(f312(f289(f859(x40341,x40341)),f312(f312(f239(x40341,x40341),x40342),x40343)),x40344)))
% 173.49/173.41 [4064]E(f312(f312(f50(a852,f860(x40641,a845)),f312(f281(a852),x40642)),f312(f312(f8(a852,f860(x40641,a845),a852),x40643),f312(f312(f7(a852,a852,a852),f89(a852)),x40644))),f312(f312(f50(a852,f860(x40641,a845)),f283(a852,x40644,f312(f312(f89(a852),x40642),x40644))),x40643))
% 173.49/173.41 [4065]E(f171(x40651,f312(f264(x40651,x40651,x40652),f312(f312(f289(x40651),x40653),f189(f860(x40651,a845)))),f312(f264(f853(x40651),f853(x40651),f154(x40651,x40652)),f312(f312(f289(f853(x40651)),x40654),f189(f860(f853(x40651),a845))))),f312(f264(f853(x40651),f853(x40651),f154(x40651,x40652)),f312(f312(f289(f853(x40651)),f312(f312(f147(x40651),x40653),x40654)),f189(f860(f853(x40651),a845)))))
% 173.49/173.41 [4123]E(f312(f173(x41231,x41232),f312(f312(f150(x41231,f859(x41231,x41232)),f312(f312(f18(x41231,x41232,f859(x41231,x41232)),f239(x41231,x41232)),x41233)),x41234)),f183(x41231,x41232,f312(f82(x41232,f856(x41232),x41231,f219(x41232)),x41233),f312(f168(x41231),x41234)))
% 173.49/173.41 [4128]E(f312(f233(x41281),f312(f312(f7(x41281,f860(x41282,a845),a845),f312(f312(f8(x41282,f860(f860(x41282,a845),a845),x41281),f314(x41282)),x41283)),x41284)),f312(f291(x41281,x41282,x41283),x41284))
% 173.49/173.41 [4224]E(f312(f233(x42241),f312(f312(f7(x42241,f860(f859(x42242,x42241),a845),a845),f312(f312(f8(f859(x42242,x42241),f860(f860(f859(x42242,x42241),a845),a845),x42241),f314(f859(x42242,x42241))),f312(f239(x42242,x42241),x42243))),x42244)),f312(f264(x42242,x42241,x42244),f312(f312(f289(x42242),x42243),f189(f860(x42242,a845)))))
% 173.49/173.41 [4238]E(f312(f312(f150(f859(x42381,a852),x42381),f246(x42381,a852)),f312(f132(f859(x42381,a852),f312(f312(f8(a852,a845,f859(x42381,a852)),x42382),f312(f312(f8(a852,a852,f859(x42381,a852)),a126),f248(x42381,a852)))),f312(f312(f177(x42381,a852),x42383),x42384))),f312(f312(f150(f859(x42381,a852),x42381),f246(x42381,a852)),f312(f132(f859(x42381,a852),f312(f312(f8(a852,a845,f859(x42381,a852)),x42382),f248(x42381,a852))),f312(f312(f177(x42381,a852),x42383),f312(f312(f150(a852,a852),a126),x42384)))))
% 173.49/173.41 [4245]P22(f312(f312(f227(f860(f860(x42451,a845),a845)),f312(f312(f50(x42452,f860(f860(x42451,a845),a845)),x42453),f312(f312(f8(f860(x42451,a845),f860(f860(x42451,a845),a845),x42452),f288(x42451)),x42454))),f312(f288(x42451),f312(f312(f50(x42452,f860(x42451,a845)),x42453),x42454))))
% 173.49/173.41 [4285]E(f312(f312(f95(a1,x42851),f312(f117(a1),f312(f312(f89(a1),x42852),a111))),f312(f312(f18(a1,x42851,x42851),f312(f312(f7(a1,x42851,f860(x42851,x42851)),f312(f312(f8(a845,f860(x42851,f860(x42851,x42851)),a1),f108(x42851)),a194)),x42853)),f312(f312(f18(a1,x42851,x42851),f312(f312(f8(a852,f860(x42851,x42851),a1),x42854),a118)),f312(f312(f8(a852,x42851,a1),f185(x42851,x42853,x42854)),a118)))),f312(f185(x42851,x42853,x42854),f312(f117(a852),x42852)))
% 173.49/173.41 [4288]E(f312(f312(f150(x42881,x42882),f312(f82(f856(x42882),x42882,x42881,f223(x42882)),x42883)),f312(f132(x42881,f312(f312(f8(a845,a845,x42881),a307),f312(f312(f7(x42881,f856(x42882),a845),f312(f312(f8(f856(x42882),f860(f856(x42882),a845),x42881),a309),x42883)),f192(x42882)))),x42884)),f159(x42881,x42882,x42883,x42884))
% 173.49/173.41 [4310]E(f312(f233(f859(x43101,x43102)),f312(f249(x43101,x43102,a845),f312(f312(f7(x43101,f860(x43102,a845),f860(x43102,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x43102,a845),f860(x43102,a845)),x43101),f8(a845,a845,x43102)),f312(f312(f8(a845,f860(a845,a845),x43101),a310),f312(f312(f7(x43101,f860(x43101,a845),a845),f314(x43101)),x43103)))),f312(f312(f7(x43102,f860(x43102,a845),a845),f314(x43102)),x43104)))),f216(x43101,x43102,x43103,x43104))
% 173.49/173.41 [4339]E(f312(f312(f50(x43391,f860(f859(x43391,x43392),a845)),x43393),f312(f312(f18(x43391,f860(x43392,f860(f859(x43391,x43392),a845)),f860(f859(x43391,x43392),a845)),f312(f312(f8(f860(x43392,a845),f860(f860(x43392,f860(f859(x43391,x43392),a845)),f860(f859(x43391,x43392),a845)),x43391),f50(x43392,f860(f859(x43391,x43392),a845))),x43394)),f312(f312(f7(x43391,f860(f859(x43391,x43392),a845),f860(x43392,f860(f859(x43391,x43392),a845))),f312(f312(f8(f860(x43392,f860(f860(f859(x43391,x43392),a845),f860(f859(x43391,x43392),a845))),f860(f860(f859(x43391,x43392),a845),f860(x43392,f860(f859(x43391,x43392),a845))),x43391),f7(x43392,f860(f859(x43391,x43392),a845),f860(f859(x43391,x43392),a845))),f312(f312(f8(f860(x43392,f859(x43391,x43392)),f860(x43392,f860(f860(f859(x43391,x43392),a845),f860(f859(x43391,x43392),a845))),x43391),f312(f8(f859(x43391,x43392),f860(f860(f859(x43391,x43392),a845),f860(f859(x43391,x43392),a845)),x43392),f289(f859(x43391,x43392)))),f239(x43391,x43392)))),f189(f860(f859(x43391,x43392),a845))))),f312(f312(f247(x43391,x43392),x43393),x43394))
% 173.49/173.41 [3903]E(f312(f312(f129(x39031),f312(f312(f169(x39031),x39032),x39033)),f312(f312(f169(x39031),f312(f312(f21(a852),x39032),f312(f190(f853(x39031)),x39033))),x39034)),f312(f312(f169(x39031),x39032),f312(f312(f129(x39031),x39033),x39034)))
% 173.49/173.41 [3904]E(f312(f312(f129(x39041),f312(f312(f134(x39041),x39042),x39043)),f312(f312(f134(x39041),f312(f312(f21(a852),x39042),f312(f190(f853(x39041)),x39043))),x39044)),f312(f312(f134(x39041),x39042),f312(f312(f129(x39041),x39043),x39044)))
% 173.49/173.41 [3953]E(f312(f312(f89(a852),f312(f312(f90(a852),x39531),x39532)),f312(f312(f89(a852),f312(f312(f90(a852),x39533),x39532)),x39534)),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f89(a852),x39531),x39533)),x39532)),x39534))
% 173.49/173.41 [4153]P22(f312(f312(f227(f860(x41531,a845)),f312(f312(f21(f860(x41531,a845)),f312(f236(x41532,x41531),x41533)),f312(f236(x41532,x41531),x41534))),f312(f236(x41532,x41531),f312(f312(f21(f860(f859(x41532,x41531),a845)),x41533),x41534))))
% 173.49/173.41 [4154]P22(f312(f312(f227(f860(x41541,a845)),f312(f312(f21(f860(x41541,a845)),f312(f238(x41541,x41542),x41543)),f312(f238(x41541,x41542),x41544))),f312(f238(x41541,x41542),f312(f312(f21(f860(f859(x41541,x41542),a845)),x41543),x41544))))
% 173.49/173.41 [4265]E(f312(f312(f89(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x42651),x42652)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x42653),x42654)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),f312(f312(f89(a852),x42651),x42653)),f312(f312(f89(a852),x42652),x42654))),f189(f860(f859(a852,a852),a845))))))
% 173.49/173.41 [4305]E(f312(f312(f90(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x43051),x43052)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x43053),x43054)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),f312(f312(f89(a852),f312(f312(f90(a852),x43051),x43053)),f312(f312(f90(a852),x43052),x43054))),f312(f312(f89(a852),f312(f312(f90(a852),x43051),x43054)),f312(f312(f90(a852),x43052),x43053)))),f189(f860(f859(a852,a852),a845))))))
% 173.49/173.41 [4322]E(f312(f233(x43221),f312(f312(f8(f860(x43222,a845),a845,x43221),f97(x43222)),f312(f312(f8(f860(x43222,a845),f860(x43222,a845),x43221),f312(f18(x43222,a845,a845),f312(f312(f8(a845,f860(a845,a845),x43222),a315),f312(f312(f7(x43222,f860(x43222,a845),a845),f314(x43222)),x43223)))),f312(f312(f7(x43221,f860(x43222,f860(x43221,a845)),f860(x43222,a845)),f312(f312(f8(f860(f860(x43221,a845),a845),f860(f860(x43222,f860(x43221,a845)),f860(x43222,a845)),x43221),f8(f860(x43221,a845),a845,x43222)),f314(x43221))),x43224)))),f312(f312(f51(x43222,f860(x43221,a845)),x43223),x43224))
% 173.49/173.41 [4355]E(f312(f312(f267(x43551,x43551,x43551),f312(f312(f289(f859(x43551,x43551)),f312(f312(f239(x43551,x43551),x43552),x43553)),x43554)),f287(x43551,f312(f312(f289(f859(x43551,x43551)),f312(f312(f239(x43551,x43551),x43552),x43553)),x43554))),f312(f312(f124(f860(f859(x43551,x43551),a845)),f312(f312(f267(x43551,x43551,x43551),x43554),f287(x43551,x43554))),f312(f233(f859(x43551,x43551)),f312(f249(x43551,x43551,a845),f312(f312(f7(x43551,f860(x43551,a845),f860(x43551,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x43551,a845),f860(x43551,a845)),x43551),f8(a845,a845,x43551)),f312(f312(f8(a845,f860(a845,a845),x43551),a310),f312(f312(f7(x43551,f860(f859(x43551,x43551),a845),a845),f312(f312(f8(f859(x43551,x43551),f860(f860(f859(x43551,x43551),a845),a845),x43551),f314(f859(x43551,x43551))),f312(f312(f7(x43551,x43551,f859(x43551,x43551)),f239(x43551,x43551)),x43552))),f287(x43551,x43554))))),f312(f312(f7(x43551,f860(f859(x43551,x43551),a845),a845),f312(f312(f8(f859(x43551,x43551),f860(f860(f859(x43551,x43551),a845),a845),x43551),f314(f859(x43551,x43551))),f312(f239(x43551,x43551),x43553))),f287(x43551,x43554)))))))
% 173.49/173.41 [4155]E(f312(f132(x41551,f312(f312(f18(x41551,a845,a845),f312(f312(f8(a845,f860(a845,a845),x41551),a310),x41552)),x41553)),x41554),f312(f132(x41551,x41553),f312(f132(x41551,x41552),x41554)))
% 173.49/173.41 [4259]E(f312(f312(f129(x42591),f312(f312(f312(f108(f853(x42591)),f312(f312(f314(a852),f2(a852)),x42592)),f312(f312(f147(x42591),x42593),f127(x42591))),f127(x42591))),f170(x42591,x42594,f312(f233(a852),f312(f312(f7(a852,f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),a852),f314(a852)),a126)),x42592)))),f170(x42591,f312(f312(f147(x42591),x42593),x42594),x42592))
% 173.49/173.41 [4350]E(f312(f233(f859(x43501,x43502)),f312(f312(f8(f860(a852,a845),a845,f859(x43501,x43502)),f96(a852)),f312(f312(f7(f859(x43501,x43502),f860(a852,a845),f860(a852,a845)),f312(f312(f8(f860(a852,f860(a845,a845)),f860(f860(a852,a845),f860(a852,a845)),f859(x43501,x43502)),f18(a852,a845,a845)),f312(f312(f8(f860(a852,a845),f860(a852,f860(a845,a845)),f859(x43501,x43502)),f312(f8(a845,f860(a845,a845),a852),a310)),f312(f312(f7(f859(x43501,x43502),f860(a852,f859(x43501,x43502)),f860(a852,a845)),f312(f312(f8(f860(f859(x43501,x43502),a845),f860(f860(a852,f859(x43501,x43502)),f860(a852,a845)),f859(x43501,x43502)),f8(f859(x43501,x43502),a845,a852)),a309)),f312(f312(f18(a852,x43502,f859(x43501,x43502)),f312(f312(f8(x43501,f860(x43502,f859(x43501,x43502)),a852),f239(x43501,x43502)),f312(f161(x43501),x43503))),f312(f161(x43502),x43504)))))),f312(f312(f7(a852,a852,a845),f228(a852)),f312(f312(f225(a852),f312(f190(f853(x43501)),x43503)),f312(f190(f853(x43502)),x43504)))))),f312(f168(f859(x43501,x43502)),f312(f312(f177(x43501,x43502),x43503),x43504)))
% 173.49/173.41 [4277]E(f312(f233(f859(x42771,x42772)),f312(f249(x42771,x42772,a845),f312(f312(f7(x42771,f860(x42772,a845),f860(x42772,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x42772,a845),f860(x42772,a845)),x42771),f8(a845,a845,x42772)),f312(f312(f8(a845,f860(a845,a845),x42771),a310),x42773))),x42774))),f312(f312(f247(x42771,x42772),f312(f233(x42771),x42773)),f312(f16(f860(x42772,a845),x42771),f312(f233(x42772),x42774))))
% 173.49/173.41 [4280]E(f312(f233(f859(x42801,x42802)),f312(f249(x42801,x42802,a845),f312(f312(f18(x42801,f860(x42802,a845),f860(x42802,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x42802,a845),f860(x42802,a845)),x42801),f8(a845,a845,x42802)),f312(f312(f8(a845,f860(a845,a845),x42801),a310),x42803))),x42804))),f312(f312(f247(x42801,x42802),f312(f233(x42801),x42803)),f312(f312(f8(f860(x42802,a845),f860(x42802,a845),x42801),f233(x42802)),x42804)))
% 173.49/173.41 [4295]E(f312(f233(x42951),f312(f312(f8(f860(x42952,a845),a845,x42951),f97(x42952)),f312(f312(f8(f860(x42952,a845),f860(x42952,a845),x42951),f312(f18(x42952,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42952),a315),f312(f312(f7(x42952,f860(x42952,a845),a845),f314(x42952)),x42953)))),x42954))),f312(f312(f51(x42952,f860(x42951,a845)),x42953),f312(f312(f8(f860(x42951,a845),f860(x42951,a845),x42952),f233(x42951)),f312(f7(x42951,x42952,a845),x42954))))
% 173.49/173.41 [4334]E(f312(f312(f150(f859(x43341,a852),x43341),f246(x43341,a852)),f312(f132(f859(x43341,a852),f312(f312(f7(f859(x43341,a852),f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),f859(x43341,a852)),f314(a852)),f248(x43341,a852))),x43342)),f312(f312(f177(x43341,a852),x43343),f135(a852,f312(f282(a852,x43344),f312(f312(f89(a852),x43344),f312(f190(f853(x43341)),x43343))))))),f312(f312(f150(f859(x43341,a852),x43341),f246(x43341,a852)),f312(f132(f859(x43341,a852),f312(f312(f7(f859(x43341,a852),f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),f859(x43341,a852)),f314(a852)),f312(f312(f7(f859(x43341,a852),a852,a852),f312(f312(f8(a852,f860(a852,a852),f859(x43341,a852)),f89(a852)),f248(x43341,a852))),x43344))),x43342)),f312(f312(f177(x43341,a852),x43343),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(x43341)),x43343)))))))
% 173.49/173.41 [4335]E(f312(a126,f312(f312(f226(a852),f312(f190(f853(x43351)),x43352)),f312(f138(a852,f853(x43353),f312(f7(f853(x43353),a852,a852),f312(f312(f8(a852,f860(a852,a852),f853(x43353)),f226(a852)),f312(f312(f7(f853(x43353),a852,a852),f312(f312(f8(a852,f860(a852,a852),f853(x43353)),f21(a852)),f190(f853(x43353)))),f312(a126,f2(a852))))),f2(a852)),f312(f165(f853(x43353)),f312(f132(f853(x43353),f312(f312(f8(a845,a845,f853(x43353)),a307),f312(f312(f7(f853(x43353),f853(x43353),a845),a309),f127(x43353)))),x43354))))),f312(f312(f226(a852),f312(a126,f312(f190(f853(x43351)),x43352))),f312(f138(a852,f853(x43353),f312(f7(f853(x43353),a852,a852),f312(f312(f8(a852,f860(a852,a852),f853(x43353)),f226(a852)),f190(f853(x43353)))),f2(a852)),f312(f165(f853(x43353)),x43354))))
% 173.49/173.41 [4294]E(f312(f312(f129(x42941),f170(x42941,x42942,x42943)),f170(x42941,x42944,f312(f233(a852),f312(f312(f7(a852,f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),a852),f314(a852)),f312(f312(f7(a852,a852,a852),f89(a852)),f312(f190(f853(x42941)),x42942)))),x42943)))),f170(x42941,f312(f312(f129(x42941),x42942),x42944),x42943))
% 173.49/173.41 [4341]E(f312(f312(f147(f853(x43411)),f312(f312(f147(x43411),x43412),f312(f138(f853(x43411),f853(x43411),f129(x43411),f127(x43411)),f312(f312(f150(f853(x43411),f853(x43411)),f152(f853(x43411),x43411,f127(x43411),f312(f312(f8(f853(x43411),f860(f853(x43411),f853(x43411)),x43411),f16(f853(x43411),f853(x43411))),f312(f312(f7(x43411,f853(x43411),f853(x43411)),f147(x43411)),f127(x43411))))),x43413)))),f175(x43411,f312(f312(f147(f853(x43411)),x43414),f312(f138(f853(f853(x43411)),f853(f853(x43411)),f129(f853(x43411)),f127(f853(x43411))),f312(f312(f150(f853(x43411),f853(f853(x43411))),f152(f853(f853(x43411)),x43411,f127(f853(x43411)),f312(f16(f860(f853(x43411),f853(f853(x43411))),x43411),f312(f312(f7(f853(x43411),f853(f853(x43411)),f853(f853(x43411))),f147(f853(x43411))),f127(f853(x43411)))))),x43413))))),f175(x43411,f312(f312(f147(f853(x43411)),f312(f312(f147(x43411),x43412),x43414)),x43413)))
% 173.49/173.41 [4351]E(f312(f233(f859(x43511,x43511)),f312(f249(x43511,x43511,a845),f312(f312(f7(x43511,f860(f859(x43512,x43512),a845),f860(x43511,a845)),f312(f312(f8(f860(x43511,f860(f860(f859(x43512,x43512),a845),a845)),f860(f860(f859(x43512,x43512),a845),f860(x43511,a845)),x43511),f7(x43511,f860(f859(x43512,x43512),a845),a845)),f312(f312(f8(f860(x43511,f859(x43512,x43512)),f860(x43511,f860(f860(f859(x43512,x43512),a845),a845)),x43511),f312(f8(f859(x43512,x43512),f860(f860(f859(x43512,x43512),a845),a845),x43511),f314(f859(x43512,x43512)))),f312(f312(f7(x43511,f860(x43511,x43512),f860(x43511,f859(x43512,x43512))),f312(f312(f8(f860(x43512,f859(x43512,x43512)),f860(f860(x43511,x43512),f860(x43511,f859(x43512,x43512))),x43511),f8(x43512,f859(x43512,x43512),x43511)),f312(f312(f8(x43512,f860(x43512,f859(x43512,x43512)),x43511),f239(x43512,x43512)),x43513))),x43513)))),x43514))),f312(f312(f266(x43512,x43511),x43514),x43513))
% 173.49/173.41 [4437]~E(f36(x44371,x44372),f33(x44373,x44374,x44375))
% 173.49/173.41 [4438]~E(f36(x44381,x44382),f32(x44383,x44384,x44385))
% 173.49/173.41 [4439]~E(f36(x44391,x44392),f31(x44393,x44394,x44395))
% 173.49/173.41 [4440]~E(f35(x44401,x44402),f33(x44403,x44404,x44405))
% 173.49/173.41 [4441]~E(f35(x44411,x44412),f32(x44413,x44414,x44415))
% 173.49/173.41 [4442]~E(f35(x44421,x44422),f31(x44423,x44424,x44425))
% 173.49/173.41 [4443]~E(f28(x44431,x44432),f33(x44433,x44434,x44435))
% 173.49/173.41 [4444]~E(f28(x44441,x44442),f32(x44443,x44444,x44445))
% 173.49/173.41 [4445]~E(f28(x44451,x44452),f31(x44453,x44454,x44455))
% 173.49/173.41 [4446]~E(f33(x44461,x44462,x44463),f36(x44464,x44465))
% 173.49/173.41 [4447]~E(f33(x44471,x44472,x44473),f35(x44474,x44475))
% 173.49/173.41 [4448]~E(f33(x44481,x44482,x44483),f28(x44484,x44485))
% 173.49/173.41 [4449]~E(f32(x44491,x44492,x44493),f36(x44494,x44495))
% 173.49/173.41 [4450]~E(f32(x44501,x44502,x44503),f35(x44504,x44505))
% 173.49/173.41 [4451]~E(f32(x44511,x44512,x44513),f28(x44514,x44515))
% 173.49/173.41 [4452]~E(f31(x44521,x44522,x44523),f36(x44524,x44525))
% 173.49/173.41 [4453]~E(f31(x44531,x44532,x44533),f35(x44534,x44535))
% 173.49/173.41 [4454]~E(f31(x44541,x44542,x44543),f28(x44544,x44545))
% 173.49/173.41 [3843]E(f312(f180(x38431,x38432,x38433,x38434),x38435),f312(f221(f856(x38432),x38432,f312(x38433,x38435),f219(x38432)),f312(x38434,x38435)))
% 173.49/173.41 [3930]E(f180(x39301,x39302,f180(x39301,x39302,x39303,x39304),x39305),f180(x39301,x39302,x39303,f180(x39301,x39302,x39304,x39305)))
% 173.49/173.41 [4111]E(f312(f312(f124(f860(x41111,a845)),f312(f168(x41111),f312(f312(f169(x41111),f312(f190(f853(x41112)),x41113)),x41114))),f179(x41111,x41112,x41115)),f179(x41111,x41112,f182(x41111,x41112,x41115,x41114,x41113)))
% 173.49/173.41 [3668]E(f312(f312(f249(x36681,x36682,x36683),x36684),x36685),f312(f312(x36684,f312(f246(x36681,x36682),x36685)),f312(f248(x36681,x36682),x36685)))
% 173.49/173.41 [3691]E(f312(f221(x36911,x36912,x36913,x36914),f312(f219(x36912),x36915)),f312(x36914,x36915))
% 173.49/173.41 [3701]E(f312(f312(f312(f74(x37011,x37012,x37013),x37014),x37015),f189(f860(x37012,a845))),x37015)
% 173.49/173.41 [3876]E(f222(x38761,x38762,x38763,x38764,f312(f219(x38762),x38765)),f312(x38764,x38765))
% 173.49/173.41 [3985]E(f312(f82(f856(x39851),f856(x39852),f856(x39853),f312(f193(x39851,x39852),x39854)),f312(f193(x39853,x39851),x39855)),f312(f193(x39853,x39852),f312(f82(x39851,x39852,x39853,x39854),x39855)))
% 173.49/173.41 [3987]E(f312(f82(f853(x39871),f853(x39872),f853(x39873),f312(f150(x39871,x39872),x39874)),f312(f150(x39873,x39871),x39875)),f312(f150(x39873,x39872),f312(f82(x39871,x39872,x39873,x39874),x39875)))
% 173.49/173.41 [4068]E(f94(x40681,f75(x40682,x40681,x40683,x40684,x40685)),f312(f312(f73(x40682,x40681,x40683),x40684),x40685))
% 173.49/173.41 [4103]E(f312(f312(f89(a852),f312(f312(f89(a852),f312(x41031,f312(f246(x41032,x41033),x41034))),f312(x41035,f312(f248(x41032,x41033),x41034)))),f312(a126,f2(a852))),f253(x41032,x41033,x41031,x41035,x41034))
% 173.49/173.41 [4290]E(f159(x42901,x42902,f312(f312(f7(x42901,f856(x42902),f856(x42902)),f312(f312(f18(x42901,f856(x42902),f860(f856(x42902),f856(x42902))),f312(f312(f8(a845,f860(f856(x42902),f860(f856(x42902),f856(x42902))),x42901),f108(f856(x42902))),x42903)),f312(f312(f8(x42902,f856(x42902),x42901),f219(x42902)),x42904))),f192(x42902)),x42905),f312(f312(f150(x42901,x42902),x42904),f312(f132(x42901,x42903),x42905)))
% 173.49/173.41 [4492]~E(f312(f312(f312(f81(x44921,f856(x44922)),x44923),x44924),f312(f219(x44922),x44925)),f312(f16(f856(x44922),x44921),f192(x44922)))
% 173.49/173.41 [3605]E(f312(f312(f169(x36051),x36052),f312(f312(f150(x36053,x36051),x36054),x36055)),f312(f312(f150(x36053,x36051),x36054),f312(f312(f169(x36053),x36052),x36055)))
% 173.49/173.41 [3606]E(f312(f312(f134(x36061),x36062),f312(f312(f150(x36063,x36061),x36064),x36065)),f312(f312(f150(x36063,x36061),x36064),f312(f312(f134(x36063),x36062),x36065)))
% 173.49/173.41 [3637]E(f312(f312(f150(x36371,x36372),x36373),f312(f312(f147(x36371),x36374),x36375)),f312(f312(f147(x36372),f312(x36373,x36374)),f312(f312(f150(x36371,x36372),x36373),x36375)))
% 173.49/173.41 [3695]E(f312(f290(x36951,x36952,x36953),f312(f312(f289(x36951),x36954),x36955)),f312(f312(f289(x36952),f312(x36953,x36954)),f312(f290(x36951,x36952,x36953),x36955)))
% 173.49/173.41 [3761]E(f312(f312(f177(x37611,x37612),f312(f312(f169(x37611),x37613),x37614)),f312(f312(f169(x37612),x37613),x37615)),f312(f312(f169(f859(x37611,x37612)),x37613),f312(f312(f177(x37611,x37612),x37614),x37615)))
% 173.49/173.41 [3762]E(f312(f312(f177(x37621,x37622),f312(f312(f134(x37621),x37623),x37624)),f312(f312(f134(x37622),x37623),x37625)),f312(f312(f134(f859(x37621,x37622)),x37623),f312(f312(f177(x37621,x37622),x37624),x37625)))
% 173.49/173.41 [3777]E(f312(f312(f155(x37771,f312(f312(f147(x37771),x37772),x37773)),f312(a126,x37774)),x37775),f312(f312(f147(x37771),x37772),f312(f312(f155(x37771,x37773),x37774),x37775)))
% 173.49/173.41 [3780]E(f312(f221(f856(x37801),x37802,f192(x37801),x37803),f312(f312(f16(f856(x37802),x37804),f192(x37802)),x37805)),f192(x37801))
% 173.49/173.41 [3782]E(f312(f312(f129(x37821),f312(f312(f150(x37822,x37821),x37823),x37824)),f312(f312(f150(x37822,x37821),x37823),x37825)),f312(f312(f150(x37822,x37821),x37823),f312(f312(f129(x37822),x37824),x37825)))
% 173.49/173.41 [3787]E(f312(f312(x37871,x37872),f312(f312(f241(x37873,x37874,x37871),x37872),x37875)),f312(f312(f241(x37873,x37874,x37871),x37872),f312(a126,x37875)))
% 173.49/173.41 [3815]E(f160(x38151,x38152,x38153,f312(f312(f147(x38151),x38154),x38155)),f312(f312(f129(x38152),f312(x38153,x38154)),f160(x38151,x38152,x38153,x38155)))
% 173.49/173.41 [3827]E(f312(f312(f267(x38271,x38272,x38273),f312(f265(x38272,x38271),x38274)),f312(f265(x38273,x38272),x38275)),f312(f265(x38273,x38271),f312(f312(f267(x38273,x38272,x38271),x38275),x38274)))
% 173.49/173.41 [3861]E(f312(f312(f312(f184(f853(x38611),f853(x38611)),x38612),f164(x38611)),f312(f312(f150(x38613,x38611),x38614),x38615)),f312(f312(f150(x38613,x38611),x38614),f312(f312(f312(f184(f853(x38613),f853(x38613)),x38612),f164(x38613)),x38615)))
% 173.49/173.41 [3862]E(f312(f312(f251(x38621,x38622,x38621,x38623),f312(f239(x38622,x38621),x38624)),x38625),f312(x38625,x38624))
% 173.49/173.41 [3890]E(f151(x38901,x38902,f312(f312(f150(x38903,x38901),x38904),x38905)),f151(x38903,f312(f82(x38901,a852,x38903,x38902),x38904),x38905))
% 173.49/173.41 [3951]E(f312(f312(f82(f856(x39511),f856(x39512),x39513,f312(f193(x39511,x39512),x39514)),f312(f16(f856(x39511),x39513),f192(x39511))),x39515),f192(x39512))
% 173.49/173.41 [3952]E(f172(f859(x39521,x39522),f312(f82(x39522,a845,f859(x39521,x39522),x39523),f248(x39521,x39522)),f312(f312(f177(x39521,x39522),x39524),x39525)),f312(f312(f177(x39521,x39522),x39524),f172(x39522,x39523,x39525)))
% 173.49/173.41 [3957]E(f312(f290(x39571,x39572,f312(f312(f8(x39573,x39572,x39571),x39574),x39575)),f235(f860(x39571,a845))),f312(f290(x39573,x39572,x39574),f312(f290(x39571,x39573,x39575),f235(f860(x39571,a845)))))
% 173.49/173.41 [3970]E(f172(f859(x39701,x39702),f312(f82(x39701,a845,f859(x39701,x39702),x39703),f246(x39701,x39702)),f312(f312(f177(x39701,x39702),x39704),x39705)),f312(f312(f177(x39701,x39702),f172(x39701,x39703,x39704)),x39705))
% 173.49/173.41 [3991]E(f312(f312(f124(f860(x39911,a845)),f312(f291(x39911,x39912,x39913),f312(f312(f289(x39912),x39914),f189(f860(x39912,a845))))),f312(f291(x39911,x39912,x39913),x39915)),f312(f291(x39911,x39912,x39913),f312(f312(f289(x39912),x39914),x39915)))
% 173.49/173.41 [4051]E(f312(f312(f129(f859(x40511,x40512)),f312(f312(f150(x40512,f859(x40511,x40512)),f312(f239(x40511,x40512),x40513)),x40514)),f68(x40511,x40512,x40515,x40514)),f68(x40511,x40512,f312(f312(f147(x40511),x40513),x40515),x40514))
% 173.49/173.41 [4052]E(f312(f312(f150(x40521,x40522),x40523),f172(x40521,f312(f82(x40522,a845,x40521,x40524),x40523),x40525)),f172(x40522,x40524,f312(f312(f150(x40521,x40522),x40523),x40525)))
% 173.49/173.41 [4059]E(f312(f138(x40591,x40592,f312(f7(x40592,x40591,x40591),f312(f7(x40591,x40592,x40591),x40593)),x40594),f312(f165(x40592),f312(f165(x40592),x40595))),f312(f138(x40591,x40592,x40593,x40594),x40595))
% 173.49/173.41 [4060]E(f312(f312(f312(f81(x40601,f856(x40602)),f183(x40601,x40602,x40603,x40604)),x40605),f312(x40603,x40605)),f183(x40601,x40602,x40603,f312(f312(f289(x40601),x40605),x40604)))
% 173.49/173.41 [4070]E(f312(f299(x40701,x40702,x40703,f312(f16(x40702,x40701),x40704),f312(f16(x40702,x40703),x40704)),x40705),x40704)
% 173.49/173.41 [4126]E(f312(f221(f853(x41261),x41261,f159(x41262,x41261,x41263,x41264),f312(f312(f7(x41261,f853(x41261),f853(x41261)),f147(x41261)),f159(x41262,x41261,x41263,x41264))),f312(x41263,x41265)),f159(x41262,x41261,x41263,f312(f312(f147(x41262),x41265),x41264)))
% 173.49/173.41 [4163]P22(f312(f312(f227(f860(x41631,a845)),f312(f290(x41632,x41631,x41633),f312(f312(f115(f860(x41632,a845)),x41634),x41635))),f312(f312(f115(f860(x41631,a845)),f312(f290(x41632,x41631,x41633),x41634)),f312(f290(x41632,x41631,x41633),x41635))))
% 173.49/173.41 [4164]P22(f312(f312(f227(f860(x41641,a845)),f312(f264(x41642,x41641,x41643),f312(f312(f115(f860(x41642,a845)),x41644),x41645))),f312(f312(f115(f860(x41641,a845)),f312(f264(x41642,x41641,x41643),x41644)),f312(f264(x41642,x41641,x41643),x41645))))
% 173.49/173.41 [4266]E(f312(f248(x42661,x42662),f312(f250(x42663,x42661,x42662,x42662,x42664,f39(x42662)),x42665)),f312(f248(x42663,x42662),x42665))
% 173.49/173.41 [4267]E(f312(f246(x42671,x42672),f312(f250(x42671,x42671,x42673,x42672,f39(x42671),x42674),x42675)),f312(f246(x42671,x42673),x42675))
% 173.49/173.41 [4345]P18(x43451,x43452,f312(f312(f289(f851(x43451)),f312(f312(f312(f100(x43451),f312(f312(f7(x43451,f860(a847,a847),f860(a847,a845)),f312(f312(f8(f860(a847,a845),f860(f860(a847,a847),f860(a847,a845)),x43451),f8(a847,a845,a847)),x43453)),f312(f312(f18(a847,a852,a847),f312(f312(f7(a847,a850,f860(a852,a847)),a201),x43454)),x43455))),f28(x43454,x43455)),x43453)),f189(f860(f851(x43451),a845))))
% 173.49/173.41 [4347]E(f312(f138(f860(x43471,f856(x43472)),f859(x43471,x43472),f312(f312(f8(f860(x43471,f860(x43472,f860(x43471,f856(x43472)))),f860(f859(x43471,x43472),f860(x43471,f856(x43472))),f860(x43471,f856(x43472))),f249(x43471,x43472,f860(x43471,f856(x43472)))),f312(f312(f7(f860(x43471,f856(x43472)),f860(x43472,f856(x43472)),f860(x43471,f860(x43472,f860(x43471,f856(x43472))))),f312(f312(f8(f860(x43471,f860(f860(x43472,f856(x43472)),f860(x43472,f860(x43471,f856(x43472))))),f860(f860(x43472,f856(x43472)),f860(x43471,f860(x43472,f860(x43471,f856(x43472))))),f860(x43471,f856(x43472))),f7(x43471,f860(x43472,f856(x43472)),f860(x43472,f860(x43471,f856(x43472))))),f312(f312(f8(f860(x43471,f860(f856(x43472),f860(x43471,f856(x43472)))),f860(x43471,f860(f860(x43472,f856(x43472)),f860(x43472,f860(x43471,f856(x43472))))),f860(x43471,f856(x43472))),f312(f8(f860(f856(x43472),f860(x43471,f856(x43472))),f860(f860(x43472,f856(x43472)),f860(x43472,f860(x43471,f856(x43472)))),x43471),f8(f856(x43472),f860(x43471,f856(x43472)),x43472))),f81(x43471,f856(x43472))))),f219(x43472))),x43473),f312(f312(f177(x43471,x43472),x43474),x43475)),f182(x43471,x43472,x43473,x43474,x43475))
% 173.49/173.41 [4349]P18(x43491,x43492,f312(f312(f289(f851(x43491)),f312(f312(f312(f100(x43491),f312(f312(f7(x43491,f860(a847,a845),f860(a847,a845)),f312(f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),x43491),f18(a847,a845,a845)),f312(f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),x43491),f312(f8(a845,f860(a845,a845),a847),a310)),x43493))),f312(f312(f8(a845,a845,a847),a307),x43494))),f35(x43494,x43495)),x43493)),f189(f860(f851(x43491),a845))))
% 173.49/173.41 [3498]E(f105(x34981,x34982,f312(f312(f312(f100(x34981),x34983),x34984),x34985)),f2(a852))
% 173.49/173.41 [3590]E(f312(f312(f312(f312(f81(x35901,x35902),x35903),x35904),x35905),x35904),x35905)
% 173.49/173.41 [3816]E(f312(f312(f50(x38161,f860(x38162,a845)),f312(f312(f289(x38161),x38163),x38164)),x38165),f312(f312(f124(f860(x38162,a845)),f312(x38165,x38163)),f312(f312(f50(x38161,f860(x38162,a845)),x38164),x38165)))
% 173.49/173.41 [3817]E(f312(f312(f51(x38171,f860(x38172,a845)),f312(f312(f289(x38171),x38173),x38174)),x38175),f312(f312(f115(f860(x38172,a845)),f312(x38175,x38173)),f312(f312(f51(x38171,f860(x38172,a845)),x38174),x38175)))
% 173.49/173.41 [3883]E(f312(f312(f124(f860(x38831,a845)),f312(f290(x38832,x38831,x38833),x38834)),f312(f290(x38832,x38831,x38833),x38835)),f312(f290(x38832,x38831,x38833),f312(f312(f124(f860(x38832,a845)),x38834),x38835)))
% 173.49/173.41 [3884]E(f312(f312(f21(f860(x38841,a845)),f312(f291(x38841,x38842,x38843),x38844)),f312(f291(x38841,x38842,x38843),x38845)),f312(f291(x38841,x38842,x38843),f312(f312(f21(f860(x38842,a845)),x38844),x38845)))
% 173.49/173.41 [3885]E(f312(f312(f124(f860(x38851,a845)),f312(f291(x38851,x38852,x38853),x38854)),f312(f291(x38851,x38852,x38853),x38855)),f312(f291(x38851,x38852,x38853),f312(f312(f124(f860(x38852,a845)),x38854),x38855)))
% 173.49/173.41 [3886]E(f312(f312(f115(f860(x38861,a845)),f312(f291(x38861,x38862,x38863),x38864)),f312(f291(x38861,x38862,x38863),x38865)),f312(f291(x38861,x38862,x38863),f312(f312(f115(f860(x38862,a845)),x38864),x38865)))
% 173.49/173.41 [3887]E(f312(f312(f124(f860(x38871,a845)),f312(f264(x38872,x38871,x38873),x38874)),f312(f264(x38872,x38871,x38873),x38875)),f312(f264(x38872,x38871,x38873),f312(f312(f124(f860(x38872,a845)),x38874),x38875)))
% 173.49/173.41 [3889]E(f183(x38891,x38892,f183(x38891,x38892,x38893,x38894),x38895),f183(x38891,x38892,x38893,f312(f312(f115(f860(x38891,a845)),x38894),x38895)))
% 173.49/173.41 [3948]E(f312(f312(f155(x39481,f312(f312(f129(x39481),x39482),f312(f312(f147(x39481),x39483),x39484))),f312(f190(f853(x39481)),x39482)),x39485),f312(f312(f129(x39481),x39482),f312(f312(f147(x39481),x39485),x39484)))
% 173.49/173.41 [3955]E(f312(f312(f51(x39551,f860(x39552,a845)),x39553),f312(f312(f8(f860(x39552,a845),f860(x39552,a845),x39551),f312(f289(x39552),x39554)),x39555)),f312(f312(f289(x39552),x39554),f312(f312(f51(x39551,f860(x39552,a845)),x39553),x39555)))
% 173.49/173.41 [4025]E(f183(x40251,x40252,f312(f312(f312(f81(x40251,f856(x40252)),x40253),x40254),f312(f219(x40252),x40255)),f312(f88(f860(x40251,a845)),f312(f312(f289(x40251),x40254),f189(f860(x40251,a845))))),f183(x40251,x40252,x40253,f312(f88(f860(x40251,a845)),f312(f312(f289(x40251),x40254),f189(f860(x40251,a845))))))
% 173.49/173.41 [4116]E(f312(f312(f150(x41161,x41162),x41163),f312(f132(x41161,f312(f82(x41162,a845,x41161,x41164),x41163)),x41165)),f312(f132(x41162,x41164),f312(f312(f150(x41161,x41162),x41163),x41165)))
% 173.49/173.41 [4120]E(f312(f190(f853(x41201)),f312(f132(x41201,x41202),f312(f312(f150(x41203,x41201),x41204),x41205))),f312(f190(f853(x41203)),f312(f132(x41203,f312(f82(x41201,a845,x41203,x41202),x41204)),x41205)))
% 173.49/173.41 [4258]E(f312(f312(f124(f860(x42581,a845)),f312(f312(f21(f860(x42581,a845)),f179(x42581,x42582,x42583)),f312(f233(x42581),f312(f312(f7(x42581,f860(x42581,a845),a845),f314(x42581)),f312(f312(f21(f860(x42581,a845)),x42584),f179(x42581,x42582,x42585)))))),f312(f233(x42581),f312(f312(f7(x42581,f860(x42581,a845),a845),f314(x42581)),f312(f312(f115(f860(x42581,a845)),x42584),f179(x42581,x42582,x42585))))),f179(x42581,x42582,f85(x42581,f856(x42582),x42583,x42585,x42584)))
% 173.49/173.41 [4326]E(f312(f152(f853(f859(x43261,x43262)),x43262,f127(f859(x43261,x43262)),f312(f312(f7(x43262,f860(f853(x43262),f853(f859(x43261,x43262))),f860(f853(x43262),f853(f859(x43261,x43262)))),f312(f312(f8(f860(f853(f859(x43261,x43262)),f853(f859(x43261,x43262))),f860(f860(f853(x43262),f853(f859(x43261,x43262))),f860(f853(x43262),f853(f859(x43261,x43262)))),x43262),f8(f853(f859(x43261,x43262)),f853(f859(x43261,x43262)),f853(x43262))),f312(f312(f8(f859(x43261,x43262),f860(f853(f859(x43261,x43262)),f853(f859(x43261,x43262))),x43262),f147(f859(x43261,x43262))),f312(f239(x43261,x43262),x43263)))),f312(f177(x43261,x43262),x43264))),x43265),f312(f312(f177(x43261,x43262),f312(f312(f147(x43261),x43263),x43264)),x43265))
% 173.49/173.41 [3811]E(f312(f312(f155(x38111,f312(f312(f155(x38111,x38112),x38113),x38114)),x38113),x38115),f312(f312(f155(x38111,x38112),x38113),x38115))
% 173.49/173.41 [3863]E(f312(f236(x38631,x38632),f312(f312(f289(f859(x38631,x38632)),f312(f312(f239(x38631,x38632),x38633),x38634)),x38635)),f312(f312(f289(x38632),x38634),f312(f236(x38631,x38632),x38635)))
% 173.49/173.41 [3864]E(f312(f238(x38641,x38642),f312(f312(f289(f859(x38641,x38642)),f312(f312(f239(x38641,x38642),x38643),x38644)),x38645)),f312(f312(f289(x38641),x38643),f312(f238(x38641,x38642),x38645)))
% 173.49/173.41 [3941]E(f312(f312(f21(f860(f859(x39411,x39412),a845)),f312(f312(f247(x39411,x39412),x39413),x39414)),f312(f312(f247(x39411,x39412),x39415),x39414)),f312(f312(f247(x39411,x39412),f312(f312(f21(f860(x39411,a845)),x39413),x39415)),x39414))
% 173.49/173.41 [3942]E(f312(f312(f124(f860(f859(x39421,x39422),a845)),f312(f312(f247(x39421,x39422),x39423),x39424)),f312(f312(f247(x39421,x39422),x39425),x39424)),f312(f312(f247(x39421,x39422),f312(f312(f124(f860(x39421,a845)),x39423),x39425)),x39424))
% 173.49/173.41 [3943]E(f312(f312(f115(f860(f859(x39431,x39432),a845)),f312(f312(f247(x39431,x39432),x39433),x39434)),f312(f312(f247(x39431,x39432),x39435),x39434)),f312(f312(f247(x39431,x39432),f312(f312(f115(f860(x39431,a845)),x39433),x39435)),x39434))
% 173.49/173.41 [4005]E(f312(f312(f124(f860(x40051,a845)),f312(f312(f50(x40052,f860(x40051,a845)),x40053),x40054)),f312(f312(f50(x40052,f860(x40051,a845)),x40055),x40054)),f312(f312(f50(x40052,f860(x40051,a845)),f312(f312(f124(f860(x40052,a845)),x40053),x40055)),x40054))
% 173.49/173.41 [4006]E(f312(f312(f115(f860(x40061,a845)),f312(f312(f51(x40062,f860(x40061,a845)),x40063),x40064)),f312(f312(f51(x40062,f860(x40061,a845)),x40065),x40064)),f312(f312(f51(x40062,f860(x40061,a845)),f312(f312(f124(f860(x40062,a845)),x40063),x40065)),x40064))
% 173.49/173.41 [4020]E(f312(f312(f50(x40201,f860(x40202,a845)),x40203),f312(f312(f8(f860(x40202,a845),f860(x40202,a845),x40201),f312(f21(f860(x40202,a845)),x40204)),x40205)),f312(f312(f21(f860(x40202,a845)),x40204),f312(f312(f51(x40201,f860(x40202,a845)),x40203),x40205)))
% 173.49/173.41 [4021]E(f312(f312(f50(x40211,f860(x40212,a845)),x40213),f312(f312(f8(f860(x40212,a845),f860(x40212,a845),x40211),f312(f115(f860(x40212,a845)),x40214)),x40215)),f312(f312(f115(f860(x40212,a845)),x40214),f312(f312(f50(x40211,f860(x40212,a845)),x40213),x40215)))
% 173.49/173.41 [4022]E(f312(f312(f51(x40221,f860(x40222,a845)),x40223),f312(f312(f8(f860(x40222,a845),f860(x40222,a845),x40221),f312(f124(f860(x40222,a845)),x40224)),x40225)),f312(f312(f124(f860(x40222,a845)),x40224),f312(f312(f51(x40221,f860(x40222,a845)),x40223),x40225)))
% 173.49/173.41 [4057]E(f180(x40571,x40572,x40573,f312(f173(x40571,x40572),f312(f165(f859(x40571,x40572)),f312(f312(f177(x40571,x40572),x40574),x40575)))),f182(x40571,x40572,x40573,x40574,x40575))
% 173.49/173.41 [4080]E(f186(f853(x40801),f312(f312(f147(x40801),x40802),x40803),f312(f312(f8(f853(x40801),f853(x40801),a852),f312(f147(x40801),x40804)),f312(f312(f7(a852,x40801,f853(x40801)),f155(x40801,x40803)),x40802)),x40805),f312(f312(f155(x40801,f312(f312(f147(x40801),x40804),x40803)),x40805),x40802))
% 173.49/173.41 [4084]E(f312(f312(f50(x40841,f860(f859(x40842,x40843),a845)),x40844),f312(f312(f8(f860(f859(x40843,x40842),a845),f860(f859(x40842,x40843),a845),x40841),f265(x40843,x40842)),x40845)),f312(f265(x40843,x40842),f312(f312(f50(x40841,f860(f859(x40843,x40842),a845)),x40844),x40845)))
% 173.49/173.41 [4085]E(f312(f312(f51(x40851,f860(f859(x40852,x40853),a845)),x40854),f312(f312(f8(f860(f859(x40853,x40852),a845),f860(f859(x40852,x40853),a845),x40851),f265(x40853,x40852)),x40855)),f312(f265(x40853,x40852),f312(f312(f51(x40851,f860(f859(x40853,x40852),a845)),x40854),x40855)))
% 173.49/173.41 [4137]E(f179(x41371,x41372,f312(f312(f18(x41371,f856(x41373),f856(x41372)),f312(f312(f8(f860(x41373,x41372),f860(f856(x41373),f856(x41372)),x41371),f193(x41373,x41372)),x41374)),x41375)),f179(x41371,x41373,x41375))
% 173.49/173.41 [4190]P22(f312(f312(f227(f860(x41901,a845)),f312(f312(f21(f860(x41901,a845)),f312(f290(x41902,x41901,x41903),x41904)),f312(f290(x41902,x41901,x41903),x41905))),f312(f290(x41902,x41901,x41903),f312(f312(f21(f860(x41902,a845)),x41904),x41905))))
% 173.49/173.41 [4330]E(f312(f152(f853(f859(x43301,x43302)),x43301,f127(f859(x43301,x43302)),f312(f312(f7(x43301,f860(f853(x43301),f853(f859(x43301,x43302))),f860(f853(x43301),f853(f859(x43301,x43302)))),f312(f312(f8(f860(f853(f859(x43301,x43302)),f853(f859(x43301,x43302))),f860(f860(f853(x43301),f853(f859(x43301,x43302))),f860(f853(x43301),f853(f859(x43301,x43302)))),x43301),f8(f853(f859(x43301,x43302)),f853(f859(x43301,x43302)),f853(x43301))),f312(f312(f8(f859(x43301,x43302),f860(f853(f859(x43301,x43302)),f853(f859(x43301,x43302))),x43301),f147(f859(x43301,x43302))),f312(f312(f7(x43301,x43302,f859(x43301,x43302)),f239(x43301,x43302)),x43303)))),f312(f312(f7(f853(x43301),f853(x43302),f853(f859(x43301,x43302))),f177(x43301,x43302)),x43304))),x43305),f312(f312(f177(x43301,x43302),x43305),f312(f312(f147(x43302),x43303),x43304)))
% 173.49/173.41 [4045]E(f312(f312(f124(f860(x40451,a845)),f312(f264(x40452,x40451,x40453),x40454)),f312(f264(x40452,x40451,x40455),x40454)),f312(f264(x40452,x40451,f312(f312(f124(f860(f859(x40452,x40451),a845)),x40453),x40455)),x40454))
% 173.49/173.41 [4087]E(f312(f312(f129(f859(x40871,x40872)),f312(f312(f177(x40871,x40872),x40873),f312(f312(f169(x40872),f312(f190(f853(x40871)),x40873)),x40874))),f312(f312(f177(x40871,x40872),x40875),f312(f312(f134(x40872),f312(f190(f853(x40871)),x40873)),x40874))),f312(f312(f177(x40871,x40872),f312(f312(f129(x40871),x40873),x40875)),x40874))
% 173.49/173.41 [4193]E(f312(f312(f247(x41931,x41932),x41933),f312(f312(f18(x41931,f860(x41932,a845),f860(x41932,a845)),f312(f312(f8(f860(x41932,a845),f860(f860(x41932,a845),f860(x41932,a845)),x41931),f21(f860(x41932,a845))),x41934)),x41935)),f312(f312(f21(f860(f859(x41931,x41932),a845)),f312(f312(f247(x41931,x41932),x41933),x41934)),f312(f312(f247(x41931,x41932),x41933),x41935)))
% 173.49/173.41 [4194]E(f312(f312(f247(x41941,x41942),x41943),f312(f312(f18(x41941,f860(x41942,a845),f860(x41942,a845)),f312(f312(f8(f860(x41942,a845),f860(f860(x41942,a845),f860(x41942,a845)),x41941),f124(f860(x41942,a845))),x41944)),x41945)),f312(f312(f124(f860(f859(x41941,x41942),a845)),f312(f312(f247(x41941,x41942),x41943),x41944)),f312(f312(f247(x41941,x41942),x41943),x41945)))
% 173.49/173.41 [4195]E(f312(f312(f247(x41951,x41952),x41953),f312(f312(f18(x41951,f860(x41952,a845),f860(x41952,a845)),f312(f312(f8(f860(x41952,a845),f860(f860(x41952,a845),f860(x41952,a845)),x41951),f115(f860(x41952,a845))),x41954)),x41955)),f312(f312(f115(f860(f859(x41951,x41952),a845)),f312(f312(f247(x41951,x41952),x41953),x41954)),f312(f312(f247(x41951,x41952),x41953),x41955)))
% 173.49/173.41 [4199]E(f312(f312(f50(x41991,f860(x41992,a845)),x41993),f312(f312(f7(x41991,f860(x41992,a845),f860(x41992,a845)),f312(f312(f8(f860(x41992,a845),f860(f860(x41992,a845),f860(x41992,a845)),x41991),f21(f860(x41992,a845))),x41994)),x41995)),f312(f312(f21(f860(x41992,a845)),f312(f312(f50(x41991,f860(x41992,a845)),x41993),x41994)),x41995))
% 173.49/173.41 [4200]E(f312(f312(f50(x42001,f860(x42002,a845)),x42003),f312(f312(f7(x42001,f860(x42002,a845),f860(x42002,a845)),f312(f312(f8(f860(x42002,a845),f860(f860(x42002,a845),f860(x42002,a845)),x42001),f115(f860(x42002,a845))),x42004)),x42005)),f312(f312(f115(f860(x42002,a845)),f312(f312(f50(x42001,f860(x42002,a845)),x42003),x42004)),x42005))
% 173.49/173.41 [4201]E(f312(f312(f51(x42011,f860(x42012,a845)),x42013),f312(f312(f7(x42011,f860(x42012,a845),f860(x42012,a845)),f312(f312(f8(f860(x42012,a845),f860(f860(x42012,a845),f860(x42012,a845)),x42011),f124(f860(x42012,a845))),x42014)),x42015)),f312(f312(f124(f860(x42012,a845)),f312(f312(f51(x42011,f860(x42012,a845)),x42013),x42014)),x42015))
% 173.49/173.41 [4205]E(f312(f312(f50(x42051,f860(x42052,a845)),x42053),f312(f312(f18(x42051,f860(x42052,a845),f860(x42052,a845)),f312(f312(f8(f860(x42052,a845),f860(f860(x42052,a845),f860(x42052,a845)),x42051),f124(f860(x42052,a845))),x42054)),x42055)),f312(f312(f124(f860(x42052,a845)),f312(f312(f50(x42051,f860(x42052,a845)),x42053),x42054)),f312(f312(f50(x42051,f860(x42052,a845)),x42053),x42055)))
% 173.49/173.41 [4206]E(f312(f312(f51(x42061,f860(x42062,a845)),x42063),f312(f312(f18(x42061,f860(x42062,a845),f860(x42062,a845)),f312(f312(f8(f860(x42062,a845),f860(f860(x42062,a845),f860(x42062,a845)),x42061),f115(f860(x42062,a845))),x42064)),x42065)),f312(f312(f115(f860(x42062,a845)),f312(f312(f51(x42061,f860(x42062,a845)),x42063),x42064)),f312(f312(f51(x42061,f860(x42062,a845)),x42063),x42065)))
% 173.49/173.41 [4220]E(f312(f312(f50(x42201,f860(x42202,a845)),x42203),f312(f312(f18(x42201,f860(x42202,a845),f860(x42202,a845)),f312(f312(f8(f860(x42202,a845),f860(f860(x42202,a845),f860(x42202,a845)),x42201),f124(f860(x42202,a845))),x42204)),x42205)),f312(f312(f124(f860(x42202,a845)),f48(f860(x42202,a845),f312(f290(x42201,f860(x42202,a845),x42204),x42203))),f48(f860(x42202,a845),f312(f290(x42201,f860(x42202,a845),x42205),x42203))))
% 173.49/173.41 [4221]E(f312(f312(f51(x42211,f860(x42212,a845)),x42213),f312(f312(f18(x42211,f860(x42212,a845),f860(x42212,a845)),f312(f312(f8(f860(x42212,a845),f860(f860(x42212,a845),f860(x42212,a845)),x42211),f115(f860(x42212,a845))),x42214)),x42215)),f312(f312(f115(f860(x42212,a845)),f49(f860(x42212,a845),f312(f290(x42211,f860(x42212,a845),x42214),x42213))),f49(f860(x42212,a845),f312(f290(x42211,f860(x42212,a845),x42215),x42213))))
% 173.49/173.41 [4254]E(f312(f312(f134(x42541),f312(f190(f853(x42541)),f172(x42541,x42542,f312(f312(f150(x42543,x42541),x42544),x42545)))),f312(f312(f150(x42543,x42541),x42544),x42545)),f312(f312(f150(x42543,x42541),x42544),f312(f312(f134(x42543),f312(f190(f853(x42543)),f172(x42543,f312(f82(x42541,a845,x42543,x42542),x42544),x42545))),x42545)))
% 173.49/173.41 [4127]E(f312(f312(f129(f859(x41271,x41272)),f312(f312(f177(x41271,x41272),f312(f312(f169(x41271),f312(f190(f853(x41272)),x41273)),x41274)),x41273)),f312(f312(f177(x41271,x41272),f312(f312(f134(x41271),f312(f190(f853(x41272)),x41273)),x41274)),x41275)),f312(f312(f177(x41271,x41272),x41274),f312(f312(f129(x41272),x41273),x41275)))
% 173.49/173.41 [4246]E(f94(x42461,f312(f312(f18(x42461,a845,a845),f312(f312(f8(a845,f860(a845,a845),x42461),a310),f312(f312(f7(x42461,f860(x42461,a845),a845),f314(x42461)),x42462))),f312(f312(f7(x42461,x42463,a845),f312(f312(f8(x42463,f860(x42463,a845),x42461),a309),x42464)),x42465))),f312(f86(x42461,x42463,x42462,x42464),x42465))
% 173.49/173.41 [4296]E(f312(f312(f95(a1,x42961),f312(f117(a1),f312(f312(f89(a1),x42962),a111))),f312(f312(f18(a1,x42961,x42961),f312(f312(f7(a1,x42961,f860(x42961,x42961)),f312(f312(f8(a845,f860(x42961,f860(x42961,x42961)),a1),f108(x42961)),a194)),f186(x42961,x42963,x42964,x42965))),f312(f312(f8(a852,x42961,a1),x42964),f312(f312(f7(a1,a852,a852),f312(f312(f8(a852,f860(a852,a852),a1),f89(a852)),a118)),x42965)))),f186(x42961,x42963,x42964,f312(f312(f89(a852),f312(f117(a852),x42962)),x42965)))
% 173.49/173.41 [4327]E(f312(f173(x43271,x43272),f312(f312(f150(f859(x43271,x43273),f859(x43271,x43272)),f312(f249(x43271,x43273,f859(x43271,x43272)),f312(f312(f7(x43271,f860(x43273,x43272),f860(x43273,f859(x43271,x43272))),f312(f312(f8(f860(x43272,f859(x43271,x43272)),f860(f860(x43273,x43272),f860(x43273,f859(x43271,x43272))),x43271),f8(x43272,f859(x43271,x43272),x43273)),f239(x43271,x43272))),x43274))),x43275)),f312(f82(f856(x43273),f856(x43272),x43271,f312(f193(x43273,x43272),x43274)),f312(f173(x43271,x43273),x43275)))
% 173.49/173.41 [4289]E(f179(x42891,x42892,f312(f312(f18(x42891,f856(x42892),f856(x42892)),f312(f312(f18(x42891,f856(x42892),f860(f856(x42892),f856(x42892))),f312(f312(f8(a845,f860(f856(x42892),f860(f856(x42892),f856(x42892))),x42891),f108(f856(x42892))),x42893)),x42894)),x42895)),f312(f312(f124(f860(x42891,a845)),f312(f312(f115(f860(x42891,a845)),f179(x42891,x42892,x42894)),f312(f233(x42891),x42893))),f312(f312(f115(f860(x42891,a845)),f179(x42891,x42892,x42895)),f312(f233(x42891),f312(f312(f8(a845,a845,x42891),a307),x42893)))))
% 173.49/173.41 [4325]E(f312(f312(f95(a1,x43251),f312(f117(a1),f312(f312(f89(a1),x43252),a111))),f312(f312(f18(a1,x43251,x43251),f312(f312(f7(a1,x43251,f860(x43251,x43251)),f312(f312(f8(a845,f860(x43251,f860(x43251,x43251)),a1),f108(x43251)),a194)),f312(f185(x43251,x43253,x43254),x43255))),f312(f312(f18(a1,x43251,x43251),f312(f312(f8(a852,f860(x43251,x43251),a1),x43254),f312(f312(f7(a1,a852,a852),f312(f312(f8(a852,f860(a852,a852),a1),f89(a852)),a118)),x43255))),f312(f312(f8(a852,x43251,a1),f185(x43251,x43253,x43254)),f312(f312(f7(a1,a852,a852),f312(f312(f8(a852,f860(a852,a852),a1),f89(a852)),a118)),x43255))))),f312(f185(x43251,x43253,x43254),f312(f312(f89(a852),f312(f117(a852),x43252)),x43255)))
% 173.49/173.41 [4373]E(f312(f233(f859(x43731,x43732)),f312(f249(x43731,x43732,a845),f312(f312(f8(f860(x43732,f860(x43733,a845)),f860(x43732,a845),x43731),f312(f8(f860(x43733,a845),a845,x43732),f96(x43733))),f312(f312(f7(x43731,f860(x43732,f860(x43733,a845)),f860(x43732,f860(x43733,a845))),f312(f312(f8(f860(f860(x43733,a845),f860(x43733,a845)),f860(f860(x43732,f860(x43733,a845)),f860(x43732,f860(x43733,a845))),x43731),f8(f860(x43733,a845),f860(x43733,a845),x43732)),f312(f312(f8(f860(x43733,f860(a845,a845)),f860(f860(x43733,a845),f860(x43733,a845)),x43731),f18(x43733,a845,a845)),f312(f312(f8(f860(x43733,a845),f860(x43733,f860(a845,a845)),x43731),f312(f8(a845,f860(a845,a845),x43733),a310)),f312(f312(f7(x43731,f860(f859(x43731,x43733),a845),f860(x43733,a845)),f312(f312(f8(f860(x43733,f860(f860(f859(x43731,x43733),a845),a845)),f860(f860(f859(x43731,x43733),a845),f860(x43733,a845)),x43731),f7(x43733,f860(f859(x43731,x43733),a845),a845)),f312(f312(f8(f860(x43733,f859(x43731,x43733)),f860(x43733,f860(f860(f859(x43731,x43733),a845),a845)),x43731),f312(f8(f859(x43731,x43733),f860(f860(f859(x43731,x43733),a845),a845),x43733),f314(f859(x43731,x43733)))),f239(x43731,x43733)))),x43734))))),f312(f312(f7(x43732,f860(f859(x43733,x43732),a845),f860(x43733,a845)),f312(f312(f8(f860(x43733,f860(f860(f859(x43733,x43732),a845),a845)),f860(f860(f859(x43733,x43732),a845),f860(x43733,a845)),x43732),f7(x43733,f860(f859(x43733,x43732),a845),a845)),f312(f312(f8(f860(x43733,f859(x43733,x43732)),f860(x43733,f860(f860(f859(x43733,x43732),a845),a845)),x43732),f312(f8(f859(x43733,x43732),f860(f860(f859(x43733,x43732),a845),a845),x43733),f314(f859(x43733,x43732)))),f312(f7(x43733,x43732,f859(x43733,x43732)),f239(x43733,x43732))))),x43735))))),f312(f312(f267(x43731,x43733,x43732),x43734),x43735))
% 173.49/173.41 [4474]~E(f32(x44741,x44742,x44743),f33(x44744,x44745,x44746))
% 173.49/173.41 [4477]~E(f31(x44771,x44772,x44773),f33(x44774,x44775,x44776))
% 173.49/173.41 [4478]~E(f31(x44781,x44782,x44783),f32(x44784,x44785,x44786))
% 173.49/173.41 [3971]E(f213(x39711,x39712,x39713,x39714,f209(x39711,x39712,x39715,x39716)),f312(f312(x39714,x39715),x39716))
% 173.49/173.41 [3972]E(f214(x39721,x39722,x39723,x39724,f209(x39721,x39722,x39725,x39726)),f312(f312(x39724,x39725),x39726))
% 173.49/173.41 [4114]E(f182(x41141,x41142,f180(x41141,x41142,x41143,x41144),x41145,x41146),f180(x41141,x41142,x41143,f182(x41141,x41142,x41144,x41145,x41146)))
% 173.49/173.41 [4236]E(f312(f82(f859(x42361,x42362),x42362,f859(x42363,x42364),f248(x42361,x42362)),f250(x42363,x42361,x42364,x42362,x42365,x42366)),f312(f82(x42364,x42362,f859(x42363,x42364),x42366),f248(x42363,x42364)))
% 173.49/173.41 [4237]E(f312(f82(f859(x42371,x42372),x42371,f859(x42373,x42374),f246(x42371,x42372)),f250(x42373,x42371,x42374,x42372,x42375,x42376)),f312(f82(x42373,x42371,f859(x42373,x42374),x42375),f246(x42373,x42374)))
% 173.49/173.41 [3838]E(f312(f312(f82(x38381,x38382,x38383,x38384),x38385),x38386),f312(x38384,f312(x38385,x38386)))
% 173.49/173.41 [4033]E(f215(x40331,x40332,x40333,x40334,f209(x40331,x40332,x40335,x40336)),f312(f312(f89(a852),f312(f312(f89(a852),f312(x40333,x40335)),f312(x40334,x40336))),f312(a126,f2(a852))))
% 173.49/173.41 [3633]E(f312(f312(f249(x36331,x36332,x36333),x36334),f312(f312(f239(x36331,x36332),x36335),x36336)),f312(f312(x36334,x36335),x36336))
% 173.49/173.41 [3692]E(f312(f312(f312(f8(x36921,x36922,x36923),x36924),x36925),x36926),f312(x36924,f312(x36925,x36926)))
% 173.49/173.41 [3693]E(f312(f312(f312(f7(x36931,x36932,x36933),x36934),x36935),x36936),f312(f312(x36934,x36936),x36935))
% 173.49/173.41 [3711]E(f312(f312(f312(f18(x37111,x37112,x37113),x37114),x37115),x37116),f312(f312(x37114,x37116),f312(x37115,x37116)))
% 173.49/173.41 [3733]E(f312(f152(x37331,x37332,x37333,x37334),f312(f312(f147(x37332),x37335),x37336)),f312(f312(x37334,x37335),x37336))
% 173.49/173.41 [3842]E(f312(f312(f147(f859(x38421,x38422)),f312(f312(f239(x38421,x38422),x38423),x38424)),f312(f312(f177(x38421,x38422),x38425),x38426)),f312(f312(f177(x38421,x38422),f312(f312(f147(x38421),x38423),x38425)),f312(f312(f147(x38422),x38424),x38426)))
% 173.49/173.41 [3844]E(f312(f312(f150(x38441,x38442),x38443),f312(f312(f155(x38441,x38444),x38445),x38446)),f312(f312(f155(x38442,f312(f312(f150(x38441,x38442),x38443),x38444)),x38445),f312(x38443,x38446)))
% 173.49/173.41 [3888]E(f312(f138(x38881,x38882,x38883,x38884),f312(f312(f147(x38882),x38885),x38886)),f312(f138(x38881,x38882,x38883,f312(f312(x38883,x38884),x38885)),x38886))
% 173.49/173.41 [3912]E(f252(x39121,x39122,x39123,x39124,f312(f312(f239(x39121,x39122),x39125),x39126)),f312(f312(x39124,x39125),x39126))
% 173.49/173.41 [3996]E(f312(f312(f50(x39961,f860(x39962,a845)),x39963),f312(f82(x39964,f860(x39962,a845),x39961,x39965),x39966)),f312(f312(f50(x39964,f860(x39962,a845)),f312(f290(x39961,x39964,x39966),x39963)),x39965))
% 173.49/173.41 [4048]E(f312(f312(f193(x40481,x40482),x40483),f312(f312(f193(x40484,x40481),x40485),x40486)),f312(f312(f193(x40484,x40482),f312(f82(x40481,x40482,x40484,x40483),x40485)),x40486))
% 173.49/173.41 [4050]E(f312(f312(f150(x40501,x40502),x40503),f312(f312(f150(x40504,x40501),x40505),x40506)),f312(f312(f150(x40504,x40502),f312(f82(x40501,x40502,x40504,x40503),x40505)),x40506))
% 173.49/173.41 [4055]E(f312(f290(x40551,x40552,f312(f82(x40553,x40552,x40551,x40554),x40555)),x40556),f312(f290(x40553,x40552,x40554),f312(f290(x40551,x40553,x40555),x40556)))
% 173.49/173.41 [4056]E(f312(f291(x40561,x40562,f312(f82(x40563,x40562,x40561,x40564),x40565)),x40566),f312(f291(x40561,x40563,x40565),f312(f291(x40563,x40562,x40564),x40566)))
% 173.49/173.41 [4086]E(f180(x40861,x40862,x40863,f312(f312(f312(f81(x40861,f856(x40862)),x40864),x40865),f312(f219(x40862),x40866))),f312(f312(f312(f81(x40861,f856(x40862)),f180(x40861,x40862,x40863,x40864)),x40865),f312(f219(x40862),x40866)))
% 173.49/173.41 [4088]E(f312(f138(x40881,x40882,x40883,f312(f138(x40881,x40882,x40883,x40884),x40885)),x40886),f312(f138(x40881,x40882,x40883,x40884),f312(f312(f129(x40882),x40885),x40886)))
% 173.49/173.41 [4226]E(f312(f250(x42261,x42261,x42262,x42263,f39(x42261),x42264),f312(f312(f239(x42261,x42262),x42265),x42266)),f312(f312(f239(x42261,x42263),x42265),f312(x42264,x42266)))
% 173.49/173.41 [4227]E(f312(f250(x42271,x42272,x42273,x42273,x42274,f39(x42273)),f312(f312(f239(x42271,x42273),x42275),x42276)),f312(f312(f239(x42272,x42273),f312(x42274,x42275)),x42276))
% 173.49/173.41 [4312]E(f312(f312(f150(f859(x43121,x43122),f859(x43121,x43123)),f312(f249(x43121,x43122,f859(x43121,x43123)),f312(f312(f7(x43121,f860(x43122,x43123),f860(x43122,f859(x43121,x43123))),f312(f312(f8(f860(x43123,f859(x43121,x43123)),f860(f860(x43122,x43123),f860(x43122,f859(x43121,x43123))),x43121),f8(x43123,f859(x43121,x43123),x43122)),f239(x43121,x43123))),x43124))),f312(f312(f177(x43121,x43122),x43125),x43126)),f312(f312(f177(x43121,x43123),x43125),f312(f312(f150(x43122,x43123),x43124),x43126)))
% 173.49/173.41 [3698]E(f106(x36981,x36982,x36983,f312(f312(f312(f100(x36981),x36984),x36985),x36986)),f312(f312(f312(x36983,x36984),x36985),x36986))
% 173.49/173.41 [3699]E(f107(x36991,x36992,x36993,f312(f312(f312(f100(x36991),x36994),x36995),x36996)),f312(f312(f312(x36993,x36994),x36995),x36996))
% 173.49/173.41 [3898]E(f312(f312(f82(x38981,x38982,x38983,f312(f16(x38982,x38981),x38984)),x38985),x38986),x38984)
% 173.49/173.41 [3932]E(f312(f290(x39321,x39322,x39323),f312(f290(x39324,x39321,x39325),x39326)),f312(f290(x39324,x39322,f312(f312(f8(x39321,x39322,x39324),x39323),x39325)),x39326))
% 173.49/173.41 [3937]E(f312(f312(f50(x39371,f860(x39372,a845)),f312(f290(x39373,x39371,x39374),x39375)),x39376),f312(f312(f50(x39373,f860(x39372,a845)),x39375),f312(f312(f8(x39371,f860(x39372,a845),x39373),x39376),x39374)))
% 173.49/173.41 [3938]E(f312(f312(f51(x39381,f860(x39382,a845)),f312(f290(x39383,x39381,x39384),x39385)),x39386),f312(f312(f51(x39383,f860(x39382,a845)),x39385),f312(f312(f8(x39381,f860(x39382,a845),x39383),x39386),x39384)))
% 173.52/173.41 [3939]E(f312(f312(f50(x39391,f860(x39392,a845)),x39393),f312(f312(f8(x39394,f860(x39392,a845),x39391),x39395),x39396)),f312(f312(f50(x39394,f860(x39392,a845)),f312(f290(x39391,x39394,x39396),x39393)),x39395))
% 173.52/173.41 [3940]E(f312(f312(f51(x39401,f860(x39402,a845)),x39403),f312(f312(f8(x39404,f860(x39402,a845),x39401),x39405),x39406)),f312(f312(f51(x39404,f860(x39402,a845)),f312(f290(x39401,x39404,x39406),x39403)),x39405))
% 173.52/173.41 [3998]E(f312(f312(f50(x39981,f860(x39982,a845)),x39983),f312(f312(f8(f860(x39984,a845),f860(x39982,a845),x39981),f290(x39984,x39982,x39985)),x39986)),f312(f290(x39984,x39982,x39985),f312(f312(f50(x39981,f860(x39984,a845)),x39983),x39986)))
% 173.52/173.41 [3999]E(f312(f312(f50(x39991,f860(x39992,a845)),x39993),f312(f312(f8(f860(x39994,a845),f860(x39992,a845),x39991),f291(x39992,x39994,x39995)),x39996)),f312(f291(x39992,x39994,x39995),f312(f312(f50(x39991,f860(x39994,a845)),x39993),x39996)))
% 173.52/173.41 [4000]E(f312(f312(f51(x40001,f860(x40002,a845)),x40003),f312(f312(f8(f860(x40004,a845),f860(x40002,a845),x40001),f291(x40002,x40004,x40005)),x40006)),f312(f291(x40002,x40004,x40005),f312(f312(f51(x40001,f860(x40004,a845)),x40003),x40006)))
% 173.52/173.41 [4001]E(f312(f312(f50(x40011,f860(x40012,a845)),x40013),f312(f312(f8(f860(x40014,a845),f860(x40012,a845),x40011),f264(x40014,x40012,x40015)),x40016)),f312(f264(x40014,x40012,x40015),f312(f312(f50(x40011,f860(x40014,a845)),x40013),x40016)))
% 173.52/173.41 [4095]E(f312(f138(x40951,x40952,f312(f7(x40952,x40951,x40951),x40953),x40954),f312(f165(x40952),f312(f312(f147(x40952),x40955),x40956))),f312(f312(x40953,x40955),f312(f138(x40951,x40952,f312(f7(x40952,x40951,x40951),x40953),x40954),f312(f165(x40952),x40956))))
% 173.52/173.41 [4150]E(f312(f312(f18(f859(x41501,x41502),x41502,x41503),f312(f312(f8(x41504,f860(x41502,x41503),f859(x41501,x41502)),x41505),f312(f312(f8(x41501,x41504,f859(x41501,x41502)),x41506),f246(x41501,x41502)))),f248(x41501,x41502)),f312(f249(x41501,x41502,x41503),f312(f312(f8(x41504,f860(x41502,x41503),x41501),x41505),x41506)))
% 173.52/173.41 [4157]E(f312(f138(x41571,x41572,f312(f7(x41572,x41571,x41571),x41573),f312(f138(x41571,x41572,f312(f7(x41572,x41571,x41571),x41573),x41574),f312(f165(x41572),x41575))),f312(f165(x41572),x41576)),f312(f138(x41571,x41572,f312(f7(x41572,x41571,x41571),x41573),x41574),f312(f165(x41572),f312(f312(f129(x41572),x41576),x41575))))
% 173.52/173.41 [4159]E(f312(f312(f150(f859(x41591,x41592),f859(x41593,x41592)),f312(f249(x41591,x41592,f859(x41593,x41592)),f312(f312(f8(x41593,f860(x41592,f859(x41593,x41592)),x41591),f239(x41593,x41592)),x41594))),f312(f312(f177(x41591,x41592),x41595),x41596)),f312(f312(f177(x41593,x41592),f312(f312(f150(x41591,x41593),x41594),x41595)),x41596))
% 173.52/173.41 [4209]P22(f312(f312(f227(f860(x42091,a845)),f312(f264(x42092,x42091,x42093),f312(f312(f51(x42094,f860(x42092,a845)),x42095),x42096))),f312(f312(f51(x42094,f860(x42091,a845)),x42095),f312(f312(f8(f860(x42092,a845),f860(x42091,a845),x42094),f264(x42092,x42091,x42093)),x42096))))
% 173.52/173.41 [4013]E(f312(f312(f177(x40131,x40132),f312(f312(f155(x40131,x40133),x40134),f312(f246(x40131,x40132),x40135))),f312(f312(f155(x40132,x40136),x40134),f312(f248(x40131,x40132),x40135))),f312(f312(f155(f859(x40131,x40132),f312(f312(f177(x40131,x40132),x40133),x40136)),x40134),x40135))
% 173.52/173.41 [4076]E(f312(f312(f124(f860(f859(x40761,x40762),a845)),f312(f312(f267(x40761,x40763,x40762),x40764),x40765)),f312(f312(f267(x40761,x40763,x40762),x40764),x40766)),f312(f312(f267(x40761,x40763,x40762),x40764),f312(f312(f124(f860(f859(x40763,x40762),a845)),x40765),x40766)))
% 173.52/173.41 [4171]E(f312(f312(f289(f859(x41711,x41712)),f312(f312(f239(x41711,x41712),x41713),x41714)),f312(f312(f124(f860(f859(x41711,x41712),a845)),f312(f312(f247(x41711,x41712),x41715),f312(f16(f860(x41712,a845),x41711),f312(f312(f289(x41712),x41714),x41716)))),f312(f312(f247(x41711,x41712),f312(f312(f289(x41711),x41713),x41715)),f312(f16(f860(x41712,a845),x41711),x41716)))),f312(f312(f247(x41711,x41712),f312(f312(f289(x41711),x41713),x41715)),f312(f16(f860(x41712,a845),x41711),f312(f312(f289(x41712),x41714),x41716))))
% 173.52/173.41 [4175]E(f312(f312(f197(x41751,x41752),x41753),f312(f312(f7(x41751,f860(x41754,f856(x41752)),f856(x41752)),f312(f312(f8(f856(x41754),f860(f860(x41754,f856(x41752)),f856(x41752)),x41751),f197(x41754,x41752)),x41755)),x41756)),f312(f312(f197(x41754,x41752),f312(f312(f197(x41751,x41754),x41753),x41755)),x41756))
% 173.52/173.41 [4249]E(f312(f312(f115(f860(x42491,a845)),f312(f291(x42491,x42492,f312(f82(f859(x42492,x42493),x42492,x42491,f246(x42492,x42493)),x42494)),x42495)),f312(f291(x42491,x42493,f312(f82(f859(x42492,x42493),x42493,x42491,f248(x42492,x42493)),x42494)),x42496)),f312(f291(x42491,f859(x42492,x42493),x42494),f312(f312(f247(x42492,x42493),x42495),f312(f16(f860(x42493,a845),x42492),x42496))))
% 173.52/173.41 [3995]E(f312(f312(f312(f81(x39951,x39952),f312(f312(f312(f81(x39951,x39952),x39953),x39954),x39955)),x39954),x39956),f312(f312(f312(f81(x39951,x39952),x39953),x39954),x39956))
% 173.52/173.41 [4100]E(f312(f312(f124(f860(f859(x41001,x41002),a845)),f312(f312(f267(x41001,x41003,x41002),x41004),x41005)),f312(f312(f267(x41001,x41003,x41002),x41006),x41005)),f312(f312(f267(x41001,x41003,x41002),f312(f312(f124(f860(f859(x41001,x41003),a845)),x41004),x41006)),x41005))
% 173.52/173.41 [4234]E(f312(f312(f50(x42341,f860(x42342,a845)),x42343),f312(f312(f7(x42341,f860(x42344,f860(x42342,a845)),f860(x42342,a845)),f312(f312(f8(f860(x42344,a845),f860(f860(x42344,f860(x42342,a845)),f860(x42342,a845)),x42341),f50(x42344,f860(x42342,a845))),x42345)),x42346)),f312(f312(f50(x42344,f860(x42342,a845)),f312(f312(f50(x42341,f860(x42344,a845)),x42343),x42345)),x42346))
% 173.52/173.41 [4235]E(f312(f312(f51(x42351,f860(x42352,a845)),x42353),f312(f312(f7(x42351,f860(x42354,f860(x42352,a845)),f860(x42352,a845)),f312(f312(f8(f860(x42354,a845),f860(f860(x42354,f860(x42352,a845)),f860(x42352,a845)),x42351),f51(x42354,f860(x42352,a845))),x42355)),x42356)),f312(f312(f51(x42354,f860(x42352,a845)),f312(f312(f50(x42351,f860(x42354,a845)),x42353),x42355)),x42356))
% 173.52/173.41 [4284]E(f312(f249(x42841,x42842,f859(x42843,x42844)),f312(f312(f7(x42841,f860(x42842,x42844),f860(x42842,f859(x42843,x42844))),f312(f312(f8(f860(x42844,f859(x42843,x42844)),f860(f860(x42842,x42844),f860(x42842,f859(x42843,x42844))),x42841),f8(x42844,f859(x42843,x42844),x42842)),f312(f312(f8(x42843,f860(x42844,f859(x42843,x42844)),x42841),f239(x42843,x42844)),x42845))),x42846)),f250(x42841,x42843,x42842,x42844,x42845,x42846))
% 173.52/173.41 [4208]E(f312(f312(f312(f81(x42081,f856(x42082)),f183(x42081,x42082,x42083,f312(f312(f21(f860(x42081,a845)),x42084),f312(f312(f289(x42081),x42085),f189(f860(x42081,a845)))))),x42085),x42086),f312(f312(f312(f81(x42081,f856(x42082)),f183(x42081,x42082,x42083,x42084)),x42085),x42086))
% 173.52/173.41 [4308]E(f312(f290(x43081,x43082,f312(f312(f18(x43081,x43082,x43082),f312(f312(f18(x43081,x43082,f860(x43082,x43082)),f312(f312(f8(a845,f860(x43082,f860(x43082,x43082)),x43081),f108(x43082)),x43083)),x43084)),x43085)),x43086),f312(f312(f124(f860(x43082,a845)),f312(f290(x43081,x43082,x43084),f312(f312(f115(f860(x43081,a845)),x43086),f312(f233(x43081),x43083)))),f312(f290(x43081,x43082,x43085),f312(f312(f115(f860(x43081,a845)),x43086),f312(f233(x43081),f312(f312(f8(a845,a845,x43081),a307),x43083))))))
% 173.52/173.41 [4317]E(f312(f290(x43171,f859(x43172,x43173),f312(f312(f18(x43171,x43173,f859(x43172,x43173)),f312(f312(f8(x43172,f860(x43173,f859(x43172,x43173)),x43171),f239(x43172,x43173)),x43174)),x43175)),x43176),f312(f312(f247(x43172,x43173),f312(f290(x43171,x43172,x43174),x43176)),f312(f312(f8(f860(x43171,a845),f860(x43173,a845),x43172),f290(x43171,x43173,x43175)),f312(f312(f7(x43172,f860(x43171,a845),f860(x43171,a845)),f312(f312(f8(f860(x43171,a845),f860(f860(x43171,a845),f860(x43171,a845)),x43172),f115(f860(x43171,a845))),f312(f312(f8(f860(x43172,a845),f860(x43171,a845),x43172),f291(x43171,x43172,x43174)),f312(f312(f7(x43172,f860(x43172,a845),f860(x43172,a845)),f289(x43172)),f189(f860(x43172,a845)))))),x43176))))
% 173.52/173.41 [4268]E(f312(f248(x42681,x42682),f312(f250(x42683,x42681,x42684,x42682,x42685,x42686),x42687)),f312(x42686,f312(f248(x42683,x42684),x42687)))
% 173.52/173.41 [4269]E(f312(f246(x42691,x42692),f312(f250(x42693,x42691,x42694,x42692,x42695,x42696),x42697)),f312(x42695,f312(f246(x42693,x42694),x42697)))
% 173.52/173.41 [3973]E(f312(f312(f177(x39731,x39732),f312(f312(f155(x39731,x39733),x39734),x39735)),f312(f312(f155(x39732,x39736),x39734),x39737)),f312(f312(f155(f859(x39731,x39732),f312(f312(f177(x39731,x39732),x39733),x39736)),x39734),f312(f312(f239(x39731,x39732),x39735),x39737)))
% 173.52/173.41 [4042]E(f312(f312(f312(f251(x40421,x40422,x40423,x40424),x40425),x40426),x40427),f312(f312(f249(x40422,x40423,x40424),x40426),f312(x40425,x40427)))
% 173.52/173.41 [4054]E(f312(f312(f312(f251(x40541,x40542,x40543,x40544),x40545),x40546),x40547),f312(f312(x40546,f312(f246(x40542,x40543),f312(x40545,x40547))),f312(f248(x40542,x40543),f312(x40545,x40547))))
% 173.52/173.41 [4090]E(f182(x40901,x40902,f312(f312(f312(f81(x40901,f856(x40902)),x40903),x40904),f312(f219(x40902),x40905)),x40906,x40907),f182(x40901,x40902,x40903,f312(f312(f147(x40901),x40904),x40906),f312(f312(f147(x40902),x40905),x40907)))
% 173.52/173.41 [4107]E(f312(f82(x41071,x41072,x41073,x41074),f312(f82(x41075,x41071,x41073,x41076),x41077)),f312(f82(x41075,x41072,x41073,f312(f82(x41071,x41072,x41075,x41074),x41076)),x41077))
% 173.52/173.41 [4166]E(f312(f82(f856(x41661),f856(x41662),x41663,f312(f193(x41661,x41662),x41664)),f312(f312(f312(f81(x41663,f856(x41661)),x41665),x41666),f312(f219(x41661),x41667))),f312(f312(f312(f81(x41663,f856(x41662)),f312(f82(f856(x41661),f856(x41662),x41663,f312(f193(x41661,x41662),x41664)),x41665)),x41666),f312(f219(x41662),f312(x41664,x41667))))
% 173.52/173.41 [4291]E(f312(f250(x42911,x42912,x42913,x42913,x42914,f39(x42913)),f312(f250(x42911,x42911,x42915,x42913,f39(x42911),x42916),x42917)),f312(f312(f239(x42912,x42913),f312(x42914,f312(f246(x42911,x42915),x42917))),f312(x42916,f312(f248(x42911,x42915),x42917))))
% 173.52/173.41 [4292]E(f312(f250(x42921,x42921,x42922,x42923,f39(x42921),x42924),f312(f250(x42925,x42921,x42922,x42922,x42926,f39(x42922)),x42927)),f312(f312(f239(x42921,x42923),f312(x42926,f312(f246(x42925,x42922),x42927))),f312(x42924,f312(f248(x42925,x42922),x42927))))
% 173.52/173.41 [4306]E(f312(f250(x43061,x43062,x43063,x43063,x43064,f39(x43063)),f312(f250(x43065,x43061,x43063,x43063,x43066,f39(x43063)),x43067)),f312(f250(x43065,x43062,x43063,x43063,f312(f82(x43061,x43062,x43065,x43064),x43066),f39(x43063)),x43067))
% 173.52/173.41 [4307]E(f312(f250(x43071,x43071,x43072,x43073,f39(x43071),x43074),f312(f250(x43071,x43071,x43075,x43072,f39(x43071),x43076),x43077)),f312(f250(x43071,x43071,x43075,x43073,f39(x43071),f312(f82(x43072,x43073,x43075,x43074),x43076)),x43077))
% 173.52/173.41 [4314]E(f312(f250(x43141,x43142,x43143,x43143,x43144,f39(x43143)),f312(f250(x43141,x43141,x43145,x43143,f39(x43141),x43146),x43147)),f312(f250(x43142,x43142,x43145,x43143,f39(x43142),x43146),f312(f250(x43141,x43142,x43145,x43145,x43144,f39(x43145)),x43147)))
% 173.52/173.41 [4010]E(f312(f312(f267(x40101,x40102,x40103),f312(f312(f267(x40101,x40104,x40102),x40105),x40106)),x40107),f312(f312(f267(x40101,x40104,x40103),x40105),f312(f312(f267(x40104,x40102,x40103),x40106),x40107)))
% 173.52/173.41 [4081]E(f312(f312(f249(x40811,x40812,x40813),f312(f82(x40814,f860(x40812,x40813),x40811,x40815),x40816)),x40817),f312(f312(x40815,f312(x40816,f312(f246(x40811,x40812),x40817))),f312(f248(x40811,x40812),x40817)))
% 173.52/173.41 [4130]E(f312(f82(x41301,x41302,x41303,x41304),f312(f312(f312(f81(x41303,x41301),x41305),x41306),x41307)),f312(f312(f312(f81(x41303,x41302),f312(f82(x41301,x41302,x41303,x41304),x41305)),x41306),f312(x41304,x41307)))
% 173.52/173.41 [4162]E(f312(f138(x41621,x41622,f312(f7(x41622,x41621,x41621),x41623),x41624),f312(f165(x41622),f312(f312(f150(x41625,x41622),x41626),x41627))),f312(f138(x41621,x41625,f312(f7(x41625,x41621,x41621),f312(f82(x41622,f860(x41621,x41621),x41625,x41623),x41626)),x41624),f312(f165(x41625),x41627)))
% 173.52/173.41 [4167]E(f299(x41671,f856(x41672),x41673,f312(f82(f856(x41674),f856(x41672),x41671,f312(f193(x41674,x41672),x41675)),x41676),f312(f82(f856(x41674),f856(x41672),x41673,f312(f193(x41674,x41672),x41675)),x41677)),f312(f82(f856(x41674),f856(x41672),f858(x41671,x41673),f312(f193(x41674,x41672),x41675)),f299(x41671,f856(x41674),x41673,x41676,x41677)))
% 173.52/173.41 [4108]E(f312(f312(f50(x41081,f860(f859(x41082,x41083),a845)),x41084),f312(f312(f8(f860(f859(x41085,x41083),a845),f860(f859(x41082,x41083),a845),x41081),f312(f267(x41082,x41085,x41083),x41086)),x41087)),f312(f312(f267(x41082,x41085,x41083),x41086),f312(f312(f50(x41081,f860(f859(x41085,x41083),a845)),x41084),x41087)))
% 173.52/173.41 [4255]E(f312(f312(f50(x42551,f860(f859(x42552,x42553),a845)),x42554),f312(f312(f7(x42551,f860(f859(x42555,x42553),a845),f860(f859(x42552,x42553),a845)),f312(f312(f8(f860(f859(x42552,x42555),a845),f860(f860(f859(x42555,x42553),a845),f860(f859(x42552,x42553),a845)),x42551),f267(x42552,x42555,x42553)),x42556)),x42557)),f312(f312(f267(x42552,x42555,x42553),f312(f312(f50(x42551,f860(f859(x42552,x42555),a845)),x42554),x42556)),x42557))
% 173.52/173.41 [4256]E(f312(f138(x42561,x42562,f312(f312(f7(x42561,f860(x42562,x42563),f860(x42562,x42561)),f312(f312(f8(f860(x42563,x42561),f860(f860(x42562,x42563),f860(x42562,x42561)),x42561),f8(x42563,x42561,x42562)),x42564)),x42565),x42566),x42567),f312(f138(x42561,x42563,x42564,x42566),f312(f312(f150(x42562,x42563),x42565),x42567)))
% 173.52/173.41 [4315]E(f312(f312(f51(x43151,f860(x43152,a845)),x43153),f312(f312(f8(f860(x43154,f860(x43152,a845)),f860(x43152,a845),x43151),f312(f51(x43154,f860(x43152,a845)),x43155)),f312(f312(f7(x43151,f860(x43154,f860(x43152,a845)),f860(x43154,f860(x43152,a845))),f312(f312(f8(f860(f860(x43152,a845),f860(x43152,a845)),f860(f860(x43154,f860(x43152,a845)),f860(x43154,f860(x43152,a845))),x43151),f8(f860(x43152,a845),f860(x43152,a845),x43154)),f312(f312(f8(f860(x43152,a845),f860(f860(x43152,a845),f860(x43152,a845)),x43151),f124(f860(x43152,a845))),x43156))),x43157))),f312(f312(f124(f860(x43152,a845)),f312(f312(f51(x43151,f860(x43152,a845)),x43153),x43156)),f312(f312(f51(x43154,f860(x43152,a845)),x43155),x43157)))
% 173.52/173.41 [4316]E(f312(f312(f50(x43161,f860(x43162,a845)),x43163),f312(f312(f8(f860(x43164,f860(x43162,a845)),f860(x43162,a845),x43161),f312(f50(x43164,f860(x43162,a845)),x43165)),f312(f312(f7(x43161,f860(x43164,f860(x43162,a845)),f860(x43164,f860(x43162,a845))),f312(f312(f8(f860(f860(x43162,a845),f860(x43162,a845)),f860(f860(x43164,f860(x43162,a845)),f860(x43164,f860(x43162,a845))),x43161),f8(f860(x43162,a845),f860(x43162,a845),x43164)),f312(f312(f8(f860(x43162,a845),f860(f860(x43162,a845),f860(x43162,a845)),x43161),f115(f860(x43162,a845))),x43166))),x43167))),f312(f312(f115(f860(x43162,a845)),f312(f312(f50(x43161,f860(x43162,a845)),x43163),x43166)),f312(f312(f50(x43164,f860(x43162,a845)),x43165),x43167)))
% 173.52/173.41 [4228]E(f312(f250(x42281,x42282,x42283,x42284,x42285,x42286),f312(f312(f239(x42281,x42283),x42287),x42288)),f312(f312(f239(x42282,x42284),f312(x42285,x42287)),f312(x42286,x42288)))
% 173.52/173.41 [4324]E(f312(f312(f150(f859(x43241,x43242),f859(x43243,x43244)),f312(f249(x43241,x43242,f859(x43243,x43244)),f312(f312(f7(x43241,f860(x43242,x43244),f860(x43242,f859(x43243,x43244))),f312(f312(f8(f860(x43244,f859(x43243,x43244)),f860(f860(x43242,x43244),f860(x43242,f859(x43243,x43244))),x43241),f8(x43244,f859(x43243,x43244),x43242)),f312(f312(f8(x43243,f860(x43244,f859(x43243,x43244)),x43241),f239(x43243,x43244)),x43245))),x43246))),f312(f312(f177(x43241,x43242),x43247),x43248)),f312(f312(f177(x43243,x43244),f312(f312(f150(x43241,x43243),x43245),x43247)),f312(f312(f150(x43242,x43244),x43246),x43248)))
% 173.52/173.41 [4328]E(f312(f312(f150(f859(x43281,x43282),x43283),f312(f249(x43281,x43282,x43283),f312(f312(f8(f860(x43282,f859(x43281,x43284)),f860(x43282,x43283),x43281),f312(f8(f859(x43281,x43284),x43283,x43282),x43285)),f312(f312(f7(x43281,f860(x43282,x43284),f860(x43282,f859(x43281,x43284))),f312(f312(f8(f860(x43284,f859(x43281,x43284)),f860(f860(x43282,x43284),f860(x43282,f859(x43281,x43284))),x43281),f8(x43284,f859(x43281,x43284),x43282)),f239(x43281,x43284))),x43286)))),f312(f312(f177(x43281,x43282),x43287),x43288)),f312(f312(f150(f859(x43281,x43284),x43283),x43285),f312(f312(f177(x43281,x43284),x43287),f312(f312(f150(x43282,x43284),x43286),x43288))))
% 173.52/173.41 [4260]E(f312(f312(f150(f859(x42601,x42602),x42603),f312(f249(x42601,x42602,x42603),f312(f312(f8(f860(x42602,f859(x42604,x42602)),f860(x42602,x42603),x42601),f312(f8(f859(x42604,x42602),x42603,x42602),x42605)),f312(f312(f8(x42604,f860(x42602,f859(x42604,x42602)),x42601),f239(x42604,x42602)),x42606)))),f312(f312(f177(x42601,x42602),x42607),x42608)),f312(f312(f150(f859(x42604,x42602),x42603),x42605),f312(f312(f177(x42604,x42602),f312(f312(f150(x42601,x42604),x42606),x42607)),x42608)))
% 173.52/173.41 [4219]E(f312(f312(f249(x42191,x42192,x42193),f312(f312(f8(f860(x42192,f859(x42194,x42195)),f860(x42192,x42193),x42191),f312(f8(f859(x42194,x42195),x42193,x42192),f312(f249(x42194,x42195,x42193),x42196))),x42197)),x42198),f312(f312(f249(x42194,x42195,x42193),x42196),f312(f312(f249(x42191,x42192,f859(x42194,x42195)),x42197),x42198)))
% 173.52/173.41 [4329]E(f312(f312(f50(f859(x43291,x43292),f860(f859(x43293,x43294),a845)),f312(f312(f247(x43291,x43292),x43295),f312(f16(f860(x43292,a845),x43291),x43296))),f312(f249(x43291,x43292,f860(f859(x43293,x43294),a845)),f312(f312(f7(x43291,f860(x43292,f860(x43293,f860(x43294,a845))),f860(x43292,f860(f859(x43293,x43294),a845))),f312(f312(f8(f860(f860(x43293,f860(x43294,a845)),f860(f859(x43293,x43294),a845)),f860(f860(x43292,f860(x43293,f860(x43294,a845))),f860(x43292,f860(f859(x43293,x43294),a845))),x43291),f8(f860(x43293,f860(x43294,a845)),f860(f859(x43293,x43294),a845),x43292)),f312(f312(f8(f860(x43293,a845),f860(f860(x43293,f860(x43294,a845)),f860(f859(x43293,x43294),a845)),x43291),f247(x43293,x43294)),x43297))),f312(f312(f8(f860(x43294,a845),f860(x43293,f860(x43294,a845)),x43292),f16(f860(x43294,a845),x43293)),x43298)))),f312(f312(f247(x43293,x43294),f312(f312(f50(x43291,f860(x43293,a845)),x43295),x43297)),f312(f16(f860(x43294,a845),x43293),f312(f312(f50(x43292,f860(x43294,a845)),x43296),x43298))))
% 173.52/173.41 [4358]E(f37(x43581,x43582,x43583,x43584,x43585,x43586,x43587,x43588,x43589,a23),x43582)
% 173.52/173.41 [4359]E(f38(x43591,x43592,x43593,x43594,x43595,x43596,x43597,x43598,x43599,a23),x43592)
% 173.52/173.41 [4273]E(f312(f312(f251(x42731,x42732,x42733,x42734),f312(f312(f251(x42731,x42735,x42736,f859(x42732,x42733)),x42737),x42738)),x42739),f312(f312(f251(x42731,x42735,x42736,x42734),x42737),f312(f312(f7(x42735,f860(x42732,f860(x42733,x42734)),f860(x42736,x42734)),f312(f312(f8(f860(x42736,f859(x42732,x42733)),f860(f860(x42732,f860(x42733,x42734)),f860(x42736,x42734)),x42735),f251(x42736,x42732,x42733,x42734)),x42738)),x42739)))
% 173.52/173.41 [4360]E(f37(x43601,x43602,x43603,x43604,x43605,x43606,x43607,x43608,x43609,f312(a27,x436010)),f312(x43608,x436010))
% 173.52/173.41 [4361]E(f38(x43611,x43612,x43613,x43614,x43615,x43616,x43617,x43618,x43619,f312(a27,x436110)),f312(x43618,x436110))
% 173.52/173.41 [4303]E(f312(f82(f859(x43031,x43032),f859(x43033,x43034),f859(x43035,x43036),f250(x43031,x43033,x43032,x43034,x43037,x43038)),f250(x43035,x43031,x43036,x43032,x43039,x430310)),f250(x43035,x43033,x43036,x43034,f312(f82(x43031,x43033,x43035,x43037),x43039),f312(f82(x43032,x43034,x43036,x43038),x430310)))
% 173.52/173.41 [4362]E(f37(x43621,x43622,x43623,x43624,x43625,x43626,x43627,x43628,x43629,f36(x436210,x436211)),f312(f312(x43625,x436210),x436211))
% 173.52/173.41 [4363]E(f37(x43631,x43632,x43633,x43634,x43635,x43636,x43637,x43638,x43639,f35(x436310,x436311)),f312(f312(x43637,x436310),x436311))
% 173.52/173.41 [4364]E(f37(x43641,x43642,x43643,x43644,x43645,x43646,x43647,x43648,x43649,f28(x436410,x436411)),f312(f312(x43643,x436410),x436411))
% 173.52/173.41 [4365]E(f38(x43651,x43652,x43653,x43654,x43655,x43656,x43657,x43658,x43659,f28(x436510,x436511)),f312(f312(x43653,x436510),x436511))
% 173.52/173.41 [4371]E(f312(f312(f312(x43711,x43712),x43713),f38(x43714,x43715,x43716,x43717,x43718,x43719,x43711,x437110,x437111,x43713)),f38(x43714,x43715,x43716,x43717,x43718,x43719,x43711,x437110,x437111,f35(x43712,x43713)))
% 173.52/173.41 [4375]E(f312(f312(f312(f312(x43751,x43752),x43753),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x43752)),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x43753)),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,f36(x43752,x43753)))
% 173.52/173.41 [4309]E(f312(f250(x43091,x43092,x43093,x43094,x43095,x43096),f312(f250(x43097,x43091,x43098,x43093,x43099,x430910),x430911)),f312(f250(x43097,x43092,x43098,x43094,f312(f82(x43091,x43092,x43097,x43095),x43099),f312(f82(x43093,x43094,x43098,x43096),x430910)),x430911))
% 173.52/173.41 [4372]E(f312(f312(f312(f312(x43721,x43722),x43723),x43724),f38(x43725,x43726,x43727,x43721,x43728,x43729,x437210,x437211,x437212,x43724)),f38(x43725,x43726,x43727,x43721,x43728,x43729,x437210,x437211,x437212,f32(x43722,x43723,x43724)))
% 173.52/173.41 [4376]E(f312(f312(f312(f312(f312(x43761,x43762),x43763),x43764),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,x43763)),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,x43764)),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,f33(x43762,x43763,x43764)))
% 173.52/173.41 [4366]E(f37(x43661,x43662,x43663,x43664,x43665,x43666,x43667,x43668,x43669,f33(x436610,x436611,x436612)),f312(f312(f312(x43666,x436610),x436611),x436612))
% 173.52/173.41 [4367]E(f37(x43671,x43672,x43673,x43674,x43675,x43676,x43677,x43678,x43679,f32(x436710,x436711,x436712)),f312(f312(f312(x43674,x436710),x436711),x436712))
% 173.52/173.41 [4368]E(f37(x43681,x43682,x43683,x43684,x43685,x43686,x43687,x43688,x43689,f31(x436810,x436811,x436812)),f312(f312(f312(x43689,x436810),x436811),x436812))
% 173.52/173.41 [4369]E(f38(x43691,x43692,x43693,x43694,x43695,x43696,x43697,x43698,x43699,f31(x436910,x436911,x436912)),f312(f312(f312(x43699,x436910),x436911),x436912))
% 173.52/173.41 [4506]~E(a522,a579)+~P1(a5000)
% 173.52/173.41 [6368]P4(a5000)+P22(f312(f312(f314(f859(a848,a846)),a583),f312(f168(f859(a848,a846)),a29)))
% 173.52/173.41 [8355]P4(a5000)+~P22(f312(f312(f249(a848,a846,a845),f312(f16(f860(a846,a845),a848),a24)),a583))
% 173.52/173.41 [4508]~E(f648(x45081),x45081)+~P1(a5000)
% 173.52/173.41 [4509]~E(f759(x45091),x45091)+E(x45091,a863)
% 173.52/173.41 [4512]~P62(x45121)+P62(f856(x45121))
% 173.52/173.41 [4513]~P63(x45131)+P63(f856(x45131))
% 173.52/173.41 [4516]~P137(x45161)+~E(f87(x45161),f2(x45161))
% 173.52/173.41 [4518]~E(x45181,f2(a113))+E(f312(a20,x45181),f2(a1))
% 173.52/173.41 [4519]~E(x45191,f2(a1))+E(f91(a1,x45191),f2(a1))
% 173.52/173.41 [4526]~P23(x45261)+P35(x45261,f2(x45261))
% 173.52/173.41 [4528]~P103(x45281)+P33(x45281,f127(x45281))
% 173.52/173.41 [4538]P22(x45381)+P22(f312(a307,x45381))
% 173.52/173.41 [4581]~P23(x45811)+~P35(x45811,f87(x45811))
% 173.52/173.41 [4631]~P22(x46311)+~P22(f312(a307,x46311))
% 173.52/173.41 [4656]E(f312(a118,x46561),f2(a852))+~P22(f312(a194,x46561))
% 173.52/173.41 [4720]~P98(x47201)+P11(x47201,x47201,f124(x47201))
% 173.52/173.41 [4721]~P99(x47211)+P11(x47211,x47211,f115(x47211))
% 173.52/173.41 [4722]~P93(x47221)+P11(x47221,x47221,f90(x47221))
% 173.52/173.41 [4723]~P103(x47231)+P11(x47231,x47231,f225(x47231))
% 173.52/173.41 [4724]~P103(x47241)+P11(x47241,x47241,f226(x47241))
% 173.52/173.41 [4523]~E(x45231,f2(a852))+E(f312(f114(a1),x45231),f2(a1))
% 173.52/173.41 [4531]~P90(x45311)+E(f312(f117(x45311),a92),f2(x45311))
% 173.52/173.41 [4534]~E(f580(x45341),f2(a852))+E(f312(f162(a852),x45341),f2(a852))
% 173.52/173.41 [4535]~P104(x45351)+E(f229(x45351,f227(x45351)),f225(x45351))
% 173.52/173.41 [4536]~P104(x45361)+E(f230(x45361,f227(x45361)),f226(x45361))
% 173.52/173.41 [4537]~P85(x45371)+E(f91(x45371,f2(x45371)),f2(x45371))
% 173.52/173.41 [4546]~P23(x45461)+E(f312(f114(x45461),f2(a852)),f2(x45461))
% 173.52/173.41 [4547]~P23(x45471)+E(f312(f114(x45471),f87(a852)),f87(x45471))
% 173.52/173.41 [4548]~P111(x45481)+E(f312(f116(x45481),f2(a1)),f2(x45481))
% 173.52/173.41 [4549]~P111(x45491)+E(f312(f116(x45491),f87(a1)),f87(x45491))
% 173.52/173.41 [4550]E(x45501,f2(a852))+~E(f312(f114(a1),x45501),f2(a1))
% 173.52/173.41 [4575]~P71(x45751)+E(f312(f88(x45751),f2(x45751)),f2(x45751))
% 173.52/173.41 [4576]~P88(x45761)+E(f312(f88(x45761),f189(x45761)),f235(x45761))
% 173.52/173.41 [4577]~P88(x45771)+E(f312(f88(x45771),f235(x45771)),f189(x45771))
% 173.52/173.41 [4578]~P83(x45781)+E(f312(f84(x45781),f2(x45781)),f2(x45781))
% 173.52/173.41 [4579]~P112(x45791)+E(f312(f84(x45791),f87(x45791)),f87(x45791))
% 173.52/173.41 [4580]~P25(x45801)+E(f312(f162(x45801),f127(x45801)),f2(x45801))
% 173.52/173.41 [4597]E(x45971,f2(a1))+E(f312(f47(a1,x45971),x45971),f87(a1))
% 173.52/173.41 [4602]~P40(x46021)+P43(f312(f168(a1),x46021))
% 173.52/173.41 [4636]~P90(x46361)+E(f312(f88(x46361),f87(x46361)),f312(f117(x46361),a111))
% 173.52/173.41 [4653]~P90(x46531)+P35(x46531,f312(f117(x46531),a92))
% 173.52/173.41 [4672]~P63(x46721)+E(f312(f168(x46721),f64(x46721)),f235(f860(x46721,a845)))
% 173.52/173.41 [4682]P40(x46821)+~P43(f312(f168(a1),x46821))
% 173.52/173.41 [4683]~P63(x46831)+P22(f312(f133(x46831),f64(x46831)))
% 173.52/173.41 [4725]E(f312(f114(a1),f312(a118,x47251)),x47251)+P22(f312(a194,x47251))
% 173.52/173.41 [4740]~P104(x47401)+E(f101(x47401,x47401,f5(x47401)),f102(x47401))
% 173.52/173.41 [4792]~P109(x47921)+E(f241(x47921,f87(x47921),f90(x47921)),f240(x47921))
% 173.52/173.41 [4822]~P90(x48221)+~P35(x48221,f312(f117(x48221),a111))
% 173.52/173.41 [4832]E(f312(a30,x48321),f192(a846))+P22(f312(a24,f312(a27,x48321)))
% 173.52/173.41 [4889]E(x48891,a863)+P22(f312(f312(f195(a861),a862),f759(x48891)))
% 173.52/173.41 [4958]E(f312(f84(a1),x49581),x49581)+P22(f312(f312(f228(a1),x49581),f2(a1)))
% 173.52/173.41 [4979]~E(f312(a118,x49791),f2(a852))+P22(f312(f312(f227(a1),x49791),f2(a1)))
% 173.52/173.41 [5042]~P22(f312(a194,x50421))+P22(f312(f312(f228(a1),x50421),f2(a1)))
% 173.52/173.41 [5084]~P111(x50841)+P22(f312(f312(f314(x50841),f2(x50841)),f123(x50841)))
% 173.52/173.41 [5085]~P23(x50851)+P22(f312(f312(f314(x50851),f2(x50851)),f187(x50851)))
% 173.52/173.41 [5086]~P111(x50861)+P22(f312(f312(f314(x50861),f87(x50861)),f123(x50861)))
% 173.52/173.41 [5087]~P23(x50871)+P22(f312(f312(f314(x50871),f87(x50871)),f187(x50871)))
% 173.52/173.41 [5088]~P117(x50881)+P22(f312(f312(f228(x50881),f2(x50881)),f87(x50881)))
% 173.52/173.41 [5089]~P117(x50891)+P22(f312(f312(f227(x50891),f2(x50891)),f87(x50891)))
% 173.52/173.41 [5092]E(f312(f219(a846),f394(x50921)),f312(a30,x50921))+~P22(f312(a24,f312(a27,x50921)))
% 173.52/173.41 [5093]E(f312(f219(a846),f429(x50931)),f312(a30,x50931))+~P22(f312(a24,f312(a27,x50931)))
% 173.52/173.41 [5148]E(x51481,f2(a852))+~P22(f312(f312(f227(a852),x51481),f2(a852)))
% 173.52/173.41 [5190]E(f312(a118,x51901),f2(a852))+~P22(f312(f312(f227(a1),x51901),f2(a1)))
% 173.52/173.41 [5248]P22(f312(a194,x52481))+~P22(f312(f312(f228(a1),x52481),f2(a1)))
% 173.52/173.41 [5270]P43(x52701)+~P22(f312(f312(f227(a1),f2(a1)),f318(x52701)))
% 173.52/173.41 [5276]E(f312(f84(a1),x52761),f312(f88(a1),x52761))+~P22(f312(f312(f228(a1),x52761),f2(a1)))
% 173.52/173.41 [5444]~P117(x54441)+~P22(f312(f312(f228(x54441),f87(x54441)),f2(x54441)))
% 173.52/173.41 [5445]~P117(x54451)+~P22(f312(f312(f227(x54451),f87(x54451)),f2(x54451)))
% 173.52/173.41 [5455]~E(x54551,f2(a1))+P22(f312(f312(f228(a1),f312(f84(a1),x54551)),f87(a1)))
% 173.52/173.41 [5456]~E(x54561,f2(a852))+P22(f312(f312(f227(a1),f312(f114(a1),x54561)),f2(a1)))
% 173.52/173.41 [5582]~P25(x55821)+E(f138(x55821,x55821,f89(x55821),f2(x55821)),f162(x55821))
% 173.52/173.41 [5740]~P100(x57401)+P19(a852,x57401,f114(x57401),f235(f860(a852,a845)))
% 173.52/173.41 [5941]E(x59411,f2(a852))+~P22(f312(f312(f227(a1),f312(f114(a1),x59411)),f2(a1)))
% 173.52/173.41 [5942]E(x59421,f2(a1))+~P22(f312(f312(f228(a1),f312(f84(a1),x59421)),f87(a1)))
% 173.52/173.41 [6716]~P22(f312(f312(f228(a1),x67161),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x67161),x67161)),f2(a1)))
% 173.52/173.41 [7257]P22(f312(f312(f228(a1),x72571),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72571),x72571)),f2(a1)))
% 173.52/173.41 [7805]E(x78051,f312(a3,f2(a852)))+P22(f312(f312(f228(a852),f312(f312(f21(a852),f312(a19,x78051)),f312(a126,f2(a852)))),f312(a19,x78051)))
% 173.52/173.41 [8578]~P22(f312(f312(f228(a1),x85781),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85781),x85781)),a111)),f2(a1)))
% 173.52/173.41 [8666]~P22(f312(f312(f228(a1),x86661),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x86661)),x86661)),f2(a1)))
% 173.52/173.41 [8985]P22(f312(f312(f228(a1),x89851),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89851),x89851)),a111)),f2(a1)))
% 173.52/173.41 [9047]P22(f312(f312(f228(a1),x90471),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x90471)),x90471)),f2(a1)))
% 173.52/173.41 [4624]~E(a92,x46241)+E(f312(f312(f89(a1),x46241),x46241),a92)
% 173.52/173.41 [4625]~E(x46251,a92)+E(f312(f312(f89(a1),x46251),x46251),a92)
% 173.52/173.41 [4769]E(x47691,a92)+~E(f312(f312(f89(a1),x47691),x47691),a92)
% 173.52/173.41 [4770]E(a92,x47701)+~E(f312(f312(f89(a1),x47701),x47701),a92)
% 173.52/173.41 [4782]~P103(x47821)+E(f135(x47821,f189(f860(x47821,a845))),f127(x47821))
% 173.52/173.41 [4783]~P31(x47831)+E(f48(x47831,f189(f860(x47831,a845))),f189(x47831))
% 173.52/173.41 [4784]~P31(x47841)+E(f48(x47841,f235(f860(x47841,a845))),f235(x47841))
% 173.52/173.41 [4785]~P31(x47851)+E(f49(x47851,f189(f860(x47851,a845))),f235(x47851))
% 173.52/173.41 [4786]~P31(x47861)+E(f49(x47861,f235(f860(x47861,a845))),f189(x47861))
% 173.52/173.41 [4919]E(x49191,f2(a852))+P22(f312(f312(f228(a852),f2(a852)),x49191))
% 173.52/173.41 [4937]~P32(x49371)+P22(f312(f312(f227(a1),f2(a1)),x49371))
% 173.52/173.41 [4970]~E(f312(f117(a852),x49701),f2(a852))+P22(f312(f312(f227(a1),x49701),a92))
% 173.52/173.41 [4975]P43(x49751)+P22(f312(f312(f314(a1),f318(x49751)),x49751))
% 173.52/173.41 [4976]E(x49761,f312(a3,f2(a852)))+P22(f312(f312(f227(a113),f87(a113)),x49761))
% 173.52/173.41 [5015]P22(f312(a194,x50151))+P22(f312(f312(f227(a1),f2(a1)),x50151))
% 173.52/173.41 [5066]E(f312(f114(a1),f312(a118,x50661)),f2(a1))+P22(f312(f312(f227(a1),f2(a1)),x50661))
% 173.52/173.41 [5134]E(f312(f114(a1),f312(f117(a852),x51341)),f312(f117(a1),x51341))+P22(f312(a194,f312(f117(a1),x51341)))
% 173.52/173.41 [5154]E(f312(f117(a852),x51541),f2(a852))+~P22(f312(a194,f312(f117(a1),x51541)))
% 173.52/173.41 [5155]E(f312(f117(a852),x51551),f2(a852))+~P22(f312(f312(f227(a1),x51551),a92))
% 173.52/173.41 [5187]P32(x51871)+~P22(f312(f312(f227(a1),f2(a1)),x51871))
% 173.52/173.41 [5255]E(f312(a126,f785(x52551)),x52551)+~P22(f312(f312(f228(a852),f2(a852)),x52551))
% 173.52/173.41 [5264]E(f312(a126,f312(f117(a852),x52641)),f87(a852))+~P22(f312(a194,f312(f117(a1),x52641)))
% 173.52/173.41 [5272]E(f312(f114(a1),f833(x52721)),x52721)+~P22(f312(f312(f228(a1),f2(a1)),x52721))
% 173.52/173.41 [5279]~E(x52791,f312(a3,f2(a852)))+~P22(f312(f312(f227(a113),f87(a113)),x52791))
% 173.52/173.41 [5286]E(f312(f114(a1),f312(f117(a852),x52861)),f2(a1))+~P22(f312(a194,f312(f117(a1),x52861)))
% 173.52/173.41 [5309]E(f312(f162(a852),x53091),f2(a852))+P22(f312(f312(f314(a852),f580(x53091)),f312(f168(a852),x53091)))
% 173.52/173.41 [5329]E(f312(f114(a1),f312(a118,x53291)),x53291)+~P22(f312(f312(f227(a1),f2(a1)),x53291))
% 173.52/173.41 [5338]~P22(f312(a194,x53381))+~P22(f312(f312(f227(a1),f2(a1)),x53381))
% 173.52/173.41 [5437]E(f312(f312(f89(a852),f87(a852)),f312(f117(a852),x54371)),f87(a852))+~P22(f312(f312(f228(a1),x54371),a92))
% 173.52/173.41 [5497]E(x54971,f2(a852))+~P22(f312(f312(f228(a852),x54971),f312(a126,f2(a852))))
% 173.52/173.41 [5539]E(f312(f312(f89(a852),f312(f117(a852),x55391)),f87(a852)),f87(a852))+~P22(f312(f312(f228(a1),x55391),a92))
% 173.52/173.41 [5540]E(f312(f312(f21(a852),f312(f117(a852),x55401)),f87(a852)),f2(a852))+~P22(f312(f312(f227(a1),x55401),a92))
% 173.52/173.41 [5552]~P43(x55521)+E(f312(f53(a852),f312(f290(a1,a852,a118),x55521)),f312(f53(a1),x55521))
% 173.52/173.41 [5583]~P103(x55831)+E(f229(x55831,f312(f7(x55831,x55831,a845),f227(x55831))),f226(x55831))
% 173.52/173.41 [5584]~P103(x55841)+E(f230(x55841,f312(f7(x55841,x55841,a845),f227(x55841))),f225(x55841))
% 173.52/173.41 [5594]E(f54(a852,f312(a126,f2(a852)),f312(f117(a852),x55941)),f312(a126,f2(a852)))+~P22(f312(a194,f312(f117(a1),x55941)))
% 173.52/173.41 [5602]P22(f312(f312(f228(a1),f2(a1)),x56021))+~P22(f312(f312(f227(a1),f87(a1)),x56021))
% 173.52/173.41 [5603]~P22(f312(f312(f228(a1),f2(a1)),x56031))+P22(f312(f312(f227(a1),f87(a1)),x56031))
% 173.52/173.41 [5609]E(f312(a126,f312(f312(f21(a852),x56091),f87(a852))),x56091)+~P22(f312(f312(f228(a852),f2(a852)),x56091))
% 173.52/173.41 [5668]P22(f312(f312(f228(a852),f2(a852)),f833(x56681)))+~P22(f312(f312(f228(a1),f2(a1)),x56681))
% 173.52/173.41 [5721]E(f54(a1,f312(f117(a1),a111),x57211),f312(f312(f21(a1),x57211),f87(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x57211))
% 173.52/173.41 [5751]~P22(f312(f312(f228(a1),a92),x57511))+P22(f312(f312(f228(a852),f2(a852)),f312(f117(a852),x57511)))
% 173.52/173.41 [5803]P22(f312(f312(f228(a852),f2(a852)),f312(a118,x58031)))+~P22(f312(f312(f228(a1),f2(a1)),x58031))
% 173.52/173.41 [5851]~P22(f312(f312(f228(a852),f2(a852)),x58511))+P22(f312(f312(f228(a1),f2(a1)),f312(f114(a1),x58511)))
% 173.52/173.41 [5889]~P22(f312(f312(f228(a852),f2(a852)),f312(a118,x58891)))+P22(f312(f312(f228(a1),f2(a1)),x58891))
% 173.52/173.41 [5909]~P43(x59091)+E(f312(f290(a852,a1,f114(a1)),f312(f290(a1,a852,a118),x59091)),x59091)
% 173.52/173.41 [5922]P22(f312(f312(f228(a1),a92),x59221))+~P22(f312(f312(f228(a852),f2(a852)),f312(f117(a852),x59221)))
% 173.52/173.41 [5966]~P63(x59661)+E(f312(f312(f147(f856(x59661)),f192(x59661)),f312(f312(f150(x59661,f856(x59661)),f219(x59661)),f64(x59661))),f64(f856(x59661)))
% 173.52/173.41 [5976]P22(f312(f312(f228(a852),f2(a852)),x59761))+~P22(f312(f312(f228(a1),f2(a1)),f312(f114(a1),x59761)))
% 173.52/173.41 [6083]E(f312(f290(a852,a1,f114(a1)),f312(f279(a852),f312(a118,x60831))),f312(f282(a1,f2(a1)),x60831))+~P22(f312(f312(f227(a1),f2(a1)),x60831))
% 173.52/173.41 [6098]~P117(x60981)+P22(f312(f312(f228(x60981),f2(x60981)),f312(f312(f89(x60981),f87(x60981)),f87(x60981))))
% 173.52/173.41 [6151]P22(f312(f312(f228(a852),f312(a126,f2(a852))),f312(a118,x61511)))+~P22(f312(f312(f228(a1),f87(a1)),x61511))
% 173.52/173.41 [6243]E(x62431,f2(a1))+P22(f312(f57(f2(a1),x62431),f312(f312(f239(a1,a1),f2(a1)),f2(a1))))
% 173.52/173.41 [6407]~P22(f312(f312(f228(a852),f312(a126,f2(a852))),f312(a118,x64071)))+P22(f312(f312(f228(a1),f87(a1)),x64071))
% 173.52/173.41 [6821]~P101(x68211)+P41(x68211,f312(f233(f859(x68211,x68211)),f312(f249(x68211,x68211,a845),f228(x68211))))
% 173.52/173.41 [5484]E(f312(f117(a852),f312(f312(f21(a1),x54841),a111)),f312(a126,f312(f117(a852),x54841)))+P22(f312(a194,f312(f117(a1),x54841)))
% 173.52/173.41 [5500]~P40(x55001)+E(f312(f312(f150(a852,a1),f114(a1)),f312(f312(f150(a1,a852),a118),x55001)),x55001)
% 173.52/173.41 [5610]E(f312(f47(a1,f312(f117(a1),a111)),x56101),f312(f117(a1),a111))+~P22(f312(f312(f228(a1),f2(a1)),x56101))
% 173.52/173.41 [5616]E(f312(f88(a1),f312(f114(a1),f312(a126,f834(x56161)))),x56161)+~P22(f312(f312(f228(a1),x56161),f2(a1)))
% 173.52/173.41 [5627]E(f312(f312(f89(a852),f87(a852)),f312(f117(a852),x56271)),f312(f117(a852),f312(f312(f21(a1),x56271),a111)))+P22(f312(f312(f228(a1),x56271),a92))
% 173.52/173.41 [5747]E(f312(f312(f89(a852),f312(f117(a852),x57471)),f87(a852)),f312(f117(a852),f312(f312(f21(a1),x57471),a111)))+P22(f312(f312(f228(a1),x57471),a92))
% 173.52/173.41 [5748]E(f312(f312(f21(a852),f312(f117(a852),x57481)),f87(a852)),f312(f117(a852),f312(f312(f89(a1),x57481),a111)))+P22(f312(f312(f227(a1),x57481),a92))
% 173.52/173.41 [5791]E(f312(a118,f312(f312(f89(a1),f87(a1)),x57911)),f312(a126,f312(a118,x57911)))+~P22(f312(f312(f227(a1),f2(a1)),x57911))
% 173.52/173.41 [5826]E(f312(a126,f312(f312(f21(a852),x58261),f312(a126,f2(a852)))),x58261)+~P22(f312(f312(f228(a852),f2(a852)),x58261))
% 173.52/173.41 [6032]E(f54(a852,f312(a126,f2(a852)),f312(f117(a852),x60321)),f312(a118,f54(a1,f87(a1),f312(f117(a1),x60321))))+P22(f312(a194,f312(f117(a1),x60321)))
% 173.52/173.41 [6074]~P22(f312(f312(f228(a1),a92),x60741))+P22(f312(f312(f228(a1),a92),f312(f312(f89(a1),x60741),x60741)))
% 173.52/173.41 [6075]~P22(f312(f312(f228(a1),a111),x60751))+P22(f312(f312(f228(a1),a111),f312(f312(f89(a1),x60751),x60751)))
% 173.52/173.41 [6076]~P22(f312(f312(f227(a1),a92),x60761))+P22(f312(f312(f227(a1),a92),f312(f312(f89(a1),x60761),x60761)))
% 173.52/173.41 [6077]~P22(f312(f312(f228(a1),a111),x60771))+P22(f312(f312(f227(a1),a111),f312(f312(f89(a1),x60771),x60771)))
% 173.52/173.41 [6256]~P22(f312(f70(x62561),f235(f860(x62561,a845))))+P22(f312(f70(f856(x62561)),f235(f860(f856(x62561),a845))))
% 173.52/173.41 [6323]E(f312(f246(a1,a1),f55(f87(a1),f312(f117(a1),x63231))),f312(f47(a1,f87(a1)),f312(f117(a1),x63231)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x63231)))
% 173.52/173.41 [6341]~P22(f312(f312(f227(a1),f2(a1)),x63411))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f89(a1),f87(a1)),x63411)))
% 173.52/173.41 [6367]E(f312(f248(a1,a1),f55(f87(a1),f312(f117(a1),x63671))),f54(a1,f87(a1),f312(f117(a1),x63671)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x63671)))
% 173.52/173.41 [6379]P22(f312(f70(x63791),f235(f860(x63791,a845))))+~P22(f312(f70(f856(x63791)),f235(f860(f856(x63791),a845))))
% 173.52/173.41 [6408]P22(f312(f312(f228(a1),a92),x64081))+~P22(f312(f312(f228(a1),a92),f312(f312(f89(a1),x64081),x64081)))
% 173.52/173.41 [6409]P22(f312(f312(f228(a1),a111),x64091))+~P22(f312(f312(f228(a1),a111),f312(f312(f89(a1),x64091),x64091)))
% 173.52/173.41 [6410]P22(f312(f312(f228(a1),a111),x64101))+~P22(f312(f312(f227(a1),a111),f312(f312(f89(a1),x64101),x64101)))
% 173.52/173.41 [6411]P22(f312(f312(f227(a1),a92),x64111))+~P22(f312(f312(f227(a1),a92),f312(f312(f89(a1),x64111),x64111)))
% 173.52/173.41 [6720]~P22(f312(f70(x67201),f235(f860(x67201,a845))))+P22(f312(f312(f228(a852),f2(a852)),f312(f53(x67201),f235(f860(x67201,a845)))))
% 173.52/173.41 [7299]P22(f312(f70(a852),x72991))+~P22(f312(f70(a1),f312(f290(a852,a1,f114(a1)),x72991)))
% 173.52/173.41 [5413]~E(a111,x54131)+E(f312(f312(f21(a1),f312(f312(f89(a1),x54131),x54131)),a111),a111)
% 173.52/173.41 [5414]~E(x54141,a111)+E(f312(f312(f21(a1),f312(f312(f89(a1),x54141),x54141)),a111),a111)
% 173.52/173.41 [5914]E(x59141,a111)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x59141),x59141)),a111),a111)
% 173.52/173.41 [5915]E(a111,x59151)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x59151),x59151)),a111),a111)
% 173.52/173.41 [6307]~E(f312(f117(a852),x63071),f2(a852))+P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x63071),a111))))
% 173.52/173.41 [6652]~P22(f312(a194,f312(f117(a1),x66521)))+P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x66521),x66521))))
% 173.52/173.41 [6653]~P22(f312(f312(f228(a1),x66531),a92))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66531),x66531)),a92))
% 173.52/173.41 [6654]~P22(f312(f312(f227(a1),x66541),a111))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66541),x66541)),a111))
% 173.52/173.41 [6655]~P22(f312(f312(f227(a1),x66551),a92))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x66551),x66551)),a92))
% 173.52/173.41 [6656]~P22(f312(f312(f227(a1),x66561),a111))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x66561),x66561)),a111))
% 173.52/173.41 [6973]E(f312(f117(a852),x69731),f2(a852))+~P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x69731),a111))))
% 173.52/173.41 [7206]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x72061)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f89(a1),x72061),x72061))))
% 173.52/173.41 [7207]P22(f312(a194,f312(f117(a1),x72071)))+~P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x72071),x72071))))
% 173.52/173.41 [7208]P22(f312(f312(f228(a1),x72081),a92))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72081),x72081)),a92))
% 173.52/173.41 [7209]P22(f312(f312(f227(a1),x72091),a92))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x72091),x72091)),a92))
% 173.52/173.41 [7210]P22(f312(f312(f227(a1),x72101),a111))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72101),x72101)),a111))
% 173.52/173.41 [7211]P22(f312(f312(f227(a1),x72111),a111))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x72111),x72111)),a111))
% 173.52/173.41 [7576]E(f312(a121,f541(x75761)),x75761)+~P22(f312(f312(f314(f860(f859(a852,a852),a845)),x75761),a112))
% 173.52/173.41 [6228]~P90(x62281)+E(f312(f117(x62281),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(x62281))
% 173.52/173.41 [6700]~P22(f312(a194,f312(f117(a1),x67001)))+E(f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x67001),x67001)),a111)),f2(a852))
% 173.52/173.41 [7725]~P22(f312(f312(f228(a1),f312(f117(a1),x77251)),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f58(f312(f88(a1),f87(a1)),f312(f88(a1),f312(f117(a1),x77251))))),f312(f47(a1,f87(a1)),f312(f117(a1),x77251)))
% 173.52/173.41 [7767]~P22(f312(f312(f228(a1),f312(f117(a1),x77671)),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f58(f312(f88(a1),f87(a1)),f312(f88(a1),f312(f117(a1),x77671))))),f54(a1,f87(a1),f312(f117(a1),x77671)))
% 173.52/173.41 [7810]~P22(f312(f312(f227(a1),a92),x78101))+P22(f312(f312(f228(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x78101),x78101)),a111)))
% 173.52/173.41 [7811]~P22(f312(f312(f228(a1),a111),x78111))+P22(f312(f312(f228(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x78111),x78111)),a111)))
% 173.52/173.41 [7812]~P22(f312(f312(f227(a1),a92),x78121))+P22(f312(f312(f227(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x78121),x78121)),a111)))
% 173.52/173.41 [7813]~P22(f312(f312(f227(a1),a111),x78131))+P22(f312(f312(f227(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x78131),x78131)),a111)))
% 173.52/173.41 [8120]~P90(x81201)+~P35(x81201,f312(f117(x81201),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 173.52/173.41 [8304]P22(f312(f312(f228(a1),a111),x83041))+~P22(f312(f312(f228(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x83041),x83041)),a111)))
% 173.52/173.41 [8305]P22(f312(f312(f227(a1),a92),x83051))+~P22(f312(f312(f228(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x83051),x83051)),a111)))
% 173.52/173.41 [8306]P22(f312(f312(f227(a1),a92),x83061))+~P22(f312(f312(f227(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x83061),x83061)),a111)))
% 173.52/173.41 [8307]P22(f312(f312(f227(a1),a111),x83071))+~P22(f312(f312(f227(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x83071),x83071)),a111)))
% 173.52/173.41 [8622]E(f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x86221),x86221)),a111)),f312(f312(f95(a852,a852),f312(f117(a852),x86221)),f312(f312(f8(a852,a852,a852),a126),f312(f312(f18(a852,a852,a852),f89(a852)),f5(a852)))))+P22(f312(a194,f312(f117(a1),x86221)))
% 173.52/173.41 [9460]E(x94601,f189(f860(f859(a852,a852),a845)))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x94601),f189(f860(f859(a852,a852),a845)))),a77))
% 173.52/173.41 [8555]~P22(f312(a194,f312(f117(a1),x85551)))+P22(f312(a194,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85551),x85551)),a111))))
% 173.52/173.41 [8556]~P22(f312(f312(f228(a1),x85561),a92))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85561),x85561)),a111)),a92))
% 173.52/173.41 [8557]~P22(f312(f312(f228(a1),x85571),a111))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85571),x85571)),a111)),a111))
% 173.52/173.41 [8558]~P22(f312(f312(f228(a1),x85581),a92))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85581),x85581)),a111)),a92))
% 173.52/173.41 [8559]~P22(f312(f312(f227(a1),x85591),a111))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85591),x85591)),a111)),a111))
% 173.52/173.41 [8659]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x86591)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86591),x86591)),a111))))
% 173.52/173.41 [8812]~P90(x88121)+E(f312(f312(f89(x88121),f87(x88121)),f87(x88121)),f312(f117(x88121),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))
% 173.52/173.41 [8970]P22(f312(a194,f312(f117(a1),x89701)))+~P22(f312(a194,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89701),x89701)),a111))))
% 173.52/173.41 [8971]P22(f312(f312(f228(a1),x89711),a92))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89711),x89711)),a111)),a92))
% 173.52/173.41 [8972]P22(f312(f312(f228(a1),x89721),a92))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89721),x89721)),a111)),a92))
% 173.52/173.41 [8973]P22(f312(f312(f228(a1),x89731),a111))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89731),x89731)),a111)),a111))
% 173.52/173.41 [8974]P22(f312(f312(f227(a1),x89741),a111))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89741),x89741)),a111)),a111))
% 173.52/173.41 [9508]~P22(f312(f70(f859(a852,a852)),x95081))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f189(f860(f859(a852,a852),a845))),x95081)),a78))
% 173.52/173.41 [9293]~P23(x92931)+E(f312(f312(f240(x92931),f2(x92931)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f2(x92931))
% 173.52/173.41 [9294]~P23(x92941)+E(f312(f312(f240(x92941),f87(x92941)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(x92941))
% 173.52/173.41 [9726]~P22(f312(f312(f228(a852),f87(a852)),x97261))+P22(f312(f312(f228(a852),f2(a852)),f312(f47(a852,x97261),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.52/173.41 [9740]~P22(f312(f312(f228(a852),f2(a852)),x97401))+P22(f312(f312(f228(a852),f2(a852)),f312(f47(a852,f312(f312(f89(a852),x97401),f87(a852))),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.52/173.41 [9780]~E(f54(a852,x97801,f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(a852))+P22(f312(f312(f228(a852),f2(a852)),f54(a852,x97801,f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.52/173.41 [9804]E(f54(a852,x98041,f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(a852))+~P22(f312(f312(f228(a852),f2(a852)),f54(a852,x98041,f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.52/173.41 [4554]~P41(x45541,x45542)+P57(x45541,x45542)
% 173.52/173.41 [4555]~P46(x45551,x45552)+P57(x45551,x45552)
% 173.52/173.41 [4510]E(x45101,x45102)+~E(f40(x45101),f40(x45102))
% 173.52/173.41 [4511]E(x45111,x45112)+~E(f41(x45111),f41(x45112))
% 173.52/173.41 [4514]~E(x45141,x45142)+E(f257(x45141,x45142),f87(a113))
% 173.52/173.41 [4517]E(f199(x45171,x45172),x45171)+~E(x45172,f2(a852))
% 173.52/173.41 [4522]P42(x45221,x45222)+~E(x45222,f192(x45221))
% 173.52/173.41 [4525]~E(x45252,f127(x45251))+E(f148(x45251,x45252),f127(x45251))
% 173.52/173.41 [4529]~P42(x45292,x45291)+E(x45291,f192(x45292))
% 173.52/173.41 [4545]~E(f148(x45452,x45451),f127(x45452))+E(x45451,f127(x45452))
% 173.52/173.41 [4559]~P24(x45592)+P24(f860(x45591,x45592))
% 173.52/173.41 [4560]~P73(x45602)+P73(f860(x45601,x45602))
% 173.52/173.41 [4561]~P79(x45612)+P79(f860(x45611,x45612))
% 173.52/173.41 [4562]~P87(x45622)+P87(f860(x45621,x45622))
% 173.52/173.41 [4563]~P88(x45632)+P88(f860(x45631,x45632))
% 173.52/173.41 [4564]~P87(x45642)+P98(f860(x45641,x45642))
% 173.52/173.41 [4565]~P95(x45652)+P94(f860(x45651,x45652))
% 173.52/173.41 [4566]~P87(x45662)+P99(f860(x45661,x45662))
% 173.52/173.41 [4567]~P96(x45672)+P96(f860(x45671,x45672))
% 173.52/173.41 [4568]~P102(x45682)+P102(f860(x45681,x45682))
% 173.52/173.41 [4569]~P106(x45692)+P106(f860(x45691,x45692))
% 173.52/173.41 [4570]~P104(x45702)+P104(f860(x45701,x45702))
% 173.52/173.41 [4571]~P105(x45712)+P105(f860(x45711,x45712))
% 173.52/173.41 [4572]~P95(x45722)+P97(f860(x45721,x45722))
% 173.52/173.41 [4573]~P31(x45732)+P31(f860(x45731,x45732))
% 173.52/173.41 [4574]~P95(x45742)+P95(f860(x45741,x45742))
% 173.52/173.41 [4586]E(x45861,x45862)+~E(f312(a27,x45861),f312(a27,x45862))
% 173.52/173.41 [4588]E(x45881,x45882)+~E(f312(a126,x45881),f312(a126,x45882))
% 173.52/173.41 [4589]E(x45891,x45892)+~E(f312(a121,x45891),f312(a121,x45892))
% 173.52/173.41 [4590]E(x45901,x45902)+~E(f312(a3,x45901),f312(a3,x45902))
% 173.52/173.41 [4592]E(x45921,x45922)+~E(f312(a19,x45921),f312(a19,x45922))
% 173.52/173.41 [4700]~P60(x47001)+E(f54(x47001,x47002,x47002),f2(x47001))
% 173.52/173.41 [4731]~P41(x47311,x47312)+P41(f853(x47311),f142(x47311,x47312))
% 173.52/173.41 [4732]~P41(x47321,x47322)+P41(f853(x47321),f141(x47321,x47322))
% 173.52/173.41 [4827]~P41(x48271,x48272)+P41(f860(x48271,a845),f305(x48271,x48272))
% 173.52/173.41 [4828]~P41(x48281,x48282)+P41(f860(x48281,a845),f303(x48281,x48282))
% 173.52/173.41 [4943]~P32(x49431)+P43(f283(a1,x49431,x49432))
% 173.52/173.41 [5045]~P41(x50451,x50452)+P59(x50451,f76(x50451,x50451,x50452))
% 173.52/173.41 [5545]~P76(x55451)+P19(x55451,x55451,f88(x55451),x55452)
% 173.52/173.41 [4540]~E(x45402,f127(x45401))+E(f312(f164(x45401),x45402),f127(x45401))
% 173.52/173.41 [4541]~E(x45412,f127(x45411))+E(f312(f165(x45411),x45412),f127(x45411))
% 173.52/173.41 [4596]E(x45961,f312(a118,x45962))+~E(f312(f114(a1),x45961),x45962)
% 173.52/173.41 [4600]E(x46001,f127(x46002))+~E(f312(f164(x46002),x46001),f127(x46002))
% 173.52/173.41 [4601]E(x46011,f127(x46012))+~E(f312(f165(x46012),x46011),f127(x46012))
% 173.52/173.41 [4612]~E(x46122,f2(a1))+E(f312(f47(a1,x46121),x46122),f2(a1))
% 173.52/173.41 [4621]~P90(x46211)+E(f312(f117(x46211),x46212),f312(f116(x46211),x46212))
% 173.52/173.41 [4628]~E(x46282,f192(x46281))+E(f218(x46281,x46282),f189(f860(x46281,a845)))
% 173.52/173.41 [4630]~P62(x46301)+P22(f312(f70(x46301),x46302))
% 173.52/173.41 [4637]E(x46371,f192(x46372))+E(f312(f219(x46372),f363(x46372,x46371)),x46371)
% 173.52/173.41 [4638]E(x46381,f192(x46382))+E(f312(f219(x46382),f494(x46382,x46381)),x46381)
% 173.52/173.41 [4639]E(x46391,f192(x46392))+E(f312(f219(x46392),f523(x46392,x46391)),x46391)
% 173.52/173.41 [4640]~E(f610(x46402,x46401),f127(x46401))+E(f175(x46401,x46402),f127(f853(x46401)))
% 173.52/173.41 [4642]~P60(x46421)+E(f312(f47(x46421,x46422),f87(x46421)),x46422)
% 173.52/173.41 [4649]~E(x46492,f127(x46491))+E(f312(f168(x46491),x46492),f189(f860(x46491,a845)))
% 173.52/173.41 [4650]~E(x46502,f127(x46501))+E(f189(f860(x46501,a845)),f312(f168(x46501),x46502))
% 173.52/173.41 [4652]E(x46521,x46522)+~E(f312(f114(a1),x46521),f312(f114(a1),x46522))
% 173.52/173.41 [4655]~P60(x46551)+E(f312(f47(x46551,x46552),f2(x46551)),f2(x46551))
% 173.52/173.41 [4657]E(f207(x46571,x46572),f2(a852))+P22(f312(f70(x46571),x46572))
% 173.52/173.41 [4677]~P112(x46771)+E(f91(x46771,f91(x46771,x46772)),f91(x46771,x46772))
% 173.52/173.41 [4691]~P107(x46911)+E(f312(f312(f240(x46911),x46912),f87(a852)),x46912)
% 173.52/173.41 [4692]~P78(x46921)+E(f312(f312(f240(x46921),x46922),f87(a852)),x46922)
% 173.52/173.41 [4694]E(x46941,x46942)+E(f257(x46941,x46942),f312(f312(f89(a113),x46942),f87(a113)))
% 173.52/173.41 [4697]E(f312(f53(x46971),x46972),f2(a852))+P22(f312(f70(x46971),x46972))
% 173.52/173.41 [4701]~E(f148(x47011,x47012),x47012)+P22(f312(f133(x47011),x47012))
% 173.52/173.41 [4704]~P25(x47041)+E(f312(f312(f89(x47041),x47042),f2(x47041)),x47042)
% 173.52/173.41 [4705]~P107(x47051)+E(f312(f312(f89(x47051),x47052),f2(x47051)),x47052)
% 173.52/173.41 [4706]~P26(x47061)+E(f312(f312(f89(x47061),x47062),f2(x47061)),x47062)
% 173.52/173.41 [4707]~P71(x47071)+E(f312(f312(f21(x47071),x47072),f2(x47071)),x47072)
% 173.52/173.41 [4708]~P94(x47081)+E(f312(f312(f124(x47081),x47082),f189(x47081)),x47082)
% 173.52/173.41 [4709]~P97(x47091)+E(f312(f312(f115(x47091),x47092),f235(x47091)),x47092)
% 173.52/173.41 [4710]~P107(x47101)+E(f312(f312(f90(x47101),x47102),f87(x47101)),x47102)
% 173.52/173.41 [4711]~P78(x47111)+E(f312(f312(f90(x47111),x47112),f87(x47111)),x47112)
% 173.52/173.41 [4712]~P72(x47121)+E(f312(f312(f90(x47121),x47122),f87(x47121)),x47122)
% 173.52/173.41 [4713]~P114(x47131)+E(f312(f312(f268(x47131),x47132),f87(x47131)),x47132)
% 173.52/173.41 [4714]~P107(x47141)+E(f312(f312(f240(x47141),x47142),f2(a852)),f87(x47141))
% 173.52/173.41 [4715]~P109(x47151)+E(f312(f312(f240(x47151),x47152),f2(a852)),f87(x47151))
% 173.52/173.41 [4716]~E(x47162,f189(f860(x47161,a845)))+E(f312(f53(x47161),x47162),f2(a852))
% 173.52/173.41 [4726]~P60(x47261)+E(f54(x47261,x47262,f2(x47261)),x47262)
% 173.52/173.41 [4733]~P97(x47331)+E(f312(f312(f124(x47331),x47332),f235(x47331)),f235(x47331))
% 173.52/173.41 [4734]~P94(x47341)+E(f312(f312(f115(x47341),x47342),f189(x47341)),f189(x47341))
% 173.52/173.41 [4735]~P107(x47351)+E(f312(f312(f90(x47351),x47352),f2(x47351)),f2(x47351))
% 173.52/173.41 [4736]~P126(x47361)+E(f312(f312(f90(x47361),x47362),f2(x47361)),f2(x47361))
% 173.52/173.41 [4737]~P115(x47371)+E(f312(f312(f268(x47371),x47372),f2(x47371)),f2(x47371))
% 173.52/173.41 [4738]E(x47381,f192(x47382))+~E(f218(x47382,x47381),f189(f860(x47382,a845)))
% 173.52/173.41 [4741]~P60(x47411)+E(f54(x47411,x47412,f87(x47411)),f2(x47411))
% 173.52/173.41 [4742]~P60(x47421)+E(f54(x47421,f2(x47421),x47422),f2(x47421))
% 173.52/173.41 [4771]E(x47711,f2(a852))+E(f63(x47712,x47711,f127(x47712)),f127(f853(x47712)))
% 173.52/173.41 [4794]P41(x47941,x47942)+~E(f686(x47942,x47941),f189(f860(x47941,a845)))
% 173.52/173.41 [4795]E(x47951,f127(x47952))+~E(f312(f168(x47952),x47951),f189(f860(x47952,a845)))
% 173.52/173.41 [4796]E(x47961,f127(x47962))+~E(f189(f860(x47962,a845)),f312(f168(x47962),x47961))
% 173.52/173.41 [4799]~E(x47991,x47992)+P22(f312(f312(a309,x47991),x47992))
% 173.52/173.41 [4809]P22(x48091)+P22(f312(f312(a315,x48091),x48092))
% 173.52/173.41 [4810]E(x48101,f127(x48102))+E(f312(f312(f161(x48102),x48101),f2(a852)),f312(f137(x48102),x48101))
% 173.52/173.41 [4813]E(f148(x48131,x48132),x48132)+~P22(f312(f133(x48131),x48132))
% 173.52/173.41 [4818]~P22(x48182)+P22(f312(f312(a315,x48181),x48182))
% 173.52/173.41 [4819]~P22(x48192)+P22(f312(f312(a311,x48191),x48192))
% 173.52/173.41 [4820]~P22(x48201)+P22(f312(f312(a311,x48201),x48202))
% 173.52/173.41 [4830]~E(f581(x48302,x48301),f598(x48302,x48301))+P22(f312(f133(x48301),x48302))
% 173.52/173.41 [4838]E(f312(f233(x48381),x48382),f189(f860(x48381,a845)))+P22(f312(x48382,f538(x48382)))
% 173.52/173.41 [4839]E(f189(f860(x48391,a845)),f312(f233(x48391),x48392))+P22(f312(x48392,f539(x48392)))
% 173.52/173.41 [4906]~P112(x49061)+E(f312(f312(f90(x49061),x49062),f91(x49061,x49062)),f312(f84(x49061),x49062))
% 173.52/173.41 [4942]~P57(x49421,x49422)+P57(x49421,f312(f265(x49421,x49421),x49422))
% 173.52/173.41 [4959]~E(f312(a30,x49591),f312(f219(a846),x49592))+P22(f312(a24,f312(a27,x49591)))
% 173.52/173.41 [4964]E(x49641,x49642)+~P22(f312(f312(a309,x49641),x49642))
% 173.52/173.41 [4968]~P22(f312(a24,x49682))+P22(f312(a24,f35(x49681,x49682)))
% 173.52/173.41 [4977]P22(x49771)+~P22(f312(f312(a310,x49772),x49771))
% 173.52/173.41 [4978]P22(x49781)+~P22(f312(f312(a310,x49781),x49782))
% 173.52/173.41 [4982]~P106(x49821)+P22(f312(f312(f227(x49821),x49822),f235(x49821)))
% 173.52/173.41 [4986]E(x49861,x49862)+~E(f312(x49861,f364(x49862,x49861)),f312(x49862,f364(x49862,x49861)))
% 173.52/173.41 [5017]E(x50171,f2(a852))+E(f199(x50171,f54(a852,x50172,x50171)),f199(x50172,x50171))
% 173.52/173.41 [5022]~P103(x50221)+P33(x50221,f312(f312(f147(x50221),x50222),f127(x50221)))
% 173.52/173.41 [5043]~E(x50431,x50432)+P22(f312(f312(f228(a852),x50431),f312(a126,x50432)))
% 173.52/173.41 [5053]~E(x50531,f2(a852))+P22(f312(f312(f228(a852),x50531),f312(a126,x50532)))
% 173.52/173.41 [5065]P22(f312(x50651,x50652))+P22(f312(f312(f227(a1),f2(a1)),f320(x50651)))
% 173.52/173.41 [5102]P22(f312(a24,x51021))+~P22(f312(a24,f35(x51022,x51021)))
% 173.52/173.41 [5104]P22(f312(a24,x51041))+~P22(f312(a24,f36(x51042,x51041)))
% 173.52/173.41 [5106]P22(f312(a24,x51061))+~P22(f312(a24,f36(x51061,x51062)))
% 173.52/173.41 [5138]P57(x51381,x51382)+~P57(x51381,f312(f265(x51381,x51381),x51382))
% 173.52/173.41 [5141]~E(f54(a852,x51412,x51411),f2(a852))+E(f312(f312(f90(a852),x51411),f325(x51411,x51412)),x51412)
% 173.52/173.41 [5142]~E(f54(a1,x51422,x51421),f2(a1))+E(f312(f312(f90(a1),x51421),f326(x51421,x51422)),x51422)
% 173.52/173.41 [5167]~P22(f312(x51671,x51672))+P22(f312(f312(f227(a1),f2(a1)),f319(x51671)))
% 173.52/173.41 [5179]E(f312(f312(f21(a852),f312(a118,x51791)),f312(a118,x51792)),f312(a118,x51791))+~P22(f312(a194,x51792))
% 173.52/173.41 [5208]E(f258(x52081,x52082),f87(a113))+~P22(f312(f312(f227(a113),x52081),f87(a113)))
% 173.52/173.41 [5296]E(f312(f312(f161(x52961),x52962),f581(x52962,x52961)),f312(f312(f161(x52961),x52962),f598(x52962,x52961)))+P22(f312(f133(x52961),x52962))
% 173.52/173.41 [5339]~P22(f312(x53391,f99(x53392,x53391)))+P22(f312(x53391,f611(x53392,x53391)))
% 173.52/173.41 [5403]P59(x54031,x54032)+~P22(f312(f300(x54031,x54032),f553(x54032,x54031)))
% 173.52/173.41 [5553]~E(f312(a126,f54(a852,x55531,x55532)),x55532)+E(f54(a852,f312(a126,x55531),x55532),f2(a852))
% 173.52/173.41 [5612]~P111(x56121)+P22(f312(f312(f314(x56121),f312(f114(x56121),x56122)),f123(x56121)))
% 173.52/173.41 [5613]~P23(x56131)+P22(f312(f312(f314(x56131),f312(f114(x56131),x56132)),f187(x56131)))
% 173.52/173.41 [5614]~P90(x56141)+P22(f312(f312(f314(x56141),f312(f117(x56141),x56142)),f123(x56141)))
% 173.52/173.41 [5615]~P111(x56151)+P22(f312(f312(f314(x56151),f312(f116(x56151),x56152)),f123(x56151)))
% 173.52/173.41 [5750]E(f312(a126,f54(a852,x57501,x57502)),x57502)+E(f54(a852,f312(a126,x57501),x57502),f312(a126,f54(a852,x57501,x57502)))
% 173.52/173.41 [6132]~E(x61321,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x61321),x61322)),f54(a1,x61321,x61322)),f312(f312(f239(a1,a1),f2(a1)),f2(a1)))
% 173.52/173.41 [6163]P41(x61631,x61632)+~P22(f312(f312(f314(x61631),f554(x61632,x61631)),f301(x61631,x61632)))
% 173.52/173.41 [6199]~P117(x61991)+~P22(f312(f312(f228(x61991),f312(f114(x61991),x61992)),f2(x61991)))
% 173.52/173.41 [6200]~P83(x62001)+~P22(f312(f312(f228(x62001),f312(f84(x62001),x62002)),f2(x62001)))
% 173.52/173.41 [6285]P22(f312(f312(f228(a1),x62851),f54(a1,x62852,x62851)))+~P22(f312(f312(f228(a1),x62851),f2(a1)))
% 173.52/173.41 [6381]E(f312(f312(f289(a852),f312(a126,x63811)),f283(a852,x63812,x63811)),f283(a852,x63812,f312(a126,x63811)))+~P22(f312(f312(f227(a852),x63812),f312(a126,x63811)))
% 173.52/173.41 [6466]~P103(x64661)+P33(x64661,f144(x64661,x64661,f5(x64661),x64662))
% 173.52/173.41 [6598]E(f312(f164(x65981),x65982),x65982)+~P22(f312(f312(f227(a852),f312(f190(f853(x65981)),x65982)),f87(a852)))
% 173.52/173.41 [6613]~P83(x66131)+P22(f312(f312(f227(x66131),f312(f88(x66131),f312(f84(x66131),x66132))),f2(x66131)))
% 173.52/173.41 [6649]~P41(x66491,x66492)+P41(x66491,f312(f312(f267(x66491,x66491,x66491),x66492),f287(x66491,x66492)))
% 173.52/173.41 [6862]~P22(f312(f312(f228(a1),x68622),f2(a1)))+P22(f312(f312(f227(a1),f54(a1,x68621,x68622)),f2(a1)))
% 173.52/173.41 [7254]~P23(x72541)+E(f191(x72541,f312(f312(f7(x72541,x72541,x72541),f89(x72541)),f87(x72541)),x72542,f2(x72541)),f312(f114(x72541),x72542))
% 173.52/173.41 [7280]~P119(x72801)+~P22(f312(f312(f228(x72801),f312(f312(f90(x72801),x72802),x72802)),f2(x72801)))
% 173.52/173.41 [9900]~P112(x99001)+~P22(f312(f312(f228(x99001),f312(f312(f240(x99001),x99002),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f2(x99001)))
% 173.52/173.41 [4598]~E(x45982,f127(x45981))+E(f312(f190(f853(x45981)),x45982),f2(a852))
% 173.52/173.41 [4641]~E(x46411,f2(a852))+E(f312(f312(f89(a852),x46411),x46412),x46412)
% 173.52/173.41 [4643]~E(x46432,f2(a852))+E(f312(f312(f90(a852),x46431),x46432),f2(a852))
% 173.52/173.41 [4645]~E(x46451,f2(a852))+E(f312(f312(f90(a852),x46451),x46452),f2(a852))
% 173.52/173.41 [4646]~E(x46462,f2(a852))+E(f312(f312(f240(a852),x46461),x46462),f87(a852))
% 173.52/173.41 [4658]E(x46581,f127(x46582))+~E(f312(f190(f853(x46582)),x46581),f2(a852))
% 173.52/173.41 [4659]~P87(x46591)+E(f312(f312(f124(x46591),x46592),x46592),x46592)
% 173.52/173.41 [4661]~P98(x46611)+E(f312(f312(f124(x46611),x46612),x46612),x46612)
% 173.52/173.41 [4662]~P87(x46621)+E(f312(f312(f115(x46621),x46622),x46622),x46622)
% 173.52/173.41 [4664]~P99(x46641)+E(f312(f312(f115(x46641),x46642),x46642),x46642)
% 173.52/173.41 [4666]~P93(x46661)+E(f312(f312(f90(x46661),x46662),x46662),x46662)
% 173.52/173.41 [4668]~P103(x46681)+E(f312(f312(f225(x46681),x46682),x46682),x46682)
% 173.52/173.41 [4670]~P103(x46701)+E(f312(f312(f226(x46701),x46702),x46702),x46702)
% 173.52/173.41 [4689]~P60(x46891)+E(f312(f47(x46891,f2(x46891)),x46892),f2(x46891))
% 173.52/173.41 [4690]~P71(x46901)+E(f312(f312(f21(x46901),x46902),x46902),f2(x46901))
% 173.52/173.41 [4702]~P71(x47021)+E(f312(f88(x47021),f312(f88(x47021),x47022)),x47022)
% 173.52/173.41 [4703]~P88(x47031)+E(f312(f88(x47031),f312(f88(x47031),x47032)),x47032)
% 173.52/173.41 [4719]~E(x47192,f2(a852))+E(f312(f312(f240(a852),x47191),x47192),f312(a126,f2(a852)))
% 173.52/173.41 [4750]~P25(x47501)+E(f312(f312(f89(x47501),f2(x47501)),x47502),x47502)
% 173.52/173.41 [4751]~P107(x47511)+E(f312(f312(f89(x47511),f2(x47511)),x47512),x47512)
% 173.52/173.41 [4752]~P26(x47521)+E(f312(f312(f89(x47521),f2(x47521)),x47522),x47522)
% 173.52/173.41 [4753]~P94(x47531)+E(f312(f312(f124(x47531),f189(x47531)),x47532),x47532)
% 173.52/173.41 [4754]~P97(x47541)+E(f312(f312(f115(x47541),f235(x47541)),x47542),x47542)
% 173.52/173.41 [4755]~P107(x47551)+E(f312(f312(f90(x47551),f87(x47551)),x47552),x47552)
% 173.52/173.41 [4756]~P78(x47561)+E(f312(f312(f90(x47561),f87(x47561)),x47562),x47562)
% 173.52/173.41 [4757]~P72(x47571)+E(f312(f312(f90(x47571),f87(x47571)),x47572),x47572)
% 173.52/173.41 [4776]~P97(x47761)+E(f312(f312(f124(x47761),f235(x47761)),x47762),f235(x47761))
% 173.52/173.41 [4777]~P94(x47771)+E(f312(f312(f115(x47771),f189(x47771)),x47772),f189(x47771))
% 173.52/173.41 [4778]~P107(x47781)+E(f312(f312(f90(x47781),f2(x47781)),x47782),f2(x47781))
% 173.52/173.41 [4779]~P126(x47791)+E(f312(f312(f90(x47791),f2(x47791)),x47792),f2(x47791))
% 173.52/173.41 [4780]~P78(x47801)+E(f312(f312(f240(x47801),f87(x47801)),x47802),f87(x47801))
% 173.52/173.41 [4781]~P114(x47811)+E(f312(f312(f268(x47811),f2(x47811)),x47812),f2(x47811))
% 173.52/173.41 [4789]E(x47891,f127(x47892))+E(f140(x47892,f312(f165(x47892),x47891)),f312(f137(x47892),x47891))
% 173.52/173.41 [4790]E(x47901,f127(x47902))+E(f312(f137(x47902),f312(f165(x47902),x47901)),f140(x47902,x47901))
% 173.52/173.41 [4791]E(x47911,f2(a852))+~E(f312(f312(f89(a852),x47912),x47911),x47912)
% 173.52/173.41 [4797]~P111(x47971)+E(f312(f116(x47971),f312(f114(a1),x47972)),f312(f114(x47971),x47972))
% 173.52/173.41 [4798]~P90(x47981)+E(f312(f116(x47981),f312(f117(a1),x47982)),f312(f117(x47981),x47982))
% 173.52/173.41 [4805]E(x48051,f2(a852))+~E(f312(f312(f89(a852),x48052),x48051),f2(a852))
% 173.52/173.41 [4806]E(x48061,f2(a852))+~E(f312(f312(f89(a852),x48061),x48062),f2(a852))
% 173.52/173.41 [4807]E(x48071,f87(a852))+~E(f312(f312(f90(a852),x48072),x48071),f87(a852))
% 173.52/173.41 [4808]E(x48081,f87(a852))+~E(f312(f312(f90(a852),x48081),x48082),f87(a852))
% 173.52/173.41 [4823]~P83(x48231)+E(f312(f84(x48231),f312(f88(x48231),x48232)),f312(f84(x48231),x48232))
% 173.52/173.41 [4824]~P112(x48241)+E(f312(f84(x48241),f312(f114(x48241),x48242)),f312(f114(x48241),x48242))
% 173.52/173.41 [4825]~P83(x48251)+E(f312(f84(x48251),f312(f84(x48251),x48252)),f312(f84(x48251),x48252))
% 173.52/173.41 [4826]~P26(x48261)+E(f312(f162(x48261),f312(f165(x48261),x48262)),f312(f162(x48261),x48262))
% 173.52/173.41 [4831]~E(x48311,f312(a126,f2(a852)))+E(f312(f312(f240(a852),x48311),x48312),f312(a126,f2(a852)))
% 173.52/173.41 [4842]~P71(x48421)+E(f312(f312(f21(x48421),f2(x48421)),x48422),f312(f88(x48421),x48422))
% 173.52/173.41 [4843]~E(x48432,f2(a852))+E(f135(a852,f312(f282(a852,x48431),x48432)),f127(a852))
% 173.52/173.41 [4852]~P90(x48521)+E(f312(f312(f89(x48521),x48522),f312(f117(x48521),a92)),x48522)
% 173.52/173.41 [4853]E(x48531,f2(a1))+E(f55(f312(f84(a1),x48532),f312(f84(a1),x48531)),f61(x48532,x48531))
% 173.52/173.41 [4867]~E(x48671,x48672)+P22(f312(f312(f227(a852),x48671),x48672))
% 173.52/173.41 [4874]~E(x48741,f2(a113))+E(f312(f312(f89(a852),f312(a19,x48741)),x48742),x48742)
% 173.52/173.41 [4875]~E(f312(f117(a1),x48752),f312(f114(a1),x48751))+E(x48751,f312(a118,f312(f117(a1),x48752)))
% 173.52/173.41 [4876]~P31(x48761)+E(f109(x48761,f312(f16(x48761,x48761),x48762)),x48762)
% 173.52/173.41 [4885]~P32(x48851)+P32(f312(f312(f240(a1),x48851),x48852))
% 173.52/173.41 [4886]~P71(x48861)+E(f312(f312(f89(x48861),x48862),f312(f88(x48861),x48862)),f2(x48861))
% 173.52/173.41 [4887]~P88(x48871)+E(f312(f312(f124(x48871),x48872),f312(f88(x48871),x48872)),f235(x48871))
% 173.52/173.41 [4888]~P88(x48881)+E(f312(f312(f115(x48881),x48882),f312(f88(x48881),x48882)),f189(x48881))
% 173.52/173.41 [4914]E(x49141,f2(a852))+~E(f312(f88(a1),f312(f114(a1),x49142)),f312(f114(a1),x49141))
% 173.52/173.41 [4915]E(x49151,f2(a852))+~E(f312(f88(a1),f312(f114(a1),x49151)),f312(f114(a1),x49152))
% 173.52/173.41 [4920]E(f196(x49201,x49202),f2(a1))+P22(f312(f312(f227(a1),x49202),x49201))
% 173.52/173.41 [4921]E(f174(x49211,x49212),f127(a1))+P22(f312(f312(f227(a1),x49211),x49212))
% 173.52/173.41 [4934]E(x49341,f312(a126,f2(a852)))+~E(f312(f312(f90(a852),x49342),x49341),f312(a126,f2(a852)))
% 173.52/173.41 [4935]E(x49351,f312(a126,f2(a852)))+~E(f312(f312(f90(a852),x49351),x49352),f312(a126,f2(a852)))
% 173.52/173.41 [4936]~P102(x49361)+P22(f312(f312(f227(x49361),x49362),x49362))
% 173.52/173.41 [4939]~P90(x49391)+E(f312(f312(f90(x49391),x49392),f312(f117(x49391),a111)),f312(f88(x49391),x49392))
% 173.52/173.41 [4956]~P90(x49561)+E(f312(f88(x49561),f312(f117(x49561),x49562)),f312(f117(x49561),f312(f88(a1),x49562)))
% 173.52/173.41 [4957]~P111(x49571)+E(f312(f88(x49571),f312(f116(x49571),x49572)),f312(f116(x49571),f312(f88(a1),x49572)))
% 173.52/173.41 [4987]~E(x49871,f312(a126,x49872))+P22(f312(f312(f228(a852),f2(a852)),x49871))
% 173.52/173.41 [5004]~P103(x50041)+E(f312(f88(f860(x50041,a845)),f312(f281(x50041),x50042)),f312(f280(x50041),x50042))
% 173.52/173.41 [5005]~P103(x50051)+E(f312(f88(f860(x50051,a845)),f312(f280(x50051),x50052)),f312(f281(x50051),x50052))
% 173.52/173.41 [5006]~P103(x50061)+E(f312(f88(f860(x50061,a845)),f312(f234(x50061),x50062)),f312(f279(x50061),x50062))
% 173.52/173.41 [5007]~P103(x50071)+E(f312(f88(f860(x50071,a845)),f312(f279(x50071),x50072)),f312(f234(x50071),x50072))
% 173.52/173.41 [5016]~E(f312(f114(a1),x50162),x50161)+P22(f312(f312(f227(a1),f2(a1)),x50161))
% 173.52/173.41 [5025]~E(x50252,f2(a1))+E(f61(x50251,x50252),f312(f312(f239(a1,a1),f2(a1)),f312(f84(a1),x50251)))
% 173.52/173.41 [5026]~P24(x50261)+P22(f312(f312(f227(x50261),f189(x50261)),x50262))
% 173.52/173.41 [5058]E(x50581,x50582)+~E(f312(f312(f89(a1),x50581),x50581),f312(f312(f89(a1),x50582),x50582))
% 173.52/173.41 [5064]~P22(f312(x50641,x50642))+P22(f312(x50641,f312(a118,f319(x50641))))
% 173.52/173.41 [5090]~P112(x50901)+E(f312(f312(f90(x50901),f91(x50901,x50902)),f312(f84(x50901),x50902)),x50902)
% 173.52/173.41 [5091]E(x50911,x50912)+~P22(f312(f312(f195(a23),x50911),x50912))
% 173.52/173.41 [5100]~E(x51002,f2(a852))+E(f94(f859(a852,a852),f56(x51001,x51002)),f312(f312(f239(a852,a852),f2(a852)),x51001))
% 173.52/173.41 [5111]~E(x51111,x51112)+~P22(f312(f312(f228(a852),x51111),x51112))
% 173.52/173.41 [5112]~E(x51121,x51122)+~P22(f312(f312(f228(a1),x51121),x51122))
% 173.52/173.41 [5115]~P23(x51151)+E(f312(f312(f89(x51151),f87(x51151)),f312(f114(x51151),x51152)),f312(f114(x51151),f312(a126,x51152)))
% 173.52/173.41 [5119]~E(x51191,f2(a852))+~P22(f312(f312(f228(a852),x51192),x51191))
% 173.52/173.41 [5135]E(f148(x51351,x51352),x51352)+~E(f312(f190(f853(x51351)),f148(x51351,x51352)),f312(f190(f853(x51351)),x51352))
% 173.52/173.41 [5136]E(f312(f53(x51361),f312(f168(x51361),x51362)),f312(f190(f853(x51361)),x51362))+~P22(f312(f133(x51361),x51362))
% 173.52/173.41 [5146]~P22(f312(x51461,f818(x51461)))+P22(f312(x51461,f312(f114(a1),x51462)))
% 173.52/173.41 [5157]E(f174(x51571,x51572),f127(a1))+~P22(f312(f312(f228(a1),x51572),x51571))
% 173.52/173.41 [5158]E(f258(x51581,x51582),f87(a113))+~P22(f312(f312(f228(a113),x51582),x51581))
% 173.52/173.41 [5161]~P105(x51611)+E(f283(x51611,x51612,x51612),f312(f312(f289(x51611),x51612),f189(f860(x51611,a845))))
% 173.52/173.41 [5182]~E(f312(f312(f21(a852),x51821),x51822),f2(a852))+P22(f312(f312(f227(a852),x51821),x51822))
% 173.52/173.41 [5205]~E(x52052,f2(a852))+E(f63(x52051,x52052,f127(x52051)),f312(f312(f147(f853(x52051)),f127(x52051)),f127(f853(x52051))))
% 173.52/173.41 [5209]~P102(x52091)+~P22(f312(f312(f228(x52091),x52092),x52092))
% 173.52/173.41 [5212]~E(f54(a1,x52121,x52122),f2(a1))+E(f54(a1,x52121,f312(f88(a1),x52122)),f2(a1))
% 173.52/173.41 [5214]~E(f54(a1,x52141,x52142),f2(a1))+E(f54(a1,f312(f88(a1),x52141),x52142),f2(a1))
% 173.52/173.41 [5221]E(f312(f282(a852,x52211),f312(a126,x52212)),f189(f860(a852,a845)))+P22(f312(f312(f227(a852),x52211),x52212))
% 173.52/173.41 [5240]E(f135(a852,f312(f282(a852,x52401),x52402)),f127(a852))+P22(f312(f312(f228(a852),x52401),x52402))
% 173.52/173.41 [5245]~E(f312(f53(x52451),f312(f168(x52451),x52452)),f312(f190(f853(x52451)),x52452))+P22(f312(f133(x52451),x52452))
% 173.52/173.41 [5249]~P22(f312(f133(x52491),x52492))+P22(f312(f133(x52491),f312(f164(x52491),x52492)))
% 173.52/173.41 [5250]~P22(f312(f133(x52501),x52502))+P22(f312(f133(x52501),f312(f167(x52501),x52502)))
% 173.52/173.41 [5251]~P22(f312(f133(x52511),x52512))+P22(f312(f133(x52511),f312(f165(x52511),x52512)))
% 173.52/173.41 [5257]E(f312(f47(a852,x52571),x52572),f2(a852))+~P22(f312(f312(f228(a852),x52571),x52572))
% 173.52/173.41 [5258]P22(f312(x52581,x52582))+~P22(f312(x52581,f312(a118,f320(x52581))))
% 173.52/173.41 [5259]P22(f312(f312(f227(a852),x52592),x52591))+P22(f312(f312(f227(a852),x52591),x52592))
% 173.52/173.41 [5260]P22(f312(f312(f227(a1),x52602),x52601))+P22(f312(f312(f227(a1),x52601),x52602))
% 173.52/173.41 [5262]~P83(x52621)+P22(f312(f312(f227(x52621),x52622),f312(f84(x52621),x52622)))
% 173.52/173.41 [5265]P22(f312(x52651,f819(x52651)))+~P22(f312(x52651,f312(f114(a1),x52652)))
% 173.52/173.41 [5290]E(f312(f312(f21(a852),x52901),x52902),f2(a852))+~P22(f312(f312(f227(a852),x52901),x52902))
% 173.52/173.41 [5307]E(f54(a852,x53071,x53072),x53071)+~P22(f312(f312(f228(a852),x53071),x53072))
% 173.52/173.41 [5315]E(f54(a1,x53151,f312(f88(a1),x53152)),f269(x53151,x53152))+P22(f312(f312(f227(a1),f2(a1)),x53152))
% 173.52/173.41 [5327]E(f312(f312(f21(a1),x53271),x53272),f196(x53271,x53272))+~P22(f312(f312(f227(a1),x53272),x53271))
% 173.52/173.41 [5346]P22(f312(f312(f227(a1),f2(a1)),f818(x53461)))+P22(f312(x53461,f312(f114(a1),x53462)))
% 173.52/173.41 [5358]~P63(x53581)+P22(f312(f312(f314(x53581),x53582),f312(f168(x53581),f64(x53581))))
% 173.52/173.41 [5360]~P117(x53601)+P22(f312(f312(f227(x53601),f2(x53601)),f312(f114(x53601),x53602)))
% 173.52/173.41 [5361]~P83(x53611)+P22(f312(f312(f227(x53611),f2(x53611)),f312(f84(x53611),x53612)))
% 173.52/173.41 [5369]E(f312(f47(a1,x53691),x53692),f270(x53691,x53692))+~P22(f312(f312(f227(a1),f2(a1)),x53692))
% 173.52/173.41 [5389]E(f312(f312(f89(a852),x53891),f820(x53892,x53891)),x53892)+~P22(f312(f312(f227(a852),x53891),x53892))
% 173.52/173.41 [5401]~E(f312(f117(a1),x54011),f312(f114(a1),x54012))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x54011)))
% 173.52/173.41 [5404]E(f283(a1,x54041,x54042),f189(f860(a1,a845)))+~P22(f312(f312(f228(a1),x54042),x54041))
% 173.52/173.41 [5407]~P112(x54071)+E(f312(f312(f90(x54071),f312(f84(x54071),x54072)),f312(f84(x54071),x54072)),f312(f312(f90(x54071),x54072),x54072))
% 173.52/173.41 [5412]E(f135(a852,f312(f282(a852,x54121),f312(a126,x54122))),f127(a852))+P22(f312(f312(f227(a852),x54121),x54122))
% 173.52/173.41 [5435]P22(f312(f133(x54351),x54352))+~P22(f312(f133(x54351),f312(f164(x54351),x54352)))
% 173.52/173.41 [5436]P22(f312(f133(x54361),x54362))+~P22(f312(f133(x54361),f312(f165(x54361),x54362)))
% 173.52/173.41 [5457]P22(f312(f70(a852),x54571))+P22(f312(f312(f314(a852),f367(x54571,x54572)),x54571))
% 173.52/173.41 [5458]P22(f312(f70(a852),x54581))+P22(f312(f312(f314(a852),f371(x54581,x54582)),x54581))
% 173.52/173.41 [5459]P22(f312(f312(f228(a852),x54592),f312(a126,x54591)))+P22(f312(f312(f228(a852),x54591),x54592))
% 173.52/173.41 [5460]E(f54(a1,x54601,x54602),f269(x54601,x54602))+~P22(f312(f312(f227(a1),f2(a1)),x54602))
% 173.52/173.41 [5463]E(f135(a852,f312(f282(a852,x54631),x54632)),f127(a852))+~P22(f312(f312(f227(a852),x54632),x54631))
% 173.52/173.41 [5464]~P76(x54641)+E(f312(f290(x54641,x54641,f88(x54641)),f312(f281(x54641),x54642)),f312(f234(x54641),f312(f88(x54641),x54642)))
% 173.52/173.41 [5465]~P76(x54651)+E(f312(f290(x54651,x54651,f88(x54651)),f312(f280(x54651),x54652)),f312(f279(x54651),f312(f88(x54651),x54652)))
% 173.52/173.41 [5466]~P76(x54661)+E(f312(f290(x54661,x54661,f88(x54661)),f312(f234(x54661),x54662)),f312(f281(x54661),f312(f88(x54661),x54662)))
% 173.52/173.41 [5467]~P76(x54671)+E(f312(f290(x54671,x54671,f88(x54671)),f312(f279(x54671),x54672)),f312(f280(x54671),f312(f88(x54671),x54672)))
% 173.52/173.41 [5480]E(x54801,f189(f860(x54802,a845)))+P22(f312(f312(f314(x54802),f786(x54801,x54802)),x54801))
% 173.52/173.41 [5481]E(x54811,f189(f860(x54812,a845)))+P22(f312(f312(f314(x54812),f760(x54811,x54812)),x54811))
% 173.52/173.41 [5492]~P22(f312(f312(f228(a852),x54921),x54922))+P22(f312(f312(f227(a852),x54921),x54922))
% 173.52/173.41 [5493]~P22(f312(f312(f228(a1),x54931),x54932))+P22(f312(f312(f227(a1),x54931),x54932))
% 173.52/173.41 [5509]E(f55(x55091,x55092),f312(f312(f239(a1,a1),f2(a1)),x55091))+~P22(f312(f312(f228(a1),x55091),x55092))
% 173.52/173.41 [5511]E(f210(f312(f88(a1),x55111),f312(f88(a1),x55112)),f210(x55111,x55112))+~P22(f312(f312(f228(a1),x55112),f2(a1)))
% 173.52/173.41 [5523]E(x55231,x55232)+~E(f312(a3,f312(a126,f312(a19,x55231))),f312(a3,f312(a126,f312(a19,x55232))))
% 173.52/173.41 [5528]E(f55(x55281,x55282),f312(f312(f239(a1,a1),f2(a1)),x55281))+~P22(f312(f312(f227(a1),x55282),f2(a1)))
% 173.52/173.41 [5559]E(f54(a852,f312(f117(a852),x55591),f312(f117(a852),x55592)),f2(a852))+~P22(f312(a194,f312(f117(a1),x55591)))
% 173.52/173.41 [5577]P22(f312(f312(f227(a1),f2(a1)),f819(x55771)))+~P22(f312(x55771,f312(f114(a1),x55772)))
% 173.52/173.41 [5606]P43(f283(a1,x56061,x56062))+~P22(f312(f312(f227(a1),f2(a1)),x56061))
% 173.52/173.41 [5607]~P22(f312(f70(x56071),x56072))+P22(f312(f70(f860(x56071,a845)),f312(f288(x56071),x56072)))
% 173.52/173.41 [5621]E(f312(f47(a852,f312(f117(a852),x56211)),f312(f117(a852),x56212)),f2(a852))+~P22(f312(a194,f312(f117(a1),x56211)))
% 173.52/173.41 [5622]E(f312(f312(f89(a1),x56221),f312(f114(a1),f821(x56222,x56221))),x56222)+~P22(f312(f312(f227(a1),x56221),x56222))
% 173.52/173.41 [5630]P22(f312(f312(f227(a852),x56301),x56302))+P22(f312(f312(f227(a852),f312(a126,x56302)),x56301))
% 173.52/173.41 [5672]E(f312(f312(f90(a852),f312(f117(a852),x56721)),f312(f117(a852),x56722)),f2(a852))+~P22(f312(f312(f228(a1),x56721),a92))
% 173.52/173.41 [5674]P22(f312(f312(f228(a852),x56741),f312(a126,x56742)))+~P22(f312(f312(f228(a852),x56741),x56742))
% 173.52/173.41 [5676]P22(f312(f312(f228(a852),x56761),f312(a126,x56762)))+~P22(f312(f312(f227(a852),x56761),x56762))
% 173.52/173.41 [5678]P22(f312(f312(f227(a852),x56781),f312(a126,x56782)))+~P22(f312(f312(f227(a852),x56781),x56782))
% 173.52/173.41 [5681]~E(x56811,x56812)+P22(f312(f312(f228(a1),x56811),f312(f312(f89(a1),x56812),f87(a1))))
% 173.52/173.41 [5684]E(f54(a1,x56841,x56842),f2(a1))+E(f312(f312(f21(a1),x56842),f54(a1,x56841,x56842)),f54(a1,f312(f88(a1),x56841),x56842))
% 173.52/173.41 [5692]E(x56921,f127(x56922))+P22(f312(f312(f314(x56922),f140(x56922,x56921)),f312(f168(x56922),x56921)))
% 173.52/173.41 [5703]E(f94(f859(a852,a852),f56(x57031,x57032)),f312(f312(f239(a852,a852),f2(a852)),x57031))+~P22(f312(f312(f228(a852),x57031),x57032))
% 173.52/173.41 [5731]E(f312(f312(f89(a852),f312(f117(a852),x57311)),f312(f117(a852),x57312)),f312(f117(a852),x57312))+~P22(f312(f312(f228(a1),x57311),a92))
% 173.52/173.41 [5732]E(f312(f312(f21(a852),f312(f117(a852),x57321)),f312(f117(a852),x57322)),f312(f117(a852),x57321))+~P22(f312(f312(f228(a1),x57322),a92))
% 173.52/173.41 [5737]E(f312(a126,f312(f312(f89(a852),x57371),f817(x57372,x57371))),x57372)+~P22(f312(f312(f228(a852),x57371),x57372))
% 173.52/173.41 [5760]P22(f312(x57601,x57602))+~P22(f312(x57601,f312(a98,f582(x57602,x57601))))
% 173.52/173.41 [5768]~P22(f312(f312(f228(a852),x57681),f312(a126,x57682)))+P22(f312(f312(f227(a852),x57681),x57682))
% 173.52/173.41 [5814]E(f312(f312(f289(a852),x58141),f312(f282(a852,x58142),x58141)),f312(f282(a852,x58142),f312(a126,x58141)))+~P22(f312(f312(f227(a852),x58142),x58141))
% 173.52/173.41 [5819]E(x58191,f127(x58192))+E(f312(f312(f129(x58192),f128(x58192,x58191)),f312(f312(f147(x58192),f140(x58192,x58191)),f127(x58192))),x58191)
% 173.52/173.41 [5831]P22(f312(f70(x58311),x58312))+~P22(f312(f312(f228(a852),f2(a852)),f312(f53(x58311),x58312)))
% 173.52/173.41 [5833]~E(x58331,f189(f860(x58332,a845)))+~P22(f312(f312(f228(a852),f2(a852)),f312(f53(x58332),x58331)))
% 173.52/173.41 [5844]~P22(f312(f312(f228(a852),x58441),x58442))+P22(f312(f312(f227(a852),f312(a126,x58441)),x58442))
% 173.52/173.41 [5852]~P103(x58521)+E(f144(x58521,x58521,f5(x58521),f148(x58521,x58522)),f135(x58521,f312(f168(x58521),x58522)))
% 173.52/173.41 [5855]E(x58551,f127(x58552))+P22(f312(f312(f314(x58552),f312(f137(x58552),x58551)),f312(f168(x58552),x58551)))
% 173.52/173.41 [5861]~P117(x58611)+P22(f312(f312(f228(x58611),x58612),f312(f312(f89(x58611),x58612),f87(x58611))))
% 173.52/173.41 [5863]~P83(x58631)+P22(f312(f312(f227(x58631),f312(f88(x58631),x58632)),f312(f84(x58631),x58632)))
% 173.52/173.41 [5901]P22(f312(f70(a852),x59011))+~P22(f312(f312(f228(a852),f371(x59011,x59012)),x59012))
% 173.52/173.41 [5902]P22(f312(f70(a852),x59021))+~P22(f312(f312(f227(a852),f367(x59021,x59022)),x59022))
% 173.52/173.41 [5906]~P22(f312(f70(f859(x59061,x59061)),x59062))+P22(f312(f70(x59061),f312(f263(x59061),x59062)))
% 173.52/173.41 [5923]E(f312(f47(a852,f312(a118,x59231)),f312(a118,x59232)),f312(a118,f312(f47(a1,x59231),x59232)))+~P22(f312(f312(f227(a1),f2(a1)),x59231))
% 173.52/173.41 [5958]~P22(f312(f312(f228(a852),x59582),f312(a126,x59581)))+~P22(f312(f312(f228(a852),x59581),x59582))
% 173.52/173.41 [5959]~P105(x59591)+E(f312(f312(f115(f860(x59591,a845)),f312(f281(x59591),x59592)),f312(f234(x59591),x59592)),f312(f312(f289(x59591),x59592),f189(f860(x59591,a845))))
% 173.52/173.41 [5971]P22(f312(f70(x59711),x59712))+~P22(f312(f70(f860(x59711,a845)),f312(f288(x59711),x59712)))
% 173.52/173.41 [5994]P22(f312(f312(f228(a852),f312(a126,x59941)),f312(a126,x59942)))+~P22(f312(f312(f228(a852),x59941),x59942))
% 173.52/173.41 [5995]P22(f312(f312(f228(a852),f312(a19,x59951)),f312(a19,x59952)))+~P22(f312(f312(f228(a113),x59951),x59952))
% 173.52/173.41 [5996]P22(f312(f312(f228(a113),f312(a3,x59961)),f312(a3,x59962)))+~P22(f312(f312(f228(a852),x59961),x59962))
% 173.52/173.41 [5997]P22(f312(f312(f227(a852),f312(a126,x59971)),f312(a126,x59972)))+~P22(f312(f312(f227(a852),x59971),x59972))
% 173.52/173.41 [5998]P22(f312(f312(f227(a852),f312(a19,x59981)),f312(a19,x59982)))+~P22(f312(f312(f227(a113),x59981),x59982))
% 173.52/173.41 [5999]P22(f312(f312(f227(a113),f312(a3,x59991)),f312(a3,x59992)))+~P22(f312(f312(f227(a852),x59991),x59992))
% 173.52/173.41 [6002]E(x60021,x60022)+~E(f312(f290(a852,a1,f114(a1)),x60021),f312(f290(a852,a1,f114(a1)),x60022))
% 173.52/173.41 [6017]P22(f312(f312(f228(a852),x60171),x60172))+~P22(f312(f312(f228(a852),f312(a126,x60171)),x60172))
% 173.52/173.41 [6020]P22(f312(f312(f228(a852),x60201),x60202))+~P22(f312(f312(f227(a852),f312(a126,x60201)),x60202))
% 173.52/173.41 [6021]P22(f312(f312(f227(a852),x60211),x60212))+~P22(f312(f312(f227(a852),f312(a126,x60211)),x60212))
% 173.52/173.41 [6035]E(f54(a1,x60351,x60352),f2(a1))+E(f312(f312(f21(a1),f54(a1,x60351,x60352)),x60352),f54(a1,x60351,f312(f88(a1),x60352)))
% 173.52/173.41 [6101]E(f312(f53(f860(x61011,a845)),f312(f288(x61011),x61012)),f312(f312(f240(a852),f312(a126,f312(a126,f2(a852)))),f312(f53(x61011),x61012)))+~P22(f312(f70(x61011),x61012))
% 173.52/173.41 [6104]E(x61041,f127(x61042))+E(f312(f312(f161(x61042),x61041),f312(f312(f21(a852),f312(f190(f853(x61042)),x61041)),f87(a852))),f140(x61042,x61041))
% 173.52/173.41 [6129]E(x61291,f127(x61292))+E(f312(f312(f129(x61292),f312(f167(x61292),x61291)),f312(f312(f147(x61292),f312(f137(x61292),x61291)),f127(x61292))),f312(f164(x61292),x61291))
% 173.52/173.41 [6160]~P22(f312(f70(x61601),f48(f860(x61601,a845),x61602)))+P22(f312(f70(f860(x61601,a845)),x61602))
% 173.52/173.41 [6183]P22(f312(f312(f227(a852),f312(f117(a852),x61831)),f312(f117(a852),x61832)))+~P22(f312(f312(f227(a1),x61831),a92))
% 173.52/173.41 [6201]~P22(f312(f312(f228(a1),x62011),x62012))+P22(f312(f312(f228(a1),x62011),f312(f312(f89(a1),x62012),f87(a1))))
% 173.52/173.41 [6202]~P22(f312(f312(f227(a1),x62021),x62022))+P22(f312(f312(f228(a1),x62021),f312(f312(f89(a1),x62022),f87(a1))))
% 173.52/173.41 [6203]~P22(f312(f312(f228(a1),x62031),x62032))+P22(f312(f312(f227(a1),x62031),f312(f312(f21(a1),x62032),f87(a1))))
% 173.52/173.41 [6206]~P22(f312(f312(f228(a852),x62061),x62062))+P22(f312(f312(f228(a1),f312(f114(a1),x62061)),f312(f114(a1),x62062)))
% 173.52/173.41 [6207]~P22(f312(f312(f228(a1),x62071),x62072))+P22(f312(f312(f228(a1),f312(f117(a1),x62071)),f312(f117(a1),x62072)))
% 173.52/173.41 [6208]~P22(f312(f312(f227(a1),x62081),x62082))+P22(f312(f312(f227(a852),f312(f117(a852),x62081)),f312(f117(a852),x62082)))
% 173.52/173.41 [6210]~P22(f312(f312(f227(a852),x62101),x62102))+P22(f312(f312(f227(a1),f312(f114(a1),x62101)),f312(f114(a1),x62102)))
% 173.52/173.41 [6211]~P22(f312(f312(f227(a1),x62111),x62112))+P22(f312(f312(f227(a1),f312(f117(a1),x62111)),f312(f117(a1),x62112)))
% 173.52/173.41 [6226]~P22(f312(f312(f227(a852),x62261),x62262))+~P22(f312(f312(f227(a852),f312(a126,x62262)),x62261))
% 173.52/173.41 [6271]~P22(f312(f312(f228(a852),f312(a126,x62711)),f312(a126,x62712)))+P22(f312(f312(f228(a852),x62711),x62712))
% 173.52/173.41 [6272]~P22(f312(f312(f228(a113),f312(a3,x62721)),f312(a3,x62722)))+P22(f312(f312(f228(a852),x62721),x62722))
% 173.52/173.41 [6273]~P22(f312(f312(f228(a852),f312(a118,x62731)),f312(a118,x62732)))+P22(f312(f312(f228(a1),x62731),x62732))
% 173.52/173.41 [6274]~P22(f312(f312(f228(a852),f312(a19,x62741)),f312(a19,x62742)))+P22(f312(f312(f228(a113),x62741),x62742))
% 173.52/173.41 [6275]~P22(f312(f312(f227(a852),f312(a126,x62751)),f312(a126,x62752)))+P22(f312(f312(f227(a852),x62751),x62752))
% 173.52/173.41 [6276]~P22(f312(f312(f227(a113),f312(a3,x62761)),f312(a3,x62762)))+P22(f312(f312(f227(a852),x62761),x62762))
% 173.52/173.41 [6277]~P22(f312(f312(f227(a852),f312(a19,x62771)),f312(a19,x62772)))+P22(f312(f312(f227(a113),x62771),x62772))
% 173.52/173.41 [6315]~P22(f312(f312(f228(a852),f312(a118,x63152)),f312(a118,x63151)))+P22(f312(f312(f228(a1),f2(a1)),x63151))
% 173.52/173.41 [6347]P22(f312(f312(f227(a1),f2(a1)),f54(a1,x63471,x63472)))+~P22(f312(f312(f228(a1),f2(a1)),x63472))
% 173.52/173.41 [6500]P41(x65001,x65002)+~E(f312(f312(f267(x65001,x65001,x65001),x65002),x65002),f189(f860(f859(x65001,x65001),a845)))
% 173.52/173.41 [6512]~P41(x65121,x65122)+P41(x65121,f312(f312(f267(x65121,x65121,x65121),x65122),x65122))
% 173.52/173.41 [6524]P22(f312(f312(f228(a1),x65241),x65242))+~P22(f312(f312(f227(a1),x65241),f312(f312(f21(a1),x65242),f87(a1))))
% 173.52/173.41 [6525]P22(f312(f312(f227(a1),x65251),x65252))+~P22(f312(f312(f228(a1),x65251),f312(f312(f89(a1),x65252),f87(a1))))
% 173.52/173.41 [6528]P22(f312(f312(f228(a852),x65281),x65282))+~P22(f312(f312(f228(a1),f312(f114(a1),x65281)),f312(f114(a1),x65282)))
% 173.52/173.41 [6529]P22(f312(f312(f228(a1),x65291),x65292))+~P22(f312(f312(f228(a852),f312(f117(a852),x65291)),f312(f117(a852),x65292)))
% 173.52/173.41 [6530]P22(f312(f312(f228(a1),x65301),x65302))+~P22(f312(f312(f228(a1),f312(f117(a1),x65301)),f312(f117(a1),x65302)))
% 173.52/173.41 [6532]P22(f312(f312(f227(a852),x65321),x65322))+~P22(f312(f312(f227(a1),f312(f114(a1),x65321)),f312(f114(a1),x65322)))
% 173.52/173.41 [6533]P22(f312(f312(f227(a1),x65331),x65332))+~P22(f312(f312(f227(a1),f312(f117(a1),x65331)),f312(f117(a1),x65332)))
% 173.52/173.41 [6628]~E(f657(x66282,x66281),f127(x66281))+E(f312(f138(f853(x66281),f853(x66281),f129(x66281),f127(x66281)),x66282),f127(x66281))
% 173.52/173.41 [6629]~E(f658(x66292,x66291),f127(x66291))+E(f312(f138(f853(x66291),f853(x66291),f129(x66291),f127(x66291)),x66292),f127(x66291))
% 173.52/173.41 [6636]~P31(x66361)+E(f312(f138(x66361,x66361,f124(x66361),f189(x66361)),x66362),f48(x66361,f312(f168(x66361),x66362)))
% 173.52/173.41 [6637]~P31(x66371)+E(f312(f138(x66371,x66371,f115(x66371),f235(x66371)),x66372),f49(x66371,f312(f168(x66371),x66372)))
% 173.52/173.41 [6650]E(x66501,f2(a113))+E(f312(f312(f89(a852),f312(a19,f312(f312(f21(a113),x66501),f87(a113)))),f312(a126,x66502)),f312(f312(f89(a852),f312(a19,x66501)),x66502))
% 173.52/173.41 [6696]P22(f312(f312(f228(a1),f312(f312(f21(a1),x66961),x66962)),f2(a1)))+~P22(f312(f312(f228(a1),x66961),x66962))
% 173.52/173.41 [6722]~P103(x67221)+E(f312(f312(f124(f860(x67221,a845)),f312(f312(f289(x67221),x67222),f189(f860(x67221,a845)))),f312(f280(x67221),x67222)),f312(f234(x67221),x67222))
% 173.52/173.41 [6790]~P59(x67901,x67902)+P41(x67901,f312(f233(f859(x67901,x67901)),f312(f249(x67901,x67901,a845),x67902)))
% 173.52/173.41 [6791]~P59(x67911,x67912)+P57(x67911,f312(f233(f859(x67911,x67911)),f312(f249(x67911,x67911,a845),x67912)))
% 173.52/173.41 [6792]E(x67921,f189(f860(x67922,a845)))+~P22(f312(f312(f227(f860(x67922,a845)),x67921),f189(f860(x67922,a845))))
% 173.52/173.41 [6879]~P22(f312(f312(f228(a852),f2(a852)),x68792))+P22(f312(f312(f228(a852),f54(a852,x68791,x68792)),x68792))
% 173.52/173.41 [6881]~P22(f312(f312(f228(a1),f2(a1)),x68812))+P22(f312(f312(f228(a1),f54(a1,x68811,x68812)),x68812))
% 173.52/173.41 [6882]~P22(f312(f312(f228(a852),f2(a852)),x68822))+P22(f312(f312(f227(a852),f54(a852,x68821,x68822)),x68822))
% 173.52/173.41 [6883]~P22(f312(f312(f227(a1),f2(a1)),x68831))+P22(f312(f312(f227(a1),f54(a1,x68831,x68832)),x68831))
% 173.52/173.41 [6962]~P105(x69621)+E(f312(f312(f21(f860(x69621,a845)),f312(f312(f289(x69621),x69622),f189(f860(x69621,a845)))),f312(f279(x69621),x69622)),f312(f312(f289(x69621),x69622),f189(f860(x69621,a845))))
% 173.52/173.41 [7035]~P52(x70351,x70352)+P50(x70351,f235(f860(x70351,a845)),f312(f233(f859(x70351,x70351)),f312(f249(x70351,x70351,a845),x70352)))
% 173.52/173.41 [7036]P22(f312(x70361,x70362))+P22(f312(f312(f314(f860(f859(a852,a852),a845)),f582(x70362,x70361)),a112))
% 173.52/173.41 [7085]E(f312(f312(f129(a852),f135(a852,f312(f282(a852,x70851),x70852))),f312(f312(f147(a852),x70852),f127(a852))),f135(a852,f312(f282(a852,x70851),f312(a126,x70852))))+~P22(f312(f312(f227(a852),x70851),x70852))
% 173.52/173.41 [7215]E(x72151,f2(a852))+~E(f312(f138(a852,a852,f89(a852),x72151),x72152),f2(a852))
% 173.52/173.41 [7245]~P22(f312(f312(f228(a1),f312(f312(f21(a1),x72451),x72452)),f2(a1)))+P22(f312(f312(f228(a1),x72451),x72452))
% 173.52/173.41 [7272]P41(x72721,x72722)+~P41(x72721,f312(f312(f267(x72721,x72721,x72721),x72722),x72722))
% 173.52/173.41 [7302]~P22(f312(f312(f227(a852),f312(a126,x73021)),x73022))+P22(f186(a845,a224,f312(f227(a852),x73021),x73022))
% 173.52/173.41 [7456]P19(a852,a852,f312(f312(f7(a852,a852,a852),f21(a852)),x74561),x74562)+P22(f312(f312(f314(a852),f840(x74561,x74562)),x74562))
% 173.52/173.41 [7512]E(f312(f312(f312(f74(a852,x75121,f89(a852)),f312(f16(a852,x75121),f87(a852))),f2(a852)),x75122),f312(f53(x75121),x75122))+~P22(f312(f70(x75121),x75122))
% 173.52/173.41 [7553]P19(a852,a852,f312(f312(f7(a852,a852,a852),f21(a852)),x75531),x75532)+~P22(f312(f312(f227(a852),x75531),f840(x75531,x75532)))
% 173.52/173.41 [7610]P41(x76101,x76102)+P22(f312(f312(f227(f860(x76101,a845)),f686(x76102,x76101)),f312(f264(x76101,x76101,x76102),f686(x76102,x76101))))
% 173.52/173.41 [7615]P59(x76151,x76152)+~P41(x76151,f312(f233(f859(x76151,x76151)),f312(f249(x76151,x76151,a845),x76152)))
% 173.52/173.41 [7687]P22(f312(f312(f227(a852),f312(a126,x76871)),x76872))+~P22(f186(a845,a224,f312(f227(a852),x76871),x76872))
% 173.52/173.41 [7744]P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x77441),x77442)),f287(a852,a302)))+~P22(f312(f312(f227(a852),x77441),x77442))
% 173.52/173.41 [7832]P52(x78321,x78322)+~P50(x78321,f235(f860(x78321,a845)),f312(f233(f859(x78321,x78321)),f312(f249(x78321,x78321,a845),x78322)))
% 173.52/173.41 [7891]~P22(f312(f133(x78911),x78912))+P22(f312(f133(f860(x78911,a845)),f312(f312(f150(f853(x78911),f860(x78911,a845)),f168(x78911)),f62(x78911,x78912))))
% 173.52/173.41 [8097]~P41(x80971,f312(f265(x80971,x80971),x80972))+P41(x80971,f312(f265(x80971,x80971),f312(f312(f267(x80971,x80971,x80971),x80972),f287(x80971,x80972))))
% 173.52/173.41 [8134]E(x81341,f2(a1))+P22(f312(f57(x81342,x81341),f312(f312(f239(a1,a1),f312(f47(a1,x81342),x81341)),f54(a1,x81342,x81341))))
% 173.52/173.41 [8219]P22(f312(f70(f859(x82191,x82191)),f312(f312(f267(x82191,x82191,x82191),x82192),f287(x82191,x82192))))+~P22(f312(f70(f859(x82191,x82191)),x82192))
% 173.52/173.41 [8264]~P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x82641),x82642)),f287(a852,a302)))+P22(f312(f312(f227(a852),x82641),x82642))
% 173.52/173.41 [8281]~P25(x82811)+E(f312(f138(x82811,x82811,f312(f7(x82811,x82811,x82811),f89(x82811)),f2(x82811)),f312(f165(x82811),x82812)),f312(f138(x82811,x82811,f89(x82811),f2(x82811)),x82812))
% 173.52/173.41 [8467]~P103(x84671)+E(f312(f138(f853(x84671),x84671,f312(f7(x84671,f853(x84671),f853(x84671)),f145(x84671,x84671,f5(x84671))),f127(x84671)),x84672),f144(x84671,x84671,f5(x84671),x84672))
% 173.52/173.41 [8577]P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x85771),x85772)),f312(f312(f267(a852,a852,a852),a302),f287(a852,a302))))+~P22(f312(f312(f228(a852),x85771),x85772))
% 173.52/173.41 [8620]~P22(f312(f70(f859(x86201,x86201)),f312(f312(f267(x86201,x86201,x86201),x86202),f287(x86201,x86202))))+P22(f312(f70(f859(x86201,x86201)),x86202))
% 173.52/173.41 [8872]P57(x88721,x88722)+P22(f312(f312(f314(f859(x88721,x88721)),f312(f312(f239(x88721,x88721),f749(x88722,x88721)),f749(x88722,x88721))),f312(f312(f267(x88721,x88721,x88721),x88722),f287(x88721,x88722))))
% 173.52/173.41 [8873]P57(x88731,x88732)+P22(f312(f312(f314(f859(x88731,x88731)),f312(f312(f239(x88731,x88731),f758(x88732,x88731)),f758(x88732,x88731))),f312(f312(f267(x88731,x88731,x88731),x88732),f287(x88731,x88732))))
% 173.52/173.41 [8988]~P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x89881),x89882)),f312(f312(f267(a852,a852,a852),a302),f287(a852,a302))))+P22(f312(f312(f228(a852),x89881),x89882))
% 173.52/173.41 [5000]~P90(x50001)+E(f312(f312(f89(x50001),f312(f117(x50001),a92)),x50002),x50002)
% 173.52/173.41 [5031]~P30(x50311)+E(f312(f312(f89(x50311),f312(f88(x50311),x50312)),x50312),f2(x50311))
% 173.52/173.41 [5032]~P71(x50321)+E(f312(f312(f89(x50321),f312(f88(x50321),x50322)),x50322),f2(x50321))
% 173.52/173.41 [5033]~P88(x50331)+E(f312(f312(f124(x50331),f312(f88(x50331),x50332)),x50332),f235(x50331))
% 173.52/173.41 [5034]~P88(x50341)+E(f312(f312(f115(x50341),f312(f88(x50341),x50342)),x50342),f189(x50341))
% 173.52/173.41 [5068]~P90(x50681)+E(f312(f312(f90(x50681),f312(f117(x50681),a111)),x50682),f312(f88(x50681),x50682))
% 173.52/173.41 [5234]~P108(x52341)+E(f312(f312(f90(x52341),f312(f88(x52341),f87(x52341))),x52342),f312(f88(x52341),x52342))
% 173.52/173.41 [5275]E(f312(f84(a1),x52751),f87(a1))+~E(f312(f84(a1),f312(f312(f90(a1),x52751),x52752)),f87(a1))
% 173.52/173.41 [5363]~P90(x53631)+E(f312(f312(f89(x53631),f87(x53631)),f312(f117(x53631),x53632)),f312(f117(x53631),f312(f312(f21(a1),x53632),a111)))
% 173.52/173.41 [5416]~P87(x54161)+E(f11(x54161,f312(f312(f289(x54161),x54162),f189(f860(x54161,a845)))),x54162)
% 173.52/173.41 [5417]~P87(x54171)+E(f10(x54171,f312(f312(f289(x54171),x54172),f189(f860(x54171,a845)))),x54172)
% 173.52/173.41 [5418]~P103(x54181)+E(f14(x54181,f312(f312(f289(x54181),x54182),f189(f860(x54181,a845)))),x54182)
% 173.52/173.41 [5419]~P103(x54191)+E(f15(x54191,f312(f312(f289(x54191),x54192),f189(f860(x54191,a845)))),x54192)
% 173.52/173.41 [5420]~P31(x54201)+E(f48(x54201,f312(f312(f289(x54201),x54202),f189(f860(x54201,a845)))),x54202)
% 173.52/173.41 [5421]~P31(x54211)+E(f49(x54211,f312(f312(f289(x54211),x54212),f189(f860(x54211,a845)))),x54212)
% 173.52/173.41 [5443]E(f312(f312(f89(a852),x54431),f312(f312(f21(a852),x54432),x54431)),x54432)+P22(f312(f312(f228(a852),x54432),x54431))
% 173.52/173.41 [5473]E(x54731,f127(x54732))+P22(f312(f312(f228(a852),f2(a852)),f312(f190(f853(x54732)),x54731)))
% 173.52/173.41 [5596]E(f312(f88(a1),f312(f47(a1,x55961),f312(f88(a1),x55962))),f270(x55961,x55962))+P22(f312(f312(f227(a1),f2(a1)),x55962))
% 173.52/173.41 [5604]~P103(x56041)+E(f12(x56041,f226(x56041),f312(f312(f289(x56041),x56042),f189(f860(x56041,a845)))),x56042)
% 173.52/173.41 [5605]~P103(x56051)+E(f13(x56051,f225(x56051),f312(f312(f289(x56051),x56052),f189(f860(x56051,a845)))),x56052)
% 173.52/173.41 [5664]E(f312(f312(f89(a852),x56641),f312(f312(f21(a852),x56642),x56641)),x56642)+~P22(f312(f312(f227(a852),x56641),x56642))
% 173.52/173.41 [5665]E(f312(f312(f21(a852),x56651),f312(f312(f21(a852),x56651),x56652)),x56652)+~P22(f312(f312(f227(a852),x56652),x56651))
% 173.52/173.41 [5683]E(f54(a852,f312(f312(f21(a852),x56831),x56832),x56832),f54(a852,x56831,x56832))+P22(f312(f312(f228(a852),x56831),x56832))
% 173.52/173.41 [5694]~E(x56942,f2(a852))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f240(a852),x56941),x56942)))
% 173.52/173.41 [5741]~P90(x57411)+E(f312(f312(f89(x57411),f312(f88(x57411),f87(x57411))),f312(f117(x57411),x57412)),f312(f117(x57411),f312(f312(f89(a1),x57412),a111)))
% 173.52/173.41 [5742]E(f312(f312(f240(a852),f312(f117(a852),x57421)),x57422),f312(f312(f240(a852),f2(a852)),x57422))+~P22(f312(a194,f312(f117(a1),x57421)))
% 173.52/173.41 [5836]E(f312(f137(a852),f135(a852,f312(f282(a852,x58361),x58362))),x58361)+~P22(f312(f312(f228(a852),x58361),x58362))
% 173.52/173.41 [5856]E(f312(f312(f90(a852),f312(f117(a852),x58561)),f312(f117(a852),x58562)),f312(f117(a852),f312(f312(f90(a1),x58561),x58562)))+P22(f312(f312(f228(a1),x58561),a92))
% 173.52/173.41 [5862]~P119(x58621)+P22(f312(f312(f227(x58621),f2(x58621)),f312(f312(f90(x58621),x58622),x58622)))
% 173.52/173.41 [5874]E(f312(f312(f21(a852),f312(a126,x58741)),x58742),f312(a126,f312(f312(f21(a852),x58741),x58742)))+~P22(f312(f312(f227(a852),x58742),x58741))
% 173.52/173.41 [5877]E(f54(a852,f312(f312(f21(a852),x58771),x58772),x58772),f54(a852,x58771,x58772))+~P22(f312(f312(f227(a852),x58772),x58771))
% 173.52/173.41 [5937]E(f312(f312(f240(a852),f312(a118,x59371)),x59372),f312(a118,f312(f312(f240(a1),x59371),x59372)))+~P22(f312(f312(f227(a1),f2(a1)),x59371))
% 173.52/173.41 [5949]P22(f312(f133(x59491),x59492))+P22(f312(f312(f228(a852),f581(x59492,x59491)),f312(f190(f853(x59491)),x59492)))
% 173.52/173.41 [5950]P22(f312(f133(x59501),x59502))+P22(f312(f312(f228(a852),f598(x59502,x59501)),f312(f190(f853(x59501)),x59502)))
% 173.52/173.41 [5965]~E(x59651,f127(x59652))+~P22(f312(f312(f228(a852),f2(a852)),f312(f190(f853(x59652)),x59651)))
% 173.52/173.41 [5978]E(f140(a852,f135(a852,f312(f282(a852,x59781),x59782))),f312(f312(f21(a852),x59782),f87(a852)))+~P22(f312(f312(f228(a852),x59781),x59782))
% 173.52/173.41 [5981]E(f312(f312(f89(a1),x59811),f312(f114(a1),f312(a126,f812(x59812,x59811)))),x59812)+~P22(f312(f312(f228(a1),x59811),x59812))
% 173.52/173.41 [5988]E(x59881,f2(a852))+E(f312(f312(f90(a852),x59882),f312(f312(f240(a852),x59882),f312(f312(f21(a852),x59881),f87(a852)))),f312(f312(f240(a852),x59882),x59881))
% 173.52/173.41 [6011]E(f312(f312(f90(a852),f312(a118,x60111)),f312(a118,x60112)),f312(a118,f312(f312(f90(a1),x60111),x60112)))+~P22(f312(f312(f227(a1),f2(a1)),x60111))
% 173.52/173.41 [6025]~P107(x60251)+E(f312(f312(f89(x60251),x60252),x60252),f312(f312(f90(x60251),f312(f312(f89(x60251),f87(x60251)),f87(x60251))),x60252))
% 173.52/173.41 [6039]E(f312(f312(f21(a1),f312(f114(a1),x60391)),f312(f114(a1),x60392)),f312(f114(a1),f312(f312(f21(a852),x60391),x60392)))+~P22(f312(f312(f227(a852),x60392),x60391))
% 173.52/173.41 [6044]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f89(a1),x60441),x60442)),f58(x60441,x60442))+~P22(f312(f312(f227(a1),x60442),f2(a1)))
% 173.52/173.41 [6080]E(f175(x60801,x60802),f127(f853(x60801)))+P22(f312(f312(f314(f853(x60801)),f610(x60802,x60801)),f312(f168(f853(x60801)),x60802)))
% 173.52/173.41 [6166]E(f312(f312(f147(a1),x61661),f174(f312(f312(f89(a1),x61661),f87(a1)),x61662)),f174(x61661,x61662))+~P22(f312(f312(f227(a1),x61661),x61662))
% 173.52/173.41 [6204]~P22(f312(f312(f228(a852),x62042),x62041))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f21(a852),x62041),x62042)))
% 173.52/173.41 [6230]~P22(f312(f312(f228(a852),x62301),f312(a118,x62302)))+P22(f312(f312(f228(a1),f312(f114(a1),x62301)),x62302))
% 173.52/173.41 [6262]~P103(x62621)+E(f312(f312(f124(f860(x62621,a845)),f312(f279(x62621),x62622)),f312(f312(f289(x62621),x62622),f189(f860(x62621,a845)))),f312(f281(x62621),x62622))
% 173.52/173.41 [6265]~P22(f312(f312(f228(a852),f2(a852)),x62651))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f240(a852),x62651),x62652)))
% 173.52/173.41 [6266]~P22(f312(f312(f227(a1),f2(a1)),x62661))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),x62661),x62662)))
% 173.52/173.41 [6294]~E(f312(x62941,f2(a852)),f2(a852))+E(f312(f312(f6(a852,a852),x62941),f283(a852,f312(a126,f2(a852)),x62942)),f312(f312(f6(a852,a852),x62941),f283(a852,f2(a852),x62942)))
% 173.52/173.41 [6354]~P90(x63541)+E(f312(f312(f90(x63541),f312(f312(f89(x63541),f87(x63541)),f87(x63541))),f312(f117(x63541),x63542)),f312(f117(x63541),f312(f312(f89(a1),x63542),x63542)))
% 173.52/173.41 [6370]E(f312(f312(f289(a1),x63701),f283(a1,f312(f312(f89(a1),x63701),f87(a1)),x63702)),f283(a1,x63701,x63702))+P22(f312(f312(f228(a1),x63702),x63701))
% 173.52/173.41 [6371]P22(f312(f312(f228(a852),x63711),f312(a118,x63712)))+~P22(f312(f312(f228(a1),f312(f114(a1),x63711)),x63712))
% 173.52/173.41 [6401]E(f312(a118,f312(f47(a1,f312(f117(a1),x64011)),f312(f117(a1),x64012))),f312(f47(a852,f312(f117(a852),x64011)),f312(f117(a852),x64012)))+P22(f312(a194,f312(f117(a1),x64011)))
% 173.52/173.41 [6526]P22(f312(f312(f228(a852),x65261),x65262))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f21(a852),x65262),x65261)))
% 173.52/173.41 [6569]P22(f312(f312(f228(a852),f2(a852)),x65691))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f90(a852),x65692),x65691)))
% 173.52/173.41 [6570]P22(f312(f312(f228(a852),f2(a852)),x65701))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f90(a852),x65701),x65702)))
% 173.52/173.41 [6592]~P22(f312(f312(f227(a1),x65921),f2(a1)))+E(f312(f312(f90(a852),f312(a118,f312(f88(a1),x65921))),f312(a118,f312(f88(a1),x65922))),f312(a118,f312(f312(f90(a1),x65921),x65922)))
% 173.52/173.41 [6647]~E(x66472,f189(f860(x66471,a845)))+P22(f312(f312(f227(f860(x66471,a845)),x66472),f312(f88(f860(x66471,a845)),x66472)))
% 173.52/173.41 [6705]~P90(x67051)+E(f312(f312(f89(x67051),f312(f312(f89(x67051),f2(x67051)),f312(f117(x67051),x67052))),f312(f117(x67051),x67052)),f312(f117(x67051),f312(f312(f89(a1),x67052),x67052)))
% 173.52/173.41 [6759]~P22(f312(f312(f228(a1),x67591),x67592))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x67591),f87(a1))),x67592))
% 173.52/173.41 [6824]E(x68241,f2(a852))+~P22(f312(f312(f227(a1),f312(f114(a1),x68242)),f312(f88(a1),f312(f114(a1),x68241))))
% 173.52/173.41 [6825]E(x68251,f2(a852))+~P22(f312(f312(f227(a1),f312(f114(a1),x68251)),f312(f88(a1),f312(f114(a1),x68252))))
% 173.52/173.41 [6935]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f89(a1),x69351),x69352)),f58(x69351,x69352))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x69351),x69352)))
% 173.52/173.41 [6975]~P20(x69751,x69752)+P41(x69751,f312(f246(f860(f859(x69751,x69751),a845),f860(f859(x69751,x69751),a845)),x69752))
% 173.52/173.41 [6997]~P22(f312(f312(f227(a852),f312(a126,f2(a852))),x69971))+P22(f312(f312(f227(a852),f312(a126,f2(a852))),f312(f312(f240(a852),x69971),x69972)))
% 173.52/173.41 [7158]~P22(f312(f312(f228(a1),x71581),x71582))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x71581),x71581)),f312(f312(f89(a1),x71582),x71582)))
% 173.52/173.41 [7169]~P22(f312(f312(f227(a1),x71691),x71692))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x71691),x71691)),f312(f312(f89(a1),x71692),x71692)))
% 173.52/173.41 [7217]~P22(f312(f312(f228(a852),f2(a852)),x72171))+P22(f312(f312(f228(a852),f312(f312(f21(a852),x72171),f312(a126,x72172))),x72171))
% 173.52/173.41 [7255]P22(f312(f312(f227(a852),f312(a126,f2(a852))),x72551))+~P22(f312(f312(f227(a852),f312(a126,f2(a852))),f312(f312(f90(a852),x72552),x72551)))
% 173.52/173.41 [7256]P22(f312(f312(f227(a852),f312(a126,f2(a852))),x72561))+~P22(f312(f312(f227(a852),f312(a126,f2(a852))),f312(f312(f90(a852),x72561),x72562)))
% 173.52/173.41 [7259]P22(f312(f312(f227(a852),f312(f312(f161(a852),x72591),x72592)),f312(f162(a852),x72591)))+~P22(f312(f312(f228(a852),x72592),f312(f190(f853(a852)),x72591)))
% 173.52/173.41 [7301]P22(f312(f312(f228(a1),x73011),x73012))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x73011),f87(a1))),x73012))
% 173.52/173.41 [7343]P22(f312(f70(x73431),f235(f860(x73431,a845))))+~P22(f312(f70(f860(x73432,x73431)),f235(f860(f860(x73432,x73431),a845))))
% 173.52/173.41 [7344]P22(f312(f70(x73441),f235(f860(x73441,a845))))+~P22(f312(f70(f858(x73442,x73441)),f235(f860(f858(x73442,x73441),a845))))
% 173.52/173.41 [7345]P22(f312(f70(x73451),f235(f860(x73451,a845))))+~P22(f312(f70(f858(x73451,x73452)),f235(f860(f858(x73451,x73452),a845))))
% 173.52/173.41 [7386]E(x73861,f189(f860(x73862,a845)))+~P22(f312(f312(f227(f860(x73862,a845)),x73861),f312(f88(f860(x73862,a845)),x73861)))
% 173.52/173.41 [7522]E(f312(f138(f853(x75221),f853(x75221),f129(x75221),f127(x75221)),x75222),f127(x75221))+P22(f312(f312(f314(f853(x75221)),f657(x75222,x75221)),f312(f168(f853(x75221)),x75222)))
% 173.52/173.41 [7523]E(f312(f138(f853(x75231),f853(x75231),f129(x75231),f127(x75231)),x75232),f127(x75231))+P22(f312(f312(f314(f853(x75231)),f658(x75232,x75231)),f312(f168(f853(x75231)),x75232)))
% 173.52/173.41 [7762]P22(f312(f312(f228(a1),x77621),x77622))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x77621),x77621)),f312(f312(f89(a1),x77622),x77622)))
% 173.52/173.41 [7765]P22(f312(f312(f227(a1),x77651),x77652))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x77651),x77651)),f312(f312(f89(a1),x77652),x77652)))
% 173.52/173.41 [7852]~P107(x78521)+E(f312(f312(f90(x78521),f312(f312(f89(x78521),f87(x78521)),f87(x78521))),f312(f312(f6(a852,x78521),f114(x78521)),f283(a852,f87(a852),x78522))),f312(f312(f90(x78521),f312(f114(x78521),x78522)),f312(f312(f89(x78521),f312(f114(x78521),x78522)),f87(x78521))))
% 173.52/173.41 [7905]P22(f312(f312(f314(a852),x79051),x79052))+~P22(f312(f312(f314(a1),f312(f114(a1),x79051)),f312(f290(a852,a1,f114(a1)),x79052)))
% 173.52/173.41 [8069]~P22(f312(f70(x80691),x80692))+E(f312(f290(a852,x80691,f556(x80692,x80691)),f312(f233(a852),f312(f312(f7(a852,a852,a845),f228(a852)),f557(x80692,x80691)))),x80692)
% 173.52/173.41 [8363]P51(x83631,x83632)+P22(f312(f312(f314(f859(x83631,x83631)),f312(f312(f239(x83631,x83631),f360(x83632,x83631)),f360(x83632,x83631))),x83632))
% 173.52/173.41 [8509]~P90(x85091)+E(f312(f312(f21(x85091),f87(x85091)),f312(f117(x85091),x85092)),f312(f117(x85091),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x85092))))
% 173.52/173.41 [8616]~P22(f312(f312(f228(f860(a852,a845)),x86161),x86162))+P22(f312(f312(f228(f860(a1,a845)),f312(f290(a852,a1,f114(a1)),x86161)),f312(f290(a852,a1,f114(a1)),x86162)))
% 173.52/173.41 [8647]~P22(f312(f312(f228(a1),x86471),x86472))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86471),x86471)),a111)),f312(f312(f89(a1),x86472),x86472)))
% 173.52/173.41 [8649]~P22(f312(f312(f228(a1),x86491),x86492))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86491),x86491)),a111)),f312(f312(f89(a1),x86492),x86492)))
% 173.52/173.41 [8717]~P22(f312(f312(f314(a852),x87171),f312(f168(a852),x87172)))+P22(f312(f312(f227(a852),x87171),f312(f138(a852,a852,f89(a852),f2(a852)),x87172)))
% 173.52/173.41 [8806]P48(x88061,x88062)+~P22(f312(f312(f314(f859(x88061,x88061)),f312(f312(f239(x88061,x88061),f342(x88062,x88061)),f342(x88062,x88061))),x88062))
% 173.52/173.41 [8956]~P22(f312(f312(f228(f860(a1,a845)),f312(f290(a852,a1,f114(a1)),x89561)),f312(f290(a852,a1,f114(a1)),x89562)))+P22(f312(f312(f228(f860(a852,a845)),x89561),x89562))
% 173.52/173.41 [8957]~P22(f312(f312(f227(f860(a1,a845)),f312(f290(a852,a1,f114(a1)),x89571)),f312(f290(a852,a1,f114(a1)),x89572)))+P22(f312(f312(f227(f860(a852,a845)),x89571),x89572))
% 173.52/173.41 [9036]P22(f312(f312(f228(a1),x90361),x90362))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x90361),x90361)),a111)),f312(f312(f89(a1),x90362),x90362)))
% 173.52/173.41 [9038]P22(f312(f312(f228(a1),x90381),x90382))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x90381),x90381)),a111)),f312(f312(f89(a1),x90382),x90382)))
% 173.52/173.41 [9940]~P22(f312(f70(x99401),x99402))+E(f312(f190(f853(x99401)),f99(f853(x99401),f312(f312(f18(f853(x99401),a845,a845),f312(f312(f8(a845,f860(a845,a845),f853(x99401)),a310),f312(f312(f7(f853(x99401),f860(x99401,a845),a845),f312(f312(f8(f860(x99401,a845),f860(f860(x99401,a845),a845),f853(x99401)),a309),f168(x99401))),x99402))),f133(x99401)))),f207(x99401,x99402))
% 173.52/173.41 [10080]~P18(a847,x100801,f312(f312(f289(f851(a847)),f312(f312(f312(f100(a847),a309),x100802),f195(x100802))),f189(f860(f851(a847),a845))))+P18(a847,x100801,f312(f312(f289(f851(a847)),f312(f312(f312(f100(a847),f312(f312(f8(f860(a847,f860(a847,a845)),f860(a847,a845),a847),f312(f8(f860(a847,a845),a845,a847),f97(a847))),f312(f312(f8(f860(a847,a845),f860(a847,f860(a847,a845)),a847),f312(f7(a847,f860(a847,a845),f860(a847,a845)),f312(f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),a847),f18(a847,a845,a845)),f312(f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),a847),f312(f8(a845,f860(a845,a845),a847),a315)),f195(x100802))))),a309))),x100802),a309)),f189(f860(f851(a847),a845))))
% 173.52/173.41 [5977]E(f312(f312(f89(a852),f312(f312(f21(a852),x59771),x59772)),x59772),x59771)+~P22(f312(f312(f227(a852),x59772),x59771))
% 173.52/173.41 [6014]E(f312(f47(a852,f312(f312(f90(a852),x60141),x60142)),x60142),x60141)+~P22(f312(f312(f228(a852),f2(a852)),x60142))
% 173.52/173.41 [6015]E(f312(f47(a852,f312(f312(f90(a852),x60151),x60152)),x60151),x60152)+~P22(f312(f312(f228(a852),f2(a852)),x60151))
% 173.52/173.41 [6040]~P26(x60401)+E(f312(f312(f6(a852,x60401),f312(f161(x60401),x60402)),f312(f282(a852,f2(a852)),f312(f190(f853(x60401)),x60402))),f312(f162(x60401),x60402))
% 173.52/173.41 [6158]E(f54(a852,f312(a126,f312(f312(f90(a852),x61581),x61582)),x61581),f87(a852))+~P22(f312(f312(f228(a852),f87(a852)),x61581))
% 173.52/173.41 [6164]E(f312(a126,f312(f312(f89(a852),f312(f117(a852),x61641)),x61642)),f312(f312(f89(a852),f87(a852)),x61642))+~P22(f312(a194,f312(f117(a1),x61641)))
% 173.52/173.41 [6192]E(f312(a118,f312(f312(f240(a1),f312(f117(a1),x61921)),x61922)),f312(f312(f240(a852),f312(f117(a852),x61921)),x61922))+P22(f312(a194,f312(f117(a1),x61921)))
% 173.52/173.41 [6424]E(f312(f312(f21(a852),x64241),f312(f117(a852),f312(f312(f89(a1),x64242),a111))),f312(f312(f21(a852),f312(a126,x64241)),f312(f117(a852),x64242)))+~P22(f312(f312(f228(a1),a92),x64242))
% 173.52/173.41 [6499]E(x64991,f2(a852))+E(f312(a126,f312(f312(f89(a852),f312(f312(f21(a852),x64991),f87(a852))),x64992)),f312(f312(f89(a852),x64991),x64992))
% 173.52/173.41 [6539]E(x65391,f2(a1))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x65391)),x65392)))
% 173.52/173.41 [6555]~E(x65552,f2(a852))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x65551)),x65552)))
% 173.52/173.41 [6596]E(x65961,f2(a852))+E(f312(f312(f89(a852),x65962),f312(f312(f90(a852),f312(f312(f21(a852),x65961),f87(a852))),x65962)),f312(f312(f90(a852),x65961),x65962))
% 173.52/173.41 [6641]~P22(f312(f312(f227(a1),x66411),x66412))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66411),a111)),x66412))
% 173.52/173.41 [6762]E(f312(f312(f147(a852),x67621),f135(a852,f312(f282(a852,f312(a126,x67621)),x67622))),f135(a852,f312(f282(a852,x67621),x67622)))+~P22(f312(f312(f228(a852),x67621),x67622))
% 173.52/173.41 [6967]E(x69671,x69672)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x69671),x69671)),a111),f312(f312(f21(a1),f312(f312(f89(a1),x69672),x69672)),a111))
% 173.52/173.41 [6970]E(x69701,f127(x69702))+E(f254(x69702,f312(f312(f150(x69702,f859(a113,x69702)),f312(f239(a113,x69702),f87(a113))),x69701)),f261(x69702,x69701))
% 173.52/173.41 [7187]P22(f312(f312(f227(a1),x71871),x71872))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x71871),a111)),x71872))
% 173.52/173.41 [7663]~P22(f312(f312(f228(a852),x76631),x76632))+P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x76631),x76632)),a232))
% 173.52/173.41 [7879]~P22(f312(f312(f228(a113),f2(a113)),x78791))+P22(f312(f312(f228(a113),f312(f246(a113,f859(a113,a113)),f312(f255(x78791),x78792))),x78791))
% 173.52/173.41 [8198]~P83(x81981)+P22(f312(f312(f227(x81981),f312(f84(x81981),f312(f162(x81981),x81982))),f312(f162(x81981),f312(f312(f150(x81981,x81981),f84(x81981)),x81982))))
% 173.52/173.41 [8221]P22(f312(f312(f228(a852),x82211),x82212))+~P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),x82211),x82212)),a232))
% 173.52/173.41 [8389]E(f312(f312(f239(x83891,x83891),f773(x83892,x83891)),f773(x83892,x83891)),x83892)+~P22(f312(f312(f314(f859(x83891,x83891)),x83892),f287(x83891,f189(f860(f859(x83891,x83891),a845)))))
% 173.52/173.41 [8429]E(f312(f282(a852,x84291),f312(f312(f89(a852),x84291),f312(f53(a852),x84292))),x84292)+~P22(f312(f312(f227(f860(a852,a845)),x84292),f312(f282(a852,x84291),f312(f312(f89(a852),x84291),f312(f53(a852),x84292)))))
% 173.52/173.41 [8747]E(f312(f47(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x87471),x87471)),a111))),f312(f117(a1),f312(f312(f89(a1),x87472),x87472))),f312(f47(a1,f312(f117(a1),x87471)),f312(f117(a1),x87472)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x87472)))
% 173.52/173.41 [8871]E(f312(f47(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x88711),x88711)),a111))),f312(f117(a1),f312(f312(f89(a1),x88712),x88712))),f312(f47(a1,f312(f312(f89(a1),f312(f117(a1),x88711)),f87(a1))),f312(f117(a1),x88712)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x88712)))
% 173.52/173.41 [8883]E(f172(f853(x88831),f312(f312(f8(a845,a845,f853(x88831)),a307),f312(f312(f7(f853(x88831),f853(x88831),a845),a309),f127(x88831))),x88832),f175(x88831,f175(x88831,x88832)))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x88831),a852),f190(f853(x88831))),x88832)))
% 173.52/173.41 [9705]P22(f312(a194,x97052))+E(f312(f312(f95(a1,a852),f312(f312(f21(a1),x97051),x97052)),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f2(a852))),a118)),f312(f312(f21(a852),f312(a118,x97051)),f312(a118,x97052)))
% 173.52/173.41 [9713]E(f312(f312(f95(a1,a852),f312(f117(a1),f312(f312(f89(a1),x97131),f312(f88(a1),x97132)))),f312(f312(f18(a1,a852,a852),f312(f312(f7(a1,a852,f860(a852,a852)),f312(f312(f8(a845,f860(a852,f860(a852,a852)),a1),f108(a852)),a194)),f2(a852))),a118)),f312(f312(f21(a852),f312(f117(a852),x97131)),f312(f117(a852),x97132)))+P22(f312(f312(f228(a1),x97132),a92))
% 173.52/173.41 [9714]~P20(x97141,x97142)+P22(f312(f312(f227(f860(f859(x97141,x97141),a845)),f312(f312(f267(x97141,x97141,x97141),f312(f246(f860(f859(x97141,x97141),a845),f860(f859(x97141,x97141),a845)),x97142)),f312(f248(f860(f859(x97141,x97141),a845),f860(f859(x97141,x97141),a845)),x97142))),f312(f246(f860(f859(x97141,x97141),a845),f860(f859(x97141,x97141),a845)),x97142)))
% 173.52/173.41 [9781]~E(f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,f860(a852,a845),a845),f314(a852)),x97811))),f312(f312(f7(a852,a852,a845),f228(a852)),f312(a126,x97812))))),f2(a852))+~P22(f312(f312(f314(a852),f2(a852)),x97811))
% 173.52/173.41 [9842]E(f54(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x98421),x98421)),a111)),f312(f117(a1),f312(f312(f89(a1),x98422),x98422))),f312(f312(f89(a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a1,f312(f117(a1),x98421),f312(f117(a1),x98422)))),f87(a1)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x98422)))
% 173.52/173.41 [9851]E(f54(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x98511),x98511)),a111)),f312(f117(a1),f312(f312(f89(a1),x98512),x98512))),f312(f312(f21(a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a1,f312(f312(f89(a1),f312(f117(a1),x98511)),f87(a1)),f312(f117(a1),x98512)))),f87(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x98512)))
% 173.52/173.41 [9907]~P31(x99071)+E(f48(x99071,f312(f233(x99071),f312(f312(f8(f860(x99071,a845),a845,x99071),f97(x99071)),f312(f312(f8(f860(x99071,a845),f860(x99071,a845),x99071),f312(f18(x99071,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99071),a315),f312(f312(f7(x99071,f860(x99071,a845),a845),f314(x99071)),x99072)))),f227(x99071))))),f49(x99071,x99072))
% 173.52/173.41 [9933]~P41(x99331,x99332)+P59(x99331,f312(f312(f7(x99331,f860(f859(x99331,x99331),a845),f860(x99331,a845)),f312(f312(f8(f860(x99331,f860(f860(f859(x99331,x99331),a845),a845)),f860(f860(f859(x99331,x99331),a845),f860(x99331,a845)),x99331),f7(x99331,f860(f859(x99331,x99331),a845),a845)),f312(f312(f8(f860(x99331,f859(x99331,x99331)),f860(x99331,f860(f860(f859(x99331,x99331),a845),a845)),x99331),f312(f8(f859(x99331,x99331),f860(f860(f859(x99331,x99331),a845),a845),x99331),f314(f859(x99331,x99331)))),f239(x99331,x99331)))),x99332))
% 173.52/173.41 [9934]~P3(x99341,f235(f860(x99341,a845)),x99342)+P2(x99341,f312(f312(f7(x99341,f860(f859(x99341,x99341),a845),f860(x99341,a845)),f312(f312(f8(f860(x99341,f860(f860(f859(x99341,x99341),a845),a845)),f860(f860(f859(x99341,x99341),a845),f860(x99341,a845)),x99341),f7(x99341,f860(f859(x99341,x99341),a845),a845)),f312(f312(f8(f860(x99341,f859(x99341,x99341)),f860(x99341,f860(f860(f859(x99341,x99341),a845),a845)),x99341),f312(f8(f859(x99341,x99341),f860(f860(f859(x99341,x99341),a845),a845),x99341),f314(f859(x99341,x99341)))),f239(x99341,x99341)))),x99342))
% 173.52/173.41 [9970]P41(x99701,x99702)+~P59(x99701,f312(f312(f7(x99701,f860(f859(x99701,x99701),a845),f860(x99701,a845)),f312(f312(f8(f860(x99701,f860(f860(f859(x99701,x99701),a845),a845)),f860(f860(f859(x99701,x99701),a845),f860(x99701,a845)),x99701),f7(x99701,f860(f859(x99701,x99701),a845),a845)),f312(f312(f8(f860(x99701,f859(x99701,x99701)),f860(x99701,f860(f860(f859(x99701,x99701),a845),a845)),x99701),f312(f8(f859(x99701,x99701),f860(f860(f859(x99701,x99701),a845),a845),x99701),f314(f859(x99701,x99701)))),f239(x99701,x99701)))),x99702))
% 173.52/173.41 [9971]P3(x99711,f235(f860(x99711,a845)),x99712)+~P2(x99711,f312(f312(f7(x99711,f860(f859(x99711,x99711),a845),f860(x99711,a845)),f312(f312(f8(f860(x99711,f860(f860(f859(x99711,x99711),a845),a845)),f860(f860(f859(x99711,x99711),a845),f860(x99711,a845)),x99711),f7(x99711,f860(f859(x99711,x99711),a845),a845)),f312(f312(f8(f860(x99711,f859(x99711,x99711)),f860(x99711,f860(f860(f859(x99711,x99711),a845),a845)),x99711),f312(f8(f859(x99711,x99711),f860(f860(f859(x99711,x99711),a845),a845),x99711),f314(f859(x99711,x99711)))),f239(x99711,x99711)))),x99712))
% 173.52/173.41 [7147]E(f312(f312(f89(a852),f312(f117(a852),f312(f312(f21(a1),x71471),a111))),x71472),f312(a126,f312(f312(f89(a852),f312(f117(a852),x71471)),x71472)))+P22(f312(a194,f312(f117(a1),x71471)))
% 173.52/173.41 [7580]~P90(x75801)+E(f312(f312(f89(x75801),f312(f312(f89(x75801),f87(x75801)),f312(f117(x75801),x75802))),f312(f117(x75801),x75802)),f312(f117(x75801),f312(f312(f21(a1),f312(f312(f89(a1),x75802),x75802)),a111)))
% 173.52/173.41 [8225]~P22(f312(f312(f227(a1),x82251),x82252))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x82251),x82251)),f312(f312(f21(a1),f312(f312(f89(a1),x82252),x82252)),a111)))
% 173.52/173.41 [8227]~P22(f312(f312(f227(a1),x82271),x82272))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x82271),x82271)),f312(f312(f21(a1),f312(f312(f89(a1),x82272),x82272)),a111)))
% 173.52/173.41 [8651]P22(f312(f312(f227(a1),x86511),x86512))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x86511),x86511)),f312(f312(f21(a1),f312(f312(f89(a1),x86512),x86512)),a111)))
% 173.52/173.41 [8653]P22(f312(f312(f227(a1),x86531),x86532))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x86531),x86531)),f312(f312(f21(a1),f312(f312(f89(a1),x86532),x86532)),a111)))
% 173.52/173.41 [8945]~P22(f312(f312(f228(a1),x89451),x89452))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89451),x89451)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x89452),x89452)),a111)))
% 173.52/173.41 [8947]~P22(f312(f312(f227(a1),x89471),x89472))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89471),x89471)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x89472),x89472)),a111)))
% 173.52/173.41 [9209]P22(f312(f312(f228(a1),x92091),x92092))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x92091),x92091)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x92092),x92092)),a111)))
% 173.52/173.41 [9211]P22(f312(f312(f227(a1),x92111),x92112))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x92111),x92111)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x92112),x92112)),a111)))
% 173.52/173.41 [9241]~P22(f312(f70(x92411),x92412))+P22(f312(f70(f860(x92411,a845)),f312(f233(f860(x92411,a845)),f312(f312(f7(f860(x92411,a845),f860(x92411,a845),a845),f227(f860(x92411,a845))),x92412))))
% 173.52/173.41 [9288]~E(f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),x92881),f189(f860(f859(a852,a852),a845)))),f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),x92882),f189(f860(f859(a852,a852),a845)))))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x92881),x92882)),a122))
% 173.52/173.41 [9371]E(f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),x93711),f189(f860(f859(a852,a852),a845)))),f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),x93712),f189(f860(f859(a852,a852),a845)))))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x93711),x93712)),a122))
% 173.52/173.41 [9918]~P31(x99181)+E(f49(x99181,f312(f233(x99181),f312(f312(f8(f860(x99181,a845),a845,x99181),f97(x99181)),f312(f312(f8(f860(x99181,a845),f860(x99181,a845),x99181),f312(f18(x99181,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99181),a315),f312(f312(f7(x99181,f860(x99181,a845),a845),f314(x99181)),x99182)))),f312(f7(x99181,x99181,a845),f227(x99181)))))),f48(x99181,x99182))
% 173.52/173.41 [9939]P22(f312(f312(f314(a852),f2(a852)),x99391))+E(f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),a852),f314(a852)),a126)),x99391))),f312(f312(f7(a852,a852,a845),f228(a852)),x99392)))),f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,f860(a852,a845),a845),f314(a852)),x99391))),f312(f312(f7(a852,a852,a845),f228(a852)),f312(a126,x99392))))))
% 173.52/173.41 [7449]~P90(x74491)+E(f312(f312(f90(x74491),x74492),f312(f117(x74491),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x74492)
% 173.52/173.41 [7713]~P90(x77131)+E(f312(f312(f89(x77131),f312(f117(x77131),x77132)),f87(x77131)),f312(f117(x77131),f312(f312(f89(a1),x77132),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))
% 173.52/173.41 [7850]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x78502)))+E(f312(f312(f240(a1),x78501),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x78502),x78502)),a111))),f87(a1))
% 173.52/173.41 [9265]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x92652)))+E(f312(f312(f240(a1),x92651),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x92652),x92652)),a111))),f312(f312(f95(a1,a1),f312(f312(f240(a1),x92651),f312(f117(a852),x92652))),f312(f312(f18(a1,a1,a1),f312(f312(f8(a1,f860(a1,a1),a1),f90(a1)),f312(f90(a1),x92651))),f5(a1))))
% 173.52/173.41 [9771]~P22(f312(f312(f228(a852),f312(f117(a852),x97711)),f312(a126,x97712)))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x97711),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),f228(a852)),a118)),x97712))))
% 173.52/173.41 [9772]~P22(f312(f312(f227(a852),f312(f117(a852),x97721)),f312(a126,x97722)))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x97721),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),f227(a852)),a118)),x97722))))
% 173.52/173.41 [9826]P22(f312(f312(f228(a852),f312(f117(a852),x98261)),f312(a126,x98262)))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98261),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),f228(a852)),a118)),x98262))))
% 173.52/173.41 [9827]P22(f312(f312(f227(a852),f312(f117(a852),x98271)),f312(a126,x98272)))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98271),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),f227(a852)),a118)),x98272))))
% 173.53/173.41 [9857]~P22(f312(f312(f228(a852),f312(a126,x98572)),f312(f117(a852),x98571)))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98571),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f8(a852,a845,a1),f312(f228(a852),x98572)),a118)))))
% 173.53/173.41 [9858]~P22(f312(f312(f227(a852),f312(a126,x98582)),f312(f117(a852),x98581)))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98581),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f8(a852,a845,a1),f312(f227(a852),x98582)),a118)))))
% 173.53/173.41 [9905]P22(f312(f312(f228(a852),f312(a126,x99051)),f312(f117(a852),x99052)))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x99052),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f8(a852,a845,a1),f312(f228(a852),x99051)),a118)))))
% 173.53/173.41 [9906]P22(f312(f312(f227(a852),f312(a126,x99061)),f312(f117(a852),x99062)))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x99062),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f8(a852,a845,a1),f312(f227(a852),x99061)),a118)))))
% 173.53/173.41 [9978]~P22(f312(f312(f314(a852),f2(a852)),x99781))+E(f312(a126,f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,f860(a852,a845),a845),f312(f312(f8(a852,f860(f860(a852,a845),a845),a852),f314(a852)),a126)),x99781))),f312(f312(f7(a852,a852,a845),f228(a852)),x99782))))),f312(f53(a852),f312(f233(a852),f312(f312(f18(a852,a845,a845),f312(f312(f8(a845,f860(a845,a845),a852),a310),f312(f312(f7(a852,f860(a852,a845),a845),f314(a852)),x99781))),f312(f312(f7(a852,a852,a845),f228(a852)),f312(a126,x99782))))))
% 173.53/173.41 [8413]~P90(x84131)+E(f312(f312(f90(x84131),f312(f117(x84131),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x84132),x84132)
% 173.53/173.41 [8476]~P90(x84761)+E(f312(f312(f89(x84761),f87(x84761)),f312(f117(x84761),x84762)),f312(f117(x84761),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x84762)))
% 173.53/173.41 [8531]~P90(x85311)+E(f312(f312(f21(x85311),f312(f117(x85311),x85312)),f87(x85311)),f312(f117(x85311),f312(f312(f89(a1),x85312),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.41 [8669]~P22(f312(f312(f228(a852),f312(f117(a852),a92)),x86692))+E(f312(f312(f21(a852),x86691),f312(f312(f21(a852),x86692),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f21(a852),f312(a126,x86691)),x86692))
% 173.53/173.41 [9304]~P107(x93041)+E(f312(f312(f90(x93041),x93042),x93042),f312(f312(f240(x93041),x93042),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.41 [9305]~P78(x93051)+E(f312(f312(f240(x93051),x93052),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f90(x93051),x93052),x93052))
% 173.53/173.41 [9307]~P90(x93071)+E(f312(f312(f90(x93071),x93072),f312(f117(x93071),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f89(x93071),x93072),x93072))
% 173.53/173.41 [9543]~P111(x95431)+E(f312(f312(f240(x95431),f312(f88(x95431),x95432)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f240(x95431),x95432),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.41 [9544]~P112(x95441)+E(f312(f312(f240(x95441),f312(f84(x95441),x95442)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f240(x95441),x95442),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.41 [9540]~P90(x95401)+E(f312(f312(f90(x95401),f312(f117(x95401),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x95402),f312(f312(f89(x95401),x95402),x95402))
% 173.53/173.41 [9663]~P112(x96631)+E(f312(f84(x96631),f312(f312(f240(x96631),x96632),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x96631),x96632),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.41 [9723]~P112(x97231)+P22(f312(f312(f227(x97231),f2(x97231)),f312(f312(f240(x97231),x97232),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.41 [9898]~E(f312(a126,x98982),f312(f117(a852),x98981))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98981),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),a309),a118)),x98982)))))
% 173.53/173.41 [9899]~E(f312(f117(a852),x98991),f312(a126,x98992))+P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x98991),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),a309),a118)),x98992)))))
% 173.53/173.41 [9942]E(f312(a126,x99421),f312(f117(a852),x99422))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x99422),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),a309),a118)),x99421)))))
% 173.53/173.41 [9943]E(f312(f117(a852),x99431),f312(a126,x99432))+~P22(f312(f312(f95(a1,a845),f312(f117(a1),f312(f312(f89(a1),x99431),a111))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a310),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f18(a1,a845,a845),f312(f312(f8(a845,f860(a845,a845),a1),a315),f312(f312(f8(a845,a845,a1),a307),a194))),f312(f312(f7(a1,a852,a845),f312(f312(f8(a852,f860(a852,a845),a1),a309),a118)),x99432)))))
% 173.53/173.41 [9719]~P90(x97191)+E(f312(f312(f240(x97191),f312(f117(x97191),a111)),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x97192)),f87(x97191))
% 173.53/173.41 [9720]~P111(x97201)+E(f312(f312(f240(x97201),f312(f88(x97201),f87(x97201))),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x97202)),f87(x97201))
% 173.53/173.41 [9725]~P78(x97251)+E(f312(f312(f240(x97251),x97252),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),a111))),f312(f312(f90(x97251),f312(f312(f90(x97251),x97252),x97252)),x97252))
% 173.53/173.41 [9921]~P22(f312(f312(f227(a1),f2(a1)),x99212))+E(f54(a1,f312(f312(f89(a1),f87(a1)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99211)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99212)),f312(f312(f89(a1),f87(a1)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a1,x99211,x99212))))
% 173.53/173.41 [9945]~P22(f312(f312(f227(a1),f2(a1)),x99452))+E(f312(f47(a1,f312(f312(f89(a1),f87(a1)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99451))),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99452)),f312(f47(a1,x99451),x99452))
% 173.53/173.41 [9947]~P22(f312(f312(f227(a1),x99472),f2(a1)))+E(f312(f47(a1,f312(f312(f89(a1),f87(a1)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99471))),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99472)),f312(f47(a1,f312(f312(f89(a1),x99471),f87(a1))),x99472))
% 173.53/173.41 [9948]~P22(f312(f312(f227(a1),x99482),f2(a1)))+E(f54(a1,f312(f312(f89(a1),f87(a1)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99481)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99482)),f312(f312(f21(a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f54(a1,f312(f312(f89(a1),x99481),f87(a1)),x99482))),f87(a1)))
% 173.53/173.41 [9817]~P90(x98171)+E(f312(f312(f240(x98171),f312(f117(x98171),a111)),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98172))),f312(f117(x98171),a111))
% 173.53/173.41 [9819]~P111(x98191)+E(f312(f312(f240(x98191),f312(f88(x98191),f87(x98191))),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98192))),f312(f88(x98191),f87(x98191)))
% 173.53/173.41 [5039]~P18(x50391,x50392,x50393)+P21(x50391,x50392,x50393)
% 173.53/173.41 [7920]~E(x79202,x79203)+P39(x79201,x79201,a309,x79202,x79203)
% 173.53/173.41 [8491]E(x84911,x84912)+~P39(x84913,x84913,a309,x84911,x84912)
% 173.53/173.41 [5044]~P41(x50441,x50443)+P41(x50441,f306(x50441,x50442,x50443))
% 173.53/173.41 [5217]P34(x52171,x52172,x52173)+~P34(x52171,f312(a126,x52172),x52173)
% 173.53/173.41 [5297]~P3(x52971,x52972,x52973)+P3(f853(x52971),f157(x52971,x52972),f154(x52971,x52973))
% 173.53/173.41 [5298]~P50(x52981,x52982,x52983)+P50(f853(x52981),f157(x52981,x52982),f154(x52981,x52983))
% 173.53/173.41 [5409]P54(x54091,x54092,x54093)+~E(f722(x54093,x54092,x54091),f723(x54093,x54092,x54091))
% 173.53/173.41 [5410]P55(x54101,x54102,x54103)+~E(f755(x54103,x54102,x54101),f756(x54103,x54102,x54101))
% 173.53/173.41 [6331]P21(x63311,x63312,x63313)+~P34(x63311,f644(x63313,x63312,x63311),f662(x63313,x63312,x63311))
% 173.53/173.41 [4594]~E(x45941,f192(x45942))+~E(x45941,f312(f219(x45942),x45943))
% 173.53/173.41 [4647]~E(f312(f165(x46472),x46471),x46473)+E(x46471,f312(f165(x46472),x46473))
% 173.53/173.41 [4648]~E(x46482,f312(f165(x46481),x46483))+E(f312(f165(x46481),x46482),x46483)
% 173.53/173.41 [4698]E(x46981,x46982)+~E(f312(f219(x46983),x46981),f312(f219(x46983),x46982))
% 173.53/173.41 [4699]E(x46991,x46992)+~E(f312(f165(x46993),x46991),f312(f165(x46993),x46992))
% 173.53/173.41 [4902]~P2(x49023,x49021)+P22(f312(f312(x49021,x49022),x49022))
% 173.53/173.41 [4903]~P52(x49033,x49031)+P22(f312(f312(x49031,x49032),x49032))
% 173.53/173.41 [4905]~P59(x49051,x49052)+P22(f312(f300(x49051,x49052),x49053))
% 173.53/173.41 [4960]~P41(x49601,x49602)+P41(f853(x49601),f312(f139(x49601,x49602),x49603))
% 173.53/173.41 [4965]~P22(f312(x49652,x49653))+~E(f312(f233(x49651),x49652),f189(f860(x49651,a845)))
% 173.53/173.41 [4966]~P22(f312(x49662,x49663))+~E(f189(f860(x49661,a845)),f312(f233(x49661),x49662))
% 173.53/173.41 [4997]~P22(f312(x49971,x49973))+P22(f312(x49971,f99(x49972,x49971)))
% 173.53/173.41 [5127]~E(x51272,x51273)+P22(f312(f312(f314(x51271),x51272),f312(a309,x51273)))
% 173.53/173.41 [5139]P22(f312(x51391,x51392))+~P22(f312(x51391,f784(x51391,x51393)))
% 173.53/173.41 [5183]E(f312(f165(x51831),x51832),f312(f312(f147(x51831),x51833),f127(x51831)))+~E(x51832,f312(f312(f147(x51831),x51833),f127(x51831)))
% 173.53/173.41 [5184]~E(x51843,f312(f312(f147(x51841),x51842),f127(x51841)))+E(f312(f312(f147(x51841),x51842),f127(x51841)),f312(f165(x51841),x51843))
% 173.53/173.41 [5210]~E(x52103,f312(f16(f856(x52102),x52101),f192(x52102)))+E(f179(x52101,x52102,x52103),f189(f860(x52101,a845)))
% 173.53/173.41 [5230]~P38(x52301,x52302,x52303)+P38(x52301,x52302,f312(f165(x52301),x52303))
% 173.53/173.41 [5233]E(f312(f53(x52331),f365(x52332,x52333,x52331)),x52332)+~E(f312(f53(x52331),x52333),f312(a126,x52332))
% 173.53/173.41 [5239]~P41(x52391,x52393)+P22(f312(f312(f314(x52391),x52392),f301(x52391,x52393)))
% 173.53/173.41 [5242]~E(f312(f165(x52422),x52421),f312(f312(f147(x52422),x52423),f127(x52422)))+E(x52421,f312(f312(f147(x52422),x52423),f127(x52422)))
% 173.53/173.41 [5243]~E(f312(f312(f147(x52432),x52433),f127(x52432)),f312(f165(x52432),x52431))+E(x52431,f312(f312(f147(x52432),x52433),f127(x52432)))
% 173.53/173.41 [5256]E(x52561,f312(f16(f856(x52562),x52563),f192(x52562)))+~E(f179(x52563,x52562,x52561),f189(f860(x52563,a845)))
% 173.53/173.41 [5263]E(f94(f859(a852,a852),f56(x52631,x52632)),x52633)+~P22(f312(f56(x52631,x52632),x52633))
% 173.53/173.41 [5271]~E(x52713,f312(f219(x52711),x52712))+P22(f312(f312(f314(x52711),x52712),f218(x52711,x52713)))
% 173.53/173.41 [5301]P38(x53011,x53012,x53013)+~P38(x53011,x53012,f312(f165(x53011),x53013))
% 173.53/173.41 [5362]~E(x53622,f127(x53621))+P22(f312(f312(f314(f853(x53621)),x53622),f157(x53621,x53623)))
% 173.53/173.41 [5370]~P50(x53701,x53702,x53703)+P50(x53701,x53702,f312(f265(x53701,x53701),x53703))
% 173.53/173.41 [5371]~P55(x53711,x53712,x53713)+P55(x53711,x53712,f312(f265(x53711,x53711),x53713))
% 173.53/173.41 [5390]~P60(x53901)+E(f54(x53901,f54(x53901,x53902,x53903),x53903),f54(x53901,x53902,x53903))
% 173.53/173.41 [5486]E(x54861,x54862)+~P22(f312(f312(f314(x54863),x54861),f312(a309,x54862)))
% 173.53/173.41 [5535]~P23(x55351)+E(f191(x55351,x55352,f2(a852),x55353),x55353)
% 173.53/173.41 [5557]P50(x55571,x55572,x55573)+~P50(x55571,x55572,f312(f265(x55571,x55571),x55573))
% 173.53/173.41 [5558]P55(x55581,x55582,x55583)+~P55(x55581,x55582,f312(f265(x55581,x55581),x55583))
% 173.53/173.41 [5562]~P103(x55622)+E(f144(x55621,x55622,x55623,f127(x55621)),f127(x55621))
% 173.53/173.41 [5578]E(f166(x55781,x55782,f148(x55781,x55783)),f148(x55781,f166(x55781,x55782,x55783)))+~P22(f312(f133(x55781),x55783))
% 173.53/173.41 [5581]E(x55811,f312(f219(x55812),x55813))+~P22(f312(f312(f314(x55812),x55813),f218(x55812,x55811)))
% 173.53/173.41 [5662]~P22(f312(a24,x56623))+P22(f312(a24,f32(x56621,x56622,x56623)))
% 173.53/173.41 [5671]E(f312(f132(x56711,x56712),x56713),f127(x56711))+P22(f312(x56712,f613(x56713,x56712,x56711)))
% 173.53/173.41 [5807]~P22(f312(f133(x58071),x58073))+P22(f312(f133(x58071),f166(x58071,x58072,x58073)))
% 173.53/173.41 [5808]~P22(f312(f133(x58081),x58082))+P22(f312(f133(x58081),f170(x58081,x58082,x58083)))
% 173.53/173.41 [5809]~P22(f312(f133(x58091),x58093))+P22(f312(f133(x58091),f172(x58091,x58092,x58093)))
% 173.53/173.41 [5810]~P22(f312(f133(x58101),x58103))+P22(f312(f133(x58101),f136(x58101,x58102,x58103)))
% 173.53/173.41 [5811]~P139(x58111,x58113,x58112)+P22(f312(x58111,f54(a1,x58112,x58113)))
% 173.53/173.41 [5829]~P38(x58293,x58291,x58292)+P22(f312(x58291,f736(x58292,x58291,x58293)))
% 173.53/173.41 [5850]E(f312(f132(x58501,x58502),x58503),f172(x58501,x58502,x58503))+P22(f312(x58502,f670(x58503,x58502,x58501)))
% 173.53/173.41 [5897]~P22(f312(f133(x58971),x58973))+P22(f312(f133(f853(x58971)),f63(x58971,x58972,x58973)))
% 173.53/173.41 [5917]P22(f312(a24,f31(x59171,x59172,x59173)))+~P22(f312(a24,f312(a27,x59172)))
% 173.53/173.41 [5932]~P105(x59321)+E(f312(f312(f115(f860(x59321,a845)),f312(f281(x59321),x59322)),f285(x59321,x59322,x59323)),f189(f860(x59321,a845)))
% 173.53/173.41 [5933]~P105(x59331)+E(f312(f312(f115(f860(x59331,a845)),f312(f281(x59331),x59332)),f284(x59331,x59332,x59333)),f189(f860(x59331,a845)))
% 173.53/173.41 [5934]~P105(x59341)+E(f312(f312(f115(f860(x59341,a845)),f312(f279(x59341),x59342)),f283(x59341,x59342,x59343)),f189(f860(x59341,a845)))
% 173.53/173.41 [6069]P22(f312(a24,x60691))+~P22(f312(a24,f32(x60692,x60693,x60691)))
% 173.53/173.41 [6071]P22(f312(a24,x60711))+~P22(f312(a24,f33(x60712,x60713,x60711)))
% 173.53/173.41 [6073]P22(f312(a24,x60731))+~P22(f312(a24,f33(x60732,x60731,x60733)))
% 173.53/173.41 [6154]E(f312(f132(x61541,x61542),x61543),x61543)+~P22(f312(x61542,f642(x61543,x61542,x61541)))
% 173.53/173.41 [6156]E(f312(f312(f289(x61561),f387(x61562,x61563,x61561)),f365(x61562,x61563,x61561)),x61563)+~E(f312(f53(x61561),x61563),f312(a126,x61562))
% 173.53/173.41 [6172]P139(x61721,x61722,x61723)+~P22(f312(x61721,f54(a1,x61723,x61722)))
% 173.53/173.41 [6220]E(f172(x62201,x62202,x62203),x62203)+~P22(f312(x62202,f656(x62203,x62202,x62201)))
% 173.53/173.41 [6258]~P22(f312(a24,f31(x62582,x62581,x62583)))+P22(f312(a24,f312(a27,x62581)))
% 173.53/173.41 [6301]~P22(f312(x63012,f795(x63013,x63012,x63011)))+P22(f312(f243(x63011,x63012),x63013))
% 173.53/173.41 [6302]~P22(f312(x63022,f643(x63023,x63022,x63021)))+P22(f312(f156(x63021,x63022),x63023))
% 173.53/173.41 [6540]~P22(f312(f300(x65401,x65402),f339(x65403,x65402,x65401)))+P22(f312(f300(x65401,x65402),x65403))
% 173.53/173.41 [6541]~P22(f312(f300(x65411,x65412),f345(x65413,x65412,x65411)))+P22(f312(f300(x65411,x65412),x65413))
% 173.53/173.41 [6897]~P60(x68971)+E(f312(f312(f89(x68971),f312(f312(f90(x68971),x68972),f312(f47(x68971,x68973),x68972))),f54(x68971,x68973,x68972)),x68973)
% 173.53/173.41 [7603]E(f312(f312(f239(x76031,x76031),f418(x76032,x76033,x76031)),f418(x76032,x76033,x76031)),x76033)+~P22(f312(f312(f314(f859(x76031,x76031)),x76033),f237(x76031,x76032)))
% 173.53/173.41 [7616]~P60(x76161)+E(f312(f312(f89(x76161),f312(f312(f90(x76161),f312(f47(x76161,x76162),x76163)),x76163)),f54(x76161,x76162,x76163)),x76162)
% 173.53/173.41 [7721]~P22(f312(f312(f314(x77211),f346(x77213,x77212,x77211)),f301(x77211,x77213)))+P22(f312(f312(f314(x77211),x77212),f301(x77211,x77213)))
% 173.53/173.41 [7722]~P22(f312(f312(f314(x77221),f725(x77223,x77222,x77221)),f301(x77221,x77223)))+P22(f312(f312(f314(x77221),x77222),f301(x77221,x77223)))
% 173.53/173.41 [7723]~P22(f312(f312(f314(x77231),f734(x77233,x77232,x77231)),f301(x77231,x77233)))+P22(f312(f312(f314(x77231),x77232),f301(x77231,x77233)))
% 173.53/173.41 [7946]~E(f312(f53(x79461),x79462),f312(a126,x79463))+~P22(f312(f312(f314(x79461),f387(x79463,x79462,x79461)),f365(x79463,x79462,x79461)))
% 173.53/173.41 [8579]P22(f312(f312(f227(f860(f859(x85791,x85791),a845)),f287(x85791,x85792)),f287(x85791,x85793)))+~P22(f312(f312(f227(f860(f859(x85791,x85791),a845)),x85792),f287(x85791,x85793)))
% 173.53/173.41 [8850]E(x88501,f127(x88502))+~P22(f312(f312(f314(f859(f853(x88502),f853(x88502))),f312(f312(f239(f853(x88502),f853(x88502)),x88501),f127(x88502))),f154(x88502,x88503)))
% 173.53/173.41 [8877]E(x88771,f127(x88772))+~P22(f312(f312(f314(f859(f853(x88772),f853(x88772))),f312(f312(f239(f853(x88772),f853(x88772)),f127(x88772)),x88771)),f154(x88772,x88773)))
% 173.53/173.41 [8999]E(f312(f312(f147(x89991),f630(x89992,x89993,x89991)),f631(x89992,x89993,x89991)),x89993)+~P22(f312(f312(f314(f859(f853(x89991),f853(x89991))),f312(f312(f239(f853(x89991),f853(x89991)),f127(x89991)),x89993)),f143(x89991,x89992)))
% 173.53/173.41 [9234]~P119(x92341)+~P22(f312(f312(f228(x92341),f312(f312(f89(x92341),f312(f312(f90(x92341),x92342),x92342)),f312(f312(f90(x92341),x92343),x92343))),f2(x92341)))
% 173.53/173.41 [9283]P22(f312(f70(x92831),x92832))+~P22(f312(f312(f314(f859(f860(x92831,a845),f860(x92831,a845))),f312(f312(f239(f860(x92831,a845),f860(x92831,a845)),x92833),x92832)),f286(x92831)))
% 173.53/173.41 [10024]~P112(x100241)+~P22(f312(f312(f228(x100241),f312(f312(f89(x100241),f312(f312(f240(x100241),x100242),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x100241),x100243),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f2(x100241)))
% 173.53/173.41 [4680]~E(x46803,f127(x46801))+E(f312(f312(f129(x46801),x46802),x46803),x46802)
% 173.53/173.41 [4681]~E(x46812,f127(x46811))+E(f312(f312(f129(x46811),x46812),x46813),x46813)
% 173.53/173.41 [4688]~E(x46882,f2(a852))+E(f312(f312(f169(x46881),x46882),x46883),f127(x46881))
% 173.53/173.41 [4693]~E(x46933,f127(x46931))+E(f312(f312(f169(x46931),x46932),x46933),f127(x46931))
% 173.53/173.41 [4730]~E(x47301,x47303)+E(x47301,f312(f312(f129(x47302),f127(x47302)),x47303))
% 173.53/173.41 [4816]~P24(x48162)+E(f312(f189(f860(x48161,x48162)),x48163),f189(x48162))
% 173.53/173.41 [4817]~P106(x48172)+E(f312(f235(f860(x48171,x48172)),x48173),f235(x48172))
% 173.53/173.41 [4836]E(x48361,f127(x48362))+~E(f312(f312(f129(x48362),x48363),x48361),x48363)
% 173.53/173.41 [4837]E(x48371,f127(x48372))+~E(f312(f312(f129(x48372),x48371),x48373),x48373)
% 173.53/173.41 [4846]E(x48461,f127(x48462))+~E(f312(f312(f129(x48462),x48463),x48461),f127(x48462))
% 173.53/173.41 [4847]E(x48471,f127(x48472))+~E(f312(f312(f129(x48472),x48471),x48473),f127(x48472))
% 173.53/173.41 [4870]~E(x48702,f2(a852))+E(f312(f312(f90(a852),x48701),x48702),f312(f312(f90(a852),x48703),x48702))
% 173.53/173.41 [4872]~E(x48721,f2(a852))+E(f312(f312(f90(a852),x48721),x48722),f312(f312(f90(a852),x48721),x48723))
% 173.53/173.41 [4922]~P107(x49221)+E(f312(f312(f89(x49221),x49222),x49223),f312(f312(f89(x49221),x49223),x49222))
% 173.53/173.41 [4923]~P87(x49231)+E(f312(f312(f124(x49231),x49232),x49233),f312(f312(f124(x49231),x49233),x49232))
% 173.53/173.41 [4925]~P98(x49251)+E(f312(f312(f124(x49251),x49252),x49253),f312(f312(f124(x49251),x49253),x49252))
% 173.53/173.41 [4926]~P87(x49261)+E(f312(f312(f115(x49261),x49262),x49263),f312(f312(f115(x49261),x49263),x49262))
% 173.53/173.41 [4928]~P99(x49281)+E(f312(f312(f115(x49281),x49282),x49283),f312(f312(f115(x49281),x49283),x49282))
% 173.53/173.41 [4929]~P107(x49291)+E(f312(f312(f90(x49291),x49292),x49293),f312(f312(f90(x49291),x49293),x49292))
% 173.53/173.41 [4931]~P103(x49311)+E(f312(f312(f225(x49311),x49312),x49313),f312(f312(f225(x49311),x49313),x49312))
% 173.53/173.41 [4933]~P103(x49331)+E(f312(f312(f226(x49331),x49332),x49333),f312(f312(f226(x49331),x49333),x49332))
% 173.53/173.41 [4992]E(f54(a852,x49921,x49922),f2(a852))+~E(x49921,f312(f312(f90(a852),x49922),x49923))
% 173.53/173.41 [4993]E(f54(a1,x49931,x49932),f2(a1))+~E(x49931,f312(f312(f90(a1),x49932),x49933))
% 173.53/173.41 [5056]E(x50561,x50562)+~E(f312(f312(f89(a852),x50563),x50561),f312(f312(f89(a852),x50563),x50562))
% 173.53/173.41 [5057]E(x50571,x50572)+~E(f312(f312(f89(a852),x50571),x50573),f312(f312(f89(a852),x50572),x50573))
% 173.53/173.41 [5069]~P30(x50691)+E(f312(f312(f89(x50691),x50692),f312(f88(x50691),x50693)),f312(f312(f21(x50691),x50692),x50693))
% 173.53/173.41 [5070]~P71(x50701)+E(f312(f312(f89(x50701),x50702),f312(f88(x50701),x50703)),f312(f312(f21(x50701),x50702),x50703))
% 173.53/173.41 [5071]~P108(x50711)+E(f312(f312(f89(x50711),x50712),f312(f88(x50711),x50713)),f312(f312(f21(x50711),x50712),x50713))
% 173.53/173.41 [5072]~P88(x50721)+E(f312(f312(f115(x50721),x50722),f312(f88(x50721),x50723)),f312(f312(f21(x50721),x50722),x50723))
% 173.53/173.41 [5073]~P71(x50731)+E(f312(f312(f21(x50731),x50732),f312(f88(x50731),x50733)),f312(f312(f89(x50731),x50732),x50733))
% 173.53/173.41 [5120]~P22(f312(x51203,x51202))+P22(f312(f312(f314(x51201),x51202),x51203))
% 173.53/173.41 [5122]~P72(x51222)+E(f312(f312(f9(x51221,x51222),x51223),f189(f860(x51221,a845))),f87(x51222))
% 173.53/173.41 [5124]~P26(x51242)+E(f312(f312(f6(x51241,x51242),x51243),f189(f860(x51241,a845))),f2(x51242))
% 173.53/173.41 [5172]~E(x51722,f312(f312(f89(a852),x51721),x51723))+P22(f312(f312(f227(a852),x51721),x51722))
% 173.53/173.41 [5175]~E(x51752,f189(f860(x51751,a845)))+E(f312(f312(f69(x51751),x51752),x51753),f189(f860(f860(x51751,a845),a845)))
% 173.53/173.41 [5176]~E(x51762,f189(f860(x51761,a845)))+E(f189(f860(f860(x51761,a845),a845)),f312(f312(f69(x51761),x51762),x51763))
% 173.53/173.41 [5246]~E(f312(f236(x52462,x52463),x52461),f189(f860(x52463,a845)))+E(x52461,f189(f860(f859(x52462,x52463),a845)))
% 173.53/173.41 [5247]~E(f312(f238(x52472,x52473),x52471),f189(f860(x52472,a845)))+E(x52471,f189(f860(f859(x52472,x52473),a845)))
% 173.53/173.41 [5277]E(f312(f236(x52771,x52772),x52773),f189(f860(x52772,a845)))+~E(x52773,f189(f860(f859(x52771,x52772),a845)))
% 173.53/173.41 [5278]E(f312(f238(x52781,x52782),x52783),f189(f860(x52781,a845)))+~E(x52783,f189(f860(f859(x52781,x52782),a845)))
% 173.53/173.41 [5281]E(f260(x52811,x52812,x52813),f312(f312(f21(a113),x52812),x52813))+P22(f312(f312(f228(a113),x52812),x52813))
% 173.53/173.41 [5295]P22(f312(x52951,x52952))+~P22(f312(f312(f314(x52953),x52952),x52951))
% 173.53/173.41 [5332]E(x53321,x53322)+~E(f312(f88(f860(x53323,a845)),x53321),f312(f88(f860(x53323,a845)),x53322))
% 173.53/173.41 [5337]E(f293(x53371,x53372,x53373),f192(f853(a308)))+~P22(f312(f312(f228(a1),x53372),x53373))
% 173.53/173.41 [5342]~E(x53421,f189(f860(x53422,a845)))+~P22(f312(f312(f314(x53422),x53423),x53421))
% 173.53/173.41 [5372]~E(x53722,f312(f312(f89(a1),x53721),f312(f114(a1),x53723)))+P22(f312(f312(f227(a1),x53721),x53722))
% 173.53/173.41 [5388]E(f312(f312(f289(x53881),x53882),x53883),x53883)+~P22(f312(f312(f314(x53881),x53882),x53883))
% 173.53/173.41 [5399]E(x53991,f189(f860(x53992,a845)))+~E(f312(f312(f69(x53992),x53991),x53993),f189(f860(f860(x53992,a845),a845)))
% 173.53/173.41 [5400]E(x54001,f189(f860(x54002,a845)))+~E(f189(f860(f860(x54002,a845),a845)),f312(f312(f69(x54002),x54001),x54003))
% 173.53/173.41 [5406]~P120(x54061)+E(f312(f312(f90(x54061),f312(f88(x54061),x54062)),f312(f88(x54061),x54063)),f312(f312(f90(x54061),x54062),x54063))
% 173.53/173.41 [5408]~P64(x54081)+E(f312(f312(f268(x54081),f312(f88(x54081),x54082)),f312(f88(x54081),x54083)),f312(f312(f268(x54081),x54082),x54083))
% 173.53/173.41 [5439]~P22(f312(x54393,x54392))+P22(f312(f312(f314(x54391),x54392),f312(f233(x54391),x54393)))
% 173.53/173.41 [5479]E(f166(x54791,x54792,x54793),x54793)+P22(f312(f312(f314(x54791),x54792),f312(f168(x54791),x54793)))
% 173.53/173.41 [5541]~P140(x55411,x55413,x55412)+P22(f312(x55411,f312(f47(a1,x55412),x55413)))
% 173.53/173.41 [5563]~P60(x55631)+E(f312(f47(x55631,f54(x55631,x55632,x55633)),x55633),f2(x55631))
% 173.53/173.41 [5567]~P22(f312(f133(x55671),x55673))+P22(f312(f133(x55671),f312(f132(x55671,x55672),x55673)))
% 173.53/173.41 [5626]E(f170(x56261,f312(f312(f147(x56261),x56262),f127(x56261)),x56263),f127(x56261))+P22(f312(f312(f314(a852),f2(a852)),x56263))
% 173.53/173.41 [5680]E(f312(f312(f147(x56801),x56802),x56803),f136(x56801,x56802,x56803))+P22(f312(f312(f314(x56801),x56802),f312(f168(x56801),x56803)))
% 173.53/173.41 [5689]E(x56891,x56892)+~E(f312(f312(f90(a852),f312(a126,x56893)),x56891),f312(f312(f90(a852),f312(a126,x56893)),x56892))
% 173.53/173.41 [5690]~E(x56902,f312(f312(f89(a1),x56901),f312(f114(a1),f312(a126,x56903))))+P22(f312(f312(f228(a1),x56901),x56902))
% 173.53/173.41 [5790]~E(x57903,f127(x57901))+E(f312(f312(f312(f184(f853(x57901),f853(x57901)),x57902),f164(x57901)),x57903),f127(x57901))
% 173.53/173.41 [5794]P22(f312(x57941,x57942))+~P22(f312(f312(f314(x57943),x57942),f312(f233(x57943),x57941)))
% 173.53/173.41 [5818]P140(x58181,x58182,x58183)+~P22(f312(x58181,f312(f47(a1,x58183),x58182)))
% 173.53/173.41 [5825]E(x58251,x58252)+~E(f312(f312(f289(x58253),x58251),f189(f860(x58253,a845))),f312(f312(f289(x58253),x58252),f189(f860(x58253,a845))))
% 173.53/173.41 [5834]~P105(x58341)+E(f312(f312(f115(f860(x58341,a845)),f312(f279(x58341),x58342)),f312(f282(x58341,x58342),x58343)),f189(f860(x58341,a845)))
% 173.53/173.41 [5876]E(f136(x58761,x58762,x58763),x58763)+~P22(f312(f312(f314(x58761),x58762),f312(f168(x58761),x58763)))
% 173.53/173.41 [5905]~P76(x59051)+E(f312(f290(x59051,x59051,f88(x59051)),f312(f282(x59051,x59052),x59053)),f284(x59051,f312(f88(x59051),x59053),f312(f88(x59051),x59052)))
% 173.53/173.41 [5913]E(f312(f190(f853(x59131)),f166(x59131,x59132,x59133)),f312(f190(f853(x59131)),x59133))+P22(f312(f312(f314(x59131),x59132),f312(f168(x59131),x59133)))
% 173.53/173.41 [5964]~P105(x59641)+E(f312(f312(f115(f860(x59641,a845)),f312(f282(x59641,x59642),x59643)),f312(f234(x59641),x59643)),f189(f860(x59641,a845)))
% 173.53/173.41 [5986]~P76(x59861)+E(f312(f290(x59861,x59861,f88(x59861)),f285(x59861,x59862,x59863)),f285(x59861,f312(f88(x59861),x59863),f312(f88(x59861),x59862)))
% 173.53/173.41 [5987]~P76(x59871)+E(f312(f290(x59871,x59871,f88(x59871)),f283(x59871,x59872,x59873)),f283(x59871,f312(f88(x59871),x59873),f312(f88(x59871),x59872)))
% 173.53/173.41 [6037]E(f170(x60371,f312(f312(f147(x60371),x60372),f127(x60371)),x60373),f312(f312(f147(x60371),x60372),f127(x60371)))+~P22(f312(f312(f314(a852),f2(a852)),x60373))
% 173.53/173.41 [6047]~P76(x60471)+E(f312(f290(x60471,x60471,f88(x60471)),f284(x60471,x60472,x60473)),f312(f282(x60471,f312(f88(x60471),x60473)),f312(f88(x60471),x60472)))
% 173.53/173.41 [6064]~P61(x60641)+E(f54(x60641,f312(f88(x60641),f54(x60641,x60642,x60643)),x60643),f54(x60641,f312(f88(x60641),x60642),x60643))
% 173.53/173.41 [6169]~P22(f312(f70(f859(x61692,x61691)),x61693))+P22(f312(f70(x61691),f312(f236(x61692,x61691),x61693)))
% 173.53/173.41 [6170]~P22(f312(f70(f859(x61701,x61702)),x61703))+P22(f312(f70(x61701),f312(f238(x61701,x61702),x61703)))
% 173.53/173.41 [6176]~P105(x61761)+E(f312(f312(f115(f860(x61761,a845)),f285(x61761,x61762,x61763)),f312(f234(x61761),x61763)),f189(f860(x61761,a845)))
% 173.53/173.41 [6177]~P105(x61771)+E(f312(f312(f115(f860(x61771,a845)),f284(x61771,x61772,x61773)),f312(f280(x61771),x61773)),f189(f860(x61771,a845)))
% 173.53/173.41 [6178]~P105(x61781)+E(f312(f312(f115(f860(x61781,a845)),f283(x61781,x61782,x61783)),f312(f280(x61781),x61783)),f189(f860(x61781,a845)))
% 173.53/173.41 [6241]E(f312(f312(f161(x62411),x62412),f599(x62412,x62413,x62411)),x62413)+~P22(f312(f312(f314(x62411),x62413),f312(f168(x62411),x62412)))
% 173.53/173.41 [6380]E(x63801,f127(x63802))+~E(f312(f312(f312(f184(f853(x63802),f853(x63802)),x63803),f164(x63802)),x63801),f127(x63802))
% 173.53/173.41 [6478]~P22(f312(f70(f859(x64782,x64781)),x64783))+P22(f312(f70(f859(x64781,x64782)),f312(f265(x64782,x64781),x64783)))
% 173.53/173.41 [6630]P55(x66301,x66302,x66303)+P22(f312(f312(f314(x66301),f756(x66303,x66302,x66301)),x66302))
% 173.53/173.41 [6631]P55(x66311,x66312,x66313)+P22(f312(f312(f314(x66311),f755(x66313,x66312,x66311)),x66312))
% 173.53/173.41 [6643]P22(f312(f300(x66431,x66432),x66433))+P22(f312(f312(x66432,f339(x66433,x66432,x66431)),x66433))
% 173.53/173.41 [6644]P22(f312(f300(x66441,x66442),x66443))+P22(f312(f312(x66442,f345(x66443,x66442,x66441)),x66443))
% 173.53/173.41 [6674]E(f312(f190(f853(x66741)),f166(x66741,x66742,x66743)),f312(f312(f21(a852),f312(f190(f853(x66741)),x66743)),f87(a852)))+~P22(f312(f312(f314(x66741),x66742),f312(f168(x66741),x66743)))
% 173.53/173.41 [6711]P22(f312(f243(x67111,x67112),x67113))+P22(f312(f312(f314(x67111),f795(x67113,x67112,x67111)),x67113))
% 173.53/173.41 [6721]~P22(f312(f70(f859(x67212,x67211)),f312(f265(x67211,x67212),x67213)))+P22(f312(f70(f859(x67211,x67212)),x67213))
% 173.53/173.41 [6773]~P22(f312(f312(f314(x67731),x67732),f312(f168(x67731),f128(x67731,x67733))))+P22(f312(f312(f314(x67731),x67732),f312(f168(x67731),x67733)))
% 173.53/173.41 [6778]P21(x67781,x67782,x67783)+P22(f312(f312(f314(f851(x67781)),f662(x67783,x67782,x67781)),x67783))
% 173.53/173.41 [6805]E(f312(f132(x68051,x68052),x68053),x68053)+P22(f312(f312(f314(x68051),f642(x68053,x68052,x68051)),f312(f168(x68051),x68053)))
% 173.53/173.41 [6820]E(f312(f132(x68201,x68202),x68203),f127(x68201))+P22(f312(f312(f314(x68201),f613(x68203,x68202,x68201)),f312(f168(x68201),x68203)))
% 173.53/173.41 [6849]E(f172(x68491,x68492,x68493),x68493)+P22(f312(f312(f314(x68491),f656(x68493,x68492,x68491)),f312(f168(x68491),x68493)))
% 173.53/173.41 [6859]~P22(f312(f312(f227(a852),x68591),x68593))+P22(f312(f312(f227(a852),f312(f47(a852,x68591),x68592)),f312(f47(a852,x68593),x68592)))
% 173.53/173.41 [6936]P22(f312(f156(x69361,x69362),x69363))+P22(f312(f312(f314(x69361),f643(x69363,x69362,x69361)),f312(f168(x69361),x69363)))
% 173.53/173.41 [6946]~P38(x69461,x69463,x69462)+P22(f312(f312(f314(x69461),f736(x69462,x69463,x69461)),f312(f168(x69461),x69462)))
% 173.53/173.41 [6981]~P26(x69811)+E(f312(f312(f89(x69811),f312(f312(f6(a852,x69811),x69812),f312(f279(a852),x69813))),f312(x69812,x69813)),f312(f312(f6(a852,x69811),x69812),f312(f279(a852),f312(a126,x69813))))
% 173.53/173.41 [7072]~P38(x70722,x70721,x70723)+P22(f312(x70721,f312(f312(f161(x70722),x70723),f743(x70723,x70721,x70722))))
% 173.53/173.41 [7086]~P22(f312(f312(f314(x70861),x70862),f744(x70862,x70863,x70861)))+P22(f312(f312(f314(x70861),x70862),f49(f860(x70861,a845),x70863)))
% 173.53/173.41 [7115]~P26(x71151)+E(f312(f312(f89(x71151),f312(f312(f6(a852,x71151),x71152),f312(f281(a852),x71153))),f312(x71152,f312(a126,x71153))),f312(f312(f6(a852,x71151),x71152),f312(f281(a852),f312(a126,x71153))))
% 173.53/173.41 [7242]P22(f312(f312(f314(f853(x72421)),x72422),f157(x72421,x72423)))+P22(f312(f312(f314(x72421),f600(x72423,x72422,x72421)),f312(f168(x72421),x72422)))
% 173.53/173.41 [7258]~P22(f312(f312(f314(f853(x72581)),x72582),f157(x72581,f301(x72581,x72583))))+P22(f312(f312(f314(f853(x72581)),x72582),f301(f853(x72581),f153(x72581,x72583))))
% 173.53/173.41 [7281]~P22(f312(f312(f314(f853(x72811)),x72812),f301(f853(x72811),f153(x72811,x72813))))+P22(f312(f312(f314(f853(x72811)),x72812),f157(x72811,f301(x72811,x72813))))
% 173.53/173.41 [7317]E(f312(f312(f312(f184(f853(x73171),f853(x73171)),x73172),f164(x73171)),x73173),x73173)+~P22(f312(f312(f227(a852),f312(f190(f853(x73171)),x73173)),f87(a852)))
% 173.53/173.41 [7352]E(f312(f312(f129(x73521),f761(x73522,x73523,x73521)),f312(f312(f147(x73521),x73523),f779(x73522,x73523,x73521))),x73522)+~P22(f312(f312(f314(x73521),x73523),f312(f168(x73521),x73522)))
% 173.53/173.41 [7353]E(f312(f312(f129(x73531),f780(x73532,x73533,x73531)),f312(f312(f147(x73531),x73533),f781(x73532,x73533,x73531))),x73532)+~P22(f312(f312(f314(x73531),x73533),f312(f168(x73531),x73532)))
% 173.53/173.41 [7354]E(f312(f312(f129(x73541),f782(x73542,x73543,x73541)),f312(f312(f147(x73541),x73543),f783(x73542,x73543,x73541))),x73542)+~P22(f312(f312(f314(x73541),x73543),f312(f168(x73541),x73542)))
% 173.53/173.41 [7377]~P19(x73771,x73772,x73773,f235(f860(x73771,a845)))+P19(f853(x73771),f853(x73772),f312(f150(x73771,x73772),x73773),f235(f860(f853(x73771),a845)))
% 173.53/173.41 [7526]E(x75261,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x75262)),x75263)),f312(f248(a852,a852),x75262)))+~P22(f312(f56(x75261,x75263),x75262))
% 173.53/173.41 [7534]P19(x75341,x75342,x75343,f235(f860(x75341,a845)))+~P19(f853(x75341),f853(x75342),f312(f150(x75341,x75342),x75343),f235(f860(f853(x75341),a845)))
% 173.53/173.41 [7570]~P22(f312(f312(f195(x75701),x75702),x75703))+P22(f312(f312(f312(f312(a198,x75701),x75702),f329(x75703,x75702,x75701)),x75703))
% 173.53/173.41 [7571]~P22(f312(f312(f195(x75711),x75712),x75713))+P22(f312(f312(f312(f312(a198,x75711),x75712),f397(x75713,x75712,x75711)),x75713))
% 173.53/173.41 [7575]P22(f312(f312(f314(f860(x75751,a845)),f744(x75752,x75753,x75751)),x75753))+P22(f312(f312(f314(x75751),x75752),f49(f860(x75751,a845),x75753)))
% 173.53/173.41 [7668]P22(f312(f312(f314(f853(x76681)),x76682),f157(x76681,x76683)))+~P22(f312(f312(f314(x76681),f600(x76683,x76682,x76681)),x76683))
% 173.53/173.41 [7793]E(x77931,x77932)+~E(f312(f312(f7(x77933,f860(x77933,a845),a845),f314(x77933)),x77931),f312(f312(f7(x77933,f860(x77933,a845),a845),f314(x77933)),x77932))
% 173.53/173.41 [7798]~P22(f312(f312(f314(f859(x77981,x77981)),x77983),f237(x77981,x77982)))+P22(f312(f312(f314(x77981),f418(x77982,x77983,x77981)),x77982))
% 173.53/173.41 [7974]~P22(f312(f312(f314(x79741),x79742),f312(f168(x79741),f781(x79743,x79742,x79741))))+~P22(f312(f312(f314(x79741),x79742),f312(f168(x79741),x79743)))
% 173.53/173.41 [7975]~P22(f312(f312(f314(x79751),x79752),f312(f168(x79751),f782(x79753,x79752,x79751))))+~P22(f312(f312(f314(x79751),x79752),f312(f168(x79751),x79753)))
% 173.53/173.41 [8068]E(f312(f221(f856(f853(a308)),f853(a308),f293(x80681,x80682,f312(f312(f89(a1),x80683),f87(a1))),f219(f853(a308))),f312(x80681,x80683)),f293(x80681,x80682,x80683))+P22(f312(f312(f228(a1),x80682),x80683))
% 173.53/173.41 [8170]E(x81701,f127(x81702))+P22(f312(f312(f314(x81702),f312(f246(x81702,f859(a113,a113)),f312(f261(x81702,x81701),x81703))),f312(f168(x81702),x81701)))
% 173.53/173.41 [8268]~P29(x82681)+E(f312(f138(x82681,x82681,f312(f7(x82681,x82681,x82681),f89(x82681)),x82682),f312(f165(x82681),x82683)),f312(f138(x82681,x82681,f89(x82681),x82682),x82683))
% 173.53/173.41 [8761]~P103(x87611)+E(f312(f168(x87611),f146(x87611,x87611,f5(x87611),x87612,x87613)),f312(f312(f289(x87611),x87612),f312(f168(x87611),x87613)))
% 173.53/173.41 [8772]P22(f312(f312(f228(a852),f2(a852)),f764(x87721,x87722,x87723)))+~P22(f312(f312(f314(f859(x87723,x87723)),x87722),f312(f312(f267(x87723,x87723,x87723),x87721),f287(x87723,x87721))))
% 173.53/173.41 [9059]~P57(x90591,x90592)+~P22(f312(f312(f314(f859(x90591,x90591)),f312(f312(f239(x90591,x90591),x90593),x90593)),f312(f312(f267(x90591,x90591,x90591),x90592),f287(x90591,x90592))))
% 173.53/173.41 [9192]~E(f312(f312(f115(f860(f859(x91921,x91921),a845)),f312(f265(x91921,x91921),x91922)),f287(x91921,x91922)),f189(f860(f859(x91921,x91921),a845)))+~P22(f312(f312(f314(f859(x91921,x91921)),f312(f312(f239(x91921,x91921),x91923),x91923)),f312(f312(f267(x91921,x91921,x91921),x91922),f287(x91921,x91922))))
% 173.53/173.41 [9367]~P22(f312(f70(x93671),x93672))+P22(f312(f312(f227(a852),f312(f53(x93671),f312(f312(f21(f860(x93671,a845)),x93672),f312(f312(f289(x93671),x93673),f189(f860(x93671,a845)))))),f312(f53(x93671),x93672)))
% 173.53/173.41 [4981]~E(x49813,f127(x49811))+E(f140(x49811,f312(f312(f147(x49811),x49812),x49813)),x49812)
% 173.53/173.41 [4989]~E(x49893,f127(x49891))+E(f128(x49891,f312(f312(f147(x49891),x49892),x49893)),f127(x49891))
% 173.53/173.41 [5019]E(x50191,f127(x50192))+E(f140(x50192,f312(f312(f147(x50192),x50193),x50191)),f140(x50192,x50191))
% 173.53/173.41 [5021]E(x50211,f127(x50212))+E(f140(x50212,f312(f312(f129(x50212),x50213),x50211)),f140(x50212,x50211))
% 173.53/173.41 [5027]~E(x50273,f127(x50271))+E(f128(x50271,f312(f312(f129(x50271),x50272),x50273)),f128(x50271,x50272))
% 173.53/173.41 [5029]~E(x50293,f127(x50291))+E(f140(x50291,f312(f312(f129(x50291),x50292),x50293)),f140(x50291,x50292))
% 173.53/173.41 [5063]E(x50631,f127(x50632))+E(f312(f137(x50632),f312(f312(f129(x50632),x50631),x50633)),f312(f137(x50632),x50631))
% 173.53/173.41 [5094]~E(x50942,f127(x50941))+E(f312(f137(x50941),f312(f312(f129(x50941),x50942),x50943)),f312(f137(x50941),x50943))
% 173.53/173.41 [5149]~P87(x51491)+E(f312(f312(f124(x51491),x51492),f312(f312(f115(x51491),x51492),x51493)),x51492)
% 173.53/173.41 [5150]~P87(x51501)+E(f312(f312(f115(x51501),x51502),f312(f312(f124(x51501),x51502),x51503)),x51502)
% 173.53/173.41 [5151]~P103(x51511)+E(f312(f312(f225(x51511),x51512),f312(f312(f226(x51511),x51512),x51513)),x51512)
% 173.53/173.41 [5152]~P103(x51521)+E(f312(f312(f226(x51521),x51522),f312(f312(f225(x51521),x51522),x51523)),x51522)
% 173.53/173.41 [5170]~P60(x51701)+E(f54(x51701,f312(f312(f90(x51701),x51702),x51703),x51703),f2(x51701))
% 173.53/173.41 [5171]~P60(x51711)+E(f54(x51711,f312(f312(f90(x51711),x51712),x51713),x51712),f2(x51711))
% 173.53/173.41 [5241]~P30(x52411)+E(f312(f88(x52411),f312(f312(f21(x52411),x52412),x52413)),f312(f312(f21(x52411),x52413),x52412))
% 173.53/173.41 [5299]E(x52991,f127(x52992))+E(f128(x52992,f312(f312(f147(x52992),x52993),x52991)),f312(f312(f147(x52992),x52993),f128(x52992,x52991)))
% 173.53/173.41 [5300]E(x53001,f127(x53002))+E(f128(x53002,f312(f312(f129(x53002),x53003),x53001)),f312(f312(f129(x53002),x53003),f128(x53002,x53001)))
% 173.53/173.41 [5302]~P31(x53021)+E(f48(x53021,f312(f312(f289(x53021),x53022),x53023)),f312(f312(f124(x53021),x53022),f48(x53021,x53023)))
% 173.53/173.41 [5303]~P31(x53031)+E(f49(x53031,f312(f312(f289(x53031),x53032),x53033)),f312(f312(f115(x53031),x53032),f49(x53031,x53033)))
% 173.53/173.41 [5347]~P87(x53471)+E(f312(f312(f124(x53471),x53472),f312(f312(f124(x53471),x53472),x53473)),f312(f312(f124(x53471),x53472),x53473))
% 173.53/173.41 [5349]~P98(x53491)+E(f312(f312(f124(x53491),x53492),f312(f312(f124(x53491),x53492),x53493)),f312(f312(f124(x53491),x53492),x53493))
% 173.53/173.41 [5350]~P87(x53501)+E(f312(f312(f115(x53501),x53502),f312(f312(f115(x53501),x53502),x53503)),f312(f312(f115(x53501),x53502),x53503))
% 173.53/173.41 [5352]~P99(x53521)+E(f312(f312(f115(x53521),x53522),f312(f312(f115(x53521),x53522),x53523)),f312(f312(f115(x53521),x53522),x53523))
% 173.53/173.41 [5353]~P93(x53531)+E(f312(f312(f90(x53531),x53532),f312(f312(f90(x53531),x53532),x53533)),f312(f312(f90(x53531),x53532),x53533))
% 173.53/173.41 [5355]~P103(x53551)+E(f312(f312(f225(x53551),x53552),f312(f312(f225(x53551),x53552),x53553)),f312(f312(f225(x53551),x53552),x53553))
% 173.53/173.41 [5357]~P103(x53571)+E(f312(f312(f226(x53571),x53572),f312(f312(f226(x53571),x53572),x53573)),f312(f312(f226(x53571),x53572),x53573))
% 173.53/173.41 [5365]~P60(x53651)+E(f54(x53651,f312(f312(f89(x53651),x53652),x53653),x53653),f54(x53651,x53652,x53653))
% 173.53/173.41 [5366]~P60(x53661)+E(f54(x53661,f312(f312(f89(x53661),x53662),x53663),x53662),f54(x53661,x53663,x53662))
% 173.53/173.41 [5373]~P120(x53731)+E(f312(f312(f90(x53731),x53732),f312(f88(x53731),x53733)),f312(f88(x53731),f312(f312(f90(x53731),x53732),x53733)))
% 173.53/173.41 [5374]~P64(x53741)+E(f312(f312(f268(x53741),x53742),f312(f88(x53741),x53743)),f312(f88(x53741),f312(f312(f268(x53741),x53742),x53743)))
% 173.53/173.41 [5375]~P25(x53751)+E(f312(f312(f89(x53751),x53752),f312(f162(x53751),x53753)),f312(f162(x53751),f312(f312(f147(x53751),x53752),x53753)))
% 173.53/173.41 [5405]~P120(x54051)+E(f312(f312(f90(x54051),f312(f88(x54051),x54052)),x54053),f312(f312(f90(x54051),x54052),f312(f88(x54051),x54053)))
% 173.53/173.41 [5411]~P3(x54111,x54112,x54113)+E(f48(f860(x54111,a845),f312(f312(f69(x54111),x54112),x54113)),x54112)
% 173.53/173.41 [5469]~P109(x54691)+E(f312(f312(f90(x54691),x54692),f312(f312(f240(x54691),x54692),x54693)),f312(f312(f240(x54691),x54692),f312(a126,x54693)))
% 173.53/173.41 [5470]~P107(x54701)+E(f312(f312(f90(x54701),x54702),f312(f312(f240(x54701),x54702),x54703)),f312(f312(f240(x54701),x54702),f312(a126,x54703)))
% 173.53/173.41 [5482]~P71(x54821)+E(f312(f312(f89(x54821),f312(f88(x54821),x54822)),f312(f312(f89(x54821),x54822),x54823)),x54823)
% 173.53/173.41 [5505]~P23(x55051)+E(f312(f312(f240(x55051),f312(f114(x55051),x55052)),x55053),f312(f114(x55051),f312(f312(f240(a852),x55052),x55053)))
% 173.53/173.41 [5506]~P111(x55061)+E(f312(f312(f240(x55061),f312(f116(x55061),x55062)),x55063),f312(f116(x55061),f312(f312(f240(a1),x55062),x55063)))
% 173.53/173.41 [5512]~P83(x55121)+E(f312(f84(x55121),f312(f312(f21(x55121),x55122),x55123)),f312(f84(x55121),f312(f312(f21(x55121),x55123),x55122)))
% 173.53/173.41 [5514]~P112(x55141)+E(f312(f312(f90(x55141),f91(x55141,x55142)),f91(x55141,x55143)),f91(x55141,f312(f312(f90(x55141),x55142),x55143)))
% 173.53/173.41 [5519]E(x55191,f127(x55192))+E(f312(f312(f129(x55192),f312(f167(x55192),x55191)),x55193),f312(f167(x55192),f312(f312(f129(x55192),x55191),x55193)))
% 173.53/173.41 [5524]~E(x55242,f312(a126,f312(f312(f89(a852),x55241),x55243)))+P22(f312(f312(f228(a852),x55241),x55242))
% 173.53/173.41 [5525]~P120(x55251)+E(f312(f312(f90(x55251),f312(f88(x55251),x55252)),x55253),f312(f88(x55251),f312(f312(f90(x55251),x55252),x55253)))
% 173.53/173.41 [5526]~P114(x55261)+E(f312(f312(f268(x55261),f312(f88(x55261),x55262)),x55263),f312(f88(x55261),f312(f312(f268(x55261),x55262),x55263)))
% 173.53/173.41 [5527]~P112(x55271)+E(f312(f312(f240(x55271),f312(f84(x55271),x55272)),x55273),f312(f84(x55271),f312(f312(f240(x55271),x55272),x55273)))
% 173.53/173.41 [5625]E(f794(x56251,x56252,x56253),f811(x56251,x56252,x56253))+E(f312(f312(f115(f860(x56253,a845)),x56252),x56251),f189(f860(x56253,a845)))
% 173.53/173.41 [5639]~P72(x56392)+E(f312(f312(f9(x56391,x56392),f312(f16(x56392,x56391),f87(x56392))),x56393),f87(x56392))
% 173.53/173.41 [5640]~P26(x56402)+E(f312(f312(f6(x56401,x56402),f312(f16(x56402,x56401),f2(x56402))),x56403),f2(x56402))
% 173.53/173.41 [5642]~P23(x56421)+E(f312(f312(f89(x56421),f312(f114(x56421),x56422)),f312(f114(x56421),x56423)),f312(f114(x56421),f312(f312(f89(a852),x56422),x56423)))
% 173.53/173.41 [5643]~P23(x56431)+E(f312(f312(f90(x56431),f312(f114(x56431),x56432)),f312(f114(x56431),x56433)),f312(f114(x56431),f312(f312(f90(a852),x56432),x56433)))
% 173.53/173.41 [5645]~P90(x56451)+E(f312(f312(f21(x56451),f312(f117(x56451),x56452)),f312(f117(x56451),x56453)),f312(f117(x56451),f312(f312(f21(a1),x56452),x56453)))
% 173.53/173.41 [5647]~P111(x56471)+E(f312(f312(f89(x56471),f312(f116(x56471),x56472)),f312(f116(x56471),x56473)),f312(f116(x56471),f312(f312(f89(a1),x56472),x56473)))
% 173.53/173.41 [5648]~P111(x56481)+E(f312(f312(f21(x56481),f312(f116(x56481),x56482)),f312(f116(x56481),x56483)),f312(f116(x56481),f312(f312(f21(a1),x56482),x56483)))
% 173.53/173.41 [5649]~P111(x56491)+E(f312(f312(f90(x56491),f312(f116(x56491),x56492)),f312(f116(x56491),x56493)),f312(f116(x56491),f312(f312(f90(a1),x56492),x56493)))
% 173.53/173.41 [5650]~P90(x56501)+E(f312(f312(f89(x56501),f312(f117(x56501),x56502)),f312(f117(x56501),x56503)),f312(f117(x56501),f312(f312(f89(a1),x56502),x56503)))
% 173.53/173.41 [5651]~P90(x56511)+E(f312(f312(f90(x56511),f312(f117(x56511),x56512)),f312(f117(x56511),x56513)),f312(f117(x56511),f312(f312(f90(a1),x56512),x56513)))
% 173.53/173.41 [5695]~E(x56953,x56952)+P22(f312(f312(f227(f860(x56951,a845)),x56952),x56953))
% 173.53/173.41 [5701]~E(x57012,x57013)+P22(f312(f312(f227(f860(x57011,a845)),x57012),x57013))
% 173.53/173.41 [5706]~P71(x57061)+E(f312(f312(f89(x57061),f312(f88(x57061),x57062)),f312(f88(x57061),x57063)),f312(f88(x57061),f312(f312(f89(x57061),x57063),x57062)))
% 173.53/173.41 [5707]~P30(x57071)+E(f312(f312(f89(x57071),f312(f88(x57071),x57072)),f312(f88(x57071),x57073)),f312(f88(x57071),f312(f312(f89(x57071),x57072),x57073)))
% 173.53/173.41 [5708]~P88(x57081)+E(f312(f312(f115(x57081),f312(f88(x57081),x57082)),f312(f88(x57081),x57083)),f312(f88(x57081),f312(f312(f124(x57081),x57082),x57083)))
% 173.53/173.41 [5709]~P88(x57091)+E(f312(f312(f124(x57091),f312(f88(x57091),x57092)),f312(f88(x57091),x57093)),f312(f88(x57091),f312(f312(f115(x57091),x57092),x57093)))
% 173.53/173.41 [5710]~P70(x57101)+E(f312(f312(f226(x57101),f312(f88(x57101),x57102)),f312(f88(x57101),x57103)),f312(f88(x57101),f312(f312(f225(x57101),x57102),x57103)))
% 173.53/173.41 [5711]~P70(x57111)+E(f312(f312(f225(x57111),f312(f88(x57111),x57112)),f312(f88(x57111),x57113)),f312(f88(x57111),f312(f312(f226(x57111),x57112),x57113)))
% 173.53/173.41 [5712]~P112(x57121)+E(f312(f312(f90(x57121),f312(f84(x57121),x57122)),f312(f84(x57121),x57123)),f312(f84(x57121),f312(f312(f90(x57121),x57122),x57123)))
% 173.53/173.41 [5713]~P66(x57131)+E(f312(f312(f268(x57131),f312(f84(x57131),x57132)),f312(f84(x57131),x57133)),f312(f84(x57131),f312(f312(f268(x57131),x57132),x57133)))
% 173.53/173.41 [5714]~P25(x57141)+E(f312(f312(f89(x57141),f312(f162(x57141),x57142)),f312(f162(x57141),x57143)),f312(f162(x57141),f312(f312(f129(x57141),x57142),x57143)))
% 173.53/173.41 [5715]E(x57151,f189(f860(x57152,a845)))+~E(f312(f312(f124(f860(x57152,a845)),x57153),x57151),f189(f860(x57152,a845)))
% 173.53/173.41 [5716]E(x57161,f189(f860(x57162,a845)))+~E(f312(f312(f124(f860(x57162,a845)),x57161),x57163),f189(f860(x57162,a845)))
% 173.53/173.41 [5762]~P22(f312(f70(x57621),x57623))+P22(f312(f70(x57621),f312(f312(f289(x57621),x57622),x57623)))
% 173.53/173.41 [5763]~P22(f312(f133(x57631),x57633))+P22(f312(f133(x57631),f312(f312(f169(x57631),x57632),x57633)))
% 173.53/173.41 [5764]~P22(f312(f133(x57641),x57643))+P22(f312(f133(x57641),f312(f312(f134(x57641),x57642),x57643)))
% 173.53/173.41 [5771]~E(x57711,f2(a852))+E(f312(f47(a852,f312(f312(f90(a852),x57711),x57712)),f312(f312(f90(a852),x57711),x57713)),f2(a852))
% 173.53/173.41 [5795]~P87(x57951)+P22(f312(f312(f227(x57951),x57952),f312(f312(f124(x57951),x57953),x57952)))
% 173.53/173.41 [5796]~P98(x57961)+P22(f312(f312(f227(x57961),x57962),f312(f312(f124(x57961),x57963),x57962)))
% 173.53/173.41 [5797]~P87(x57971)+P22(f312(f312(f227(x57971),x57972),f312(f312(f124(x57971),x57972),x57973)))
% 173.53/173.41 [5798]~P98(x57981)+P22(f312(f312(f227(x57981),x57982),f312(f312(f124(x57981),x57982),x57983)))
% 173.53/173.41 [5799]~P103(x57991)+P22(f312(f312(f227(x57991),x57992),f312(f312(f226(x57991),x57993),x57992)))
% 173.53/173.41 [5800]~P103(x58001)+P22(f312(f312(f227(x58001),x58002),f312(f312(f226(x58001),x58002),x58003)))
% 173.53/173.41 [5879]P22(f312(x58791,x58792))+P22(f312(f312(f195(f35(x58791,x58793)),x58792),x58792))
% 173.53/173.41 [5896]E(x58961,f2(a852))+E(f312(f47(a852,f312(f312(f90(a852),x58961),x58962)),f312(f312(f90(a852),x58961),x58963)),f312(f47(a852,x58962),x58963))
% 173.53/173.41 [5899]~P90(x58991)+E(f312(f312(f21(x58991),f312(f117(x58991),x58992)),f312(f117(x58991),x58993)),f312(f117(x58991),f312(f312(f89(a1),x58992),f312(f88(a1),x58993))))
% 173.53/173.41 [5984]E(f148(x59841,f312(f312(f147(x59841),x59842),x59843)),f312(f312(f147(x59841),x59842),f148(x59841,x59843)))+P22(f312(f312(f314(x59841),x59842),f312(f168(x59841),x59843)))
% 173.53/173.41 [6085]E(x60851,f127(x60852))+E(f312(f312(f147(x60852),f312(f137(x60852),x60851)),f312(f312(f169(x60852),x60853),f312(f167(x60852),x60851))),f312(f312(f169(x60852),f312(a126,x60853)),x60851))
% 173.53/173.41 [6091]E(f312(f312(f21(f860(x60911,a845)),x60912),x60913),x60912)+~E(f312(f312(f115(f860(x60911,a845)),x60912),x60913),f189(f860(x60911,a845)))
% 173.53/173.41 [6105]E(f148(x61051,f312(f312(f147(x61051),x61052),x61053)),f148(x61051,x61053))+~P22(f312(f312(f314(x61051),x61052),f312(f168(x61051),x61053)))
% 173.53/173.41 [6142]~P22(f312(f312(f228(a852),x61421),x61423))+P22(f312(f312(f228(a852),x61421),f312(f312(f89(a852),x61422),x61423)))
% 173.53/173.41 [6144]~P22(f312(f312(f228(a852),x61441),x61442))+P22(f312(f312(f228(a852),x61441),f312(f312(f89(a852),x61442),x61443)))
% 173.53/173.41 [6146]~P22(f312(f312(f227(a852),x61461),x61463))+P22(f312(f312(f227(a852),x61461),f312(f312(f89(a852),x61462),x61463)))
% 173.53/173.41 [6148]~P22(f312(f312(f227(a852),x61481),x61482))+P22(f312(f312(f227(a852),x61481),f312(f312(f89(a852),x61482),x61483)))
% 173.53/173.41 [6185]P22(f312(f70(x61851),x61852))+~P22(f312(f70(x61851),f312(f312(f289(x61851),x61853),x61852)))
% 173.53/173.41 [6186]P22(f312(f133(x61861),x61862))+~P22(f312(f133(x61861),f312(f312(f147(x61861),x61863),x61862)))
% 173.53/173.41 [6187]P22(f312(f133(x61871),x61872))+~P22(f312(f133(x61871),f312(f312(f129(x61871),x61873),x61872)))
% 173.53/173.41 [6188]P22(f312(f133(x61881),x61882))+~P22(f312(f133(x61881),f312(f312(f129(x61881),x61882),x61883)))
% 173.53/173.41 [6229]~P107(x62291)+E(f312(f312(f89(x62291),x62292),f312(f312(f90(x62291),x62293),x62292)),f312(f312(f90(x62291),f312(f312(f89(x62291),x62293),f87(x62291))),x62292))
% 173.53/173.41 [6278]~E(x62781,x62782)+~P22(f312(f312(f228(f860(x62783,a845)),x62781),x62782))
% 173.53/173.41 [6320]P22(f312(f312(f314(x63201),x63202),x63203))+P22(f312(f312(f314(x63201),x63202),f312(f88(f860(x63201,a845)),x63203)))
% 173.53/173.41 [6327]E(f312(f47(a1,x63271),f312(f312(f90(a1),x63272),x63273)),f312(f47(a1,f312(f47(a1,x63271),x63272)),x63273))+~P22(f312(f312(f228(a1),f2(a1)),x63273))
% 173.53/173.41 [6328]E(f140(x63281,f312(f312(f134(x63281),x63282),x63283)),f140(x63281,x63283))+~P22(f312(f312(f228(a852),x63282),f312(f190(f853(x63281)),x63283)))
% 173.53/173.41 [6329]E(f312(f312(f169(x63291),x63292),f128(x63291,x63293)),f312(f312(f169(x63291),x63292),x63293))+~P22(f312(f312(f228(a852),x63292),f312(f190(f853(x63291)),x63293)))
% 173.53/173.41 [6382]E(f312(f312(f312(f184(f853(x63821),f853(x63821)),x63822),f164(x63821)),x63823),x63823)+~E(f54(a852,x63822,f312(f190(f853(x63821)),x63823)),f2(a852))
% 173.53/173.41 [6389]~P3(x63891,x63893,x63892)+E(f312(f312(f267(x63891,x63891,x63891),f312(f265(x63891,x63891),x63892)),x63892),x63892)
% 173.53/173.41 [6420]E(f312(f47(a852,f312(f312(f90(a852),x64201),x64202)),f312(f312(f90(a852),x64201),x64203)),f312(f47(a852,x64202),x64203))+~P22(f312(f312(f228(a852),f2(a852)),x64201))
% 173.53/173.41 [6427]~E(f312(f312(f124(f860(x64271,a845)),x64272),x64273),x64273)+P22(f312(f312(f227(f860(x64271,a845)),x64272),x64273))
% 173.53/173.41 [6432]~P54(x64321,x64321,x64323)+P54(x64321,x64321,f312(f312(f184(f859(x64321,x64321),a845),x64322),x64323))
% 173.53/173.41 [6434]~P22(f312(f312(f314(x64341),x64343),f312(f168(x64341),x64342)))+P22(f312(f312(f228(a852),f2(a852)),f312(f190(f853(x64341)),x64342)))
% 173.53/173.41 [6461]~P83(x64611)+E(f312(f84(x64611),f312(f312(f89(x64611),f312(f84(x64611),x64612)),f312(f84(x64611),x64613))),f312(f312(f89(x64611),f312(f84(x64611),x64612)),f312(f84(x64611),x64613)))
% 173.53/173.41 [6519]E(x65191,x65192)+~P22(f312(f312(f312(f312(a198,a23),x65191),x65193),x65192))
% 173.53/173.41 [6607]~P22(f312(f70(x66071),x66073))+E(f312(f312(f73(x66071,f860(x66071,a845),f289(x66071)),x66072),x66073),f312(f312(f124(f860(x66071,a845)),x66073),x66072))
% 173.53/173.41 [6667]E(f312(f312(f124(f860(x66671,a845)),x66672),x66673),x66672)+~P22(f312(f312(f227(f860(x66671,a845)),x66673),x66672))
% 173.53/173.41 [6669]E(f312(f312(f124(f860(x66691,a845)),x66692),x66693),x66693)+~P22(f312(f312(f227(f860(x66691,a845)),x66692),x66693))
% 173.53/173.41 [6670]E(f312(f312(f115(f860(x66701,a845)),x66702),x66703),x66703)+~P22(f312(f312(f227(f860(x66701,a845)),x66703),x66702))
% 173.53/173.41 [6671]E(f312(f312(f115(f860(x66711,a845)),x66712),x66713),x66712)+~P22(f312(f312(f227(f860(x66711,a845)),x66712),x66713))
% 173.53/173.41 [6719]~P22(f312(f133(x67191),x67192))+E(f312(f312(f21(f860(x67191,a845)),f312(f168(x67191),x67192)),f312(f312(f289(x67191),x67193),f189(f860(x67191,a845)))),f312(f168(x67191),f166(x67191,x67193,x67192)))
% 173.53/173.41 [6769]P41(x67691,x67692)+~P41(x67691,f312(f312(f184(f859(x67691,x67691),a845),x67693),x67692))
% 173.53/173.41 [6833]P22(f312(f57(x68331,x68332),f312(a59,x68333)))+~P22(f312(f57(f312(f88(a1),x68331),f312(f88(a1),x68332)),x68333))
% 173.53/173.41 [6839]E(f312(f312(f21(f860(x68391,a845)),f312(f312(f289(x68391),x68392),x68393)),f312(f312(f289(x68391),x68392),f189(f860(x68391,a845)))),x68393)+P22(f312(f312(f314(x68391),x68392),x68393))
% 173.53/173.41 [6860]E(f312(f312(f115(f860(x68601,a845)),f312(f168(x68601),x68602)),f312(f168(x68601),x68603)),f189(f860(x68601,a845)))+~P22(f312(f133(x68601),f312(f312(f129(x68601),x68602),x68603)))
% 173.53/173.41 [6875]~P22(f312(f312(f314(x68751),x68752),f312(f168(x68751),x68753)))+~P22(f312(f133(x68751),f312(f312(f147(x68751),x68752),x68753)))
% 173.53/173.41 [6960]E(f312(f312(f115(f860(x69601,a845)),x69602),x69603),f189(f860(x69601,a845)))+P22(f312(f312(f314(x69601),f794(x69603,x69602,x69601)),x69602))
% 173.53/173.41 [6961]E(f312(f312(f115(f860(x69611,a845)),x69612),x69613),f189(f860(x69611,a845)))+P22(f312(f312(f314(x69611),f811(x69613,x69612,x69611)),x69613))
% 173.53/173.41 [6965]E(f128(x69651,f312(f312(f169(x69651),x69652),x69653)),f312(f312(f169(x69651),f312(f312(f21(a852),x69652),f87(a852))),x69653))+~P22(f312(f312(f227(a852),x69652),f312(f190(f853(x69651)),x69653)))
% 173.53/173.41 [7025]~P38(x70253,x70252,x70251)+P22(f312(f312(f228(a852),f743(x70251,x70252,x70253)),f312(f190(f853(x70253)),x70251)))
% 173.53/173.41 [7042]P22(f312(f312(f228(a852),f2(a852)),x70421))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x70422),x70421)),f312(f312(f90(a852),x70423),x70421)))
% 173.53/173.41 [7043]P22(f312(f312(f228(a852),f2(a852)),x70431))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x70431),x70432)),f312(f312(f90(a852),x70431),x70433)))
% 173.53/173.41 [7046]~P22(f312(f312(f314(x70461),x70462),x70463))+~P22(f312(f312(f314(x70461),x70462),f312(f88(f860(x70461,a845)),x70463)))
% 173.53/173.41 [7055]~P22(f312(f312(f228(f860(x70551,a845)),x70552),x70553))+P22(f312(f312(f227(f860(x70551,a845)),x70552),x70553))
% 173.53/173.41 [7154]~P22(f312(f312(f228(a852),x71542),x71543))+P22(f312(f312(f228(a852),f312(f312(f89(a852),x71541),x71542)),f312(f312(f89(a852),x71541),x71543)))
% 173.53/173.41 [7155]~P22(f312(f312(f228(a852),x71551),x71553))+P22(f312(f312(f228(a852),f312(f312(f89(a852),x71551),x71552)),f312(f312(f89(a852),x71553),x71552)))
% 173.53/173.41 [7156]~P22(f312(f312(f228(a1),x71561),x71563))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x71561),x71562)),f312(f312(f89(a1),x71563),x71562)))
% 173.53/173.41 [7159]~P22(f312(f312(f227(a852),x71592),x71593))+P22(f312(f312(f227(a852),f312(f312(f89(a852),x71591),x71592)),f312(f312(f89(a852),x71591),x71593)))
% 173.53/173.41 [7160]~P22(f312(f312(f227(a852),x71601),x71603))+P22(f312(f312(f227(a852),f312(f312(f89(a852),x71601),x71602)),f312(f312(f89(a852),x71603),x71602)))
% 173.53/173.41 [7161]~P22(f312(f312(f227(a852),x71613),x71612))+P22(f312(f312(f227(a852),f312(f312(f21(a852),x71611),x71612)),f312(f312(f21(a852),x71611),x71613)))
% 173.53/173.41 [7162]~P22(f312(f312(f227(a852),x71621),x71623))+P22(f312(f312(f227(a852),f312(f312(f21(a852),x71621),x71622)),f312(f312(f21(a852),x71623),x71622)))
% 173.53/173.41 [7164]~P22(f312(f312(f227(a852),x71642),x71643))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x71641),x71642)),f312(f312(f90(a852),x71641),x71643)))
% 173.53/173.41 [7166]~P22(f312(f312(f227(a852),x71661),x71663))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x71661),x71662)),f312(f312(f90(a852),x71663),x71662)))
% 173.53/173.41 [7167]~P22(f312(f312(f227(a1),x71672),x71673))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x71671),x71672)),f312(f312(f89(a1),x71671),x71673)))
% 173.53/173.41 [7241]E(x72411,x72412)+~P22(f312(f312(f314(x72413),x72411),f312(f312(f289(x72413),x72412),f189(f860(x72413,a845)))))
% 173.53/173.41 [7243]~E(f312(f312(f115(f860(x72431,a845)),x72432),x72433),f189(f860(x72431,a845)))+P22(f312(f312(f227(f860(x72431,a845)),x72432),f312(f88(f860(x72431,a845)),x72433)))
% 173.53/173.41 [7251]P22(f312(f312(f314(f860(x72511,a845)),x72512),f312(f288(x72511),x72513)))+~P22(f312(f312(f227(f860(x72511,a845)),x72512),x72513))
% 173.53/173.41 [7303]E(f312(f312(f147(x73031),f312(f312(f161(x73031),x73032),x73033)),f312(f312(f134(x73031),f312(a126,x73033)),x73032)),f312(f312(f134(x73031),x73033),x73032))+~P22(f312(f312(f228(a852),x73033),f312(f190(f853(x73031)),x73032)))
% 173.53/173.41 [7328]P22(f312(f312(f314(f859(x73281,x73281)),x73282),f287(x73281,x73283)))+~P22(f312(f312(f314(f859(x73281,x73281)),x73282),x73283))
% 173.53/173.41 [7338]~P22(f312(f312(f314(f860(x73381,a845)),x73382),f312(f288(x73381),x73383)))+P22(f312(f312(f227(f860(x73381,a845)),x73382),x73383))
% 173.53/173.41 [7383]P22(f312(f312(f227(f860(x73831,a845)),x73832),f48(f860(x73831,a845),x73833)))+~P22(f312(f312(f314(f860(x73831,a845)),x73832),x73833))
% 173.53/173.41 [7407]~P111(x74071)+E(f312(f312(f90(x74071),f312(f312(f240(x74071),f312(f88(x74071),f87(x74071))),x74072)),f312(f312(f240(x74071),x74073),x74072)),f312(f312(f240(x74071),f312(f88(x74071),x74073)),x74072))
% 173.53/173.41 [7428]E(f312(f312(f161(x74281),x74282),f312(f312(f21(a852),f312(f190(f853(x74281)),x74282)),f312(a126,x74283))),f312(f312(f161(x74281),f312(f165(x74281),x74282)),x74283))+~P22(f312(f312(f228(a852),x74283),f312(f190(f853(x74281)),x74282)))
% 173.53/173.41 [7445]~E(f312(f312(f115(f860(x74451,a845)),f677(x74453,x74452,x74451)),x74453),f189(f860(x74451,a845)))+E(f312(f312(f115(f860(x74451,a845)),f48(f860(x74451,a845),x74452)),x74453),f189(f860(x74451,a845)))
% 173.53/173.41 [7507]~P22(f312(f312(f314(x75073),x75072),f312(f168(x75073),x75071)))+P22(f312(f312(f228(a852),f599(x75071,x75072,x75073)),f312(f190(f853(x75073)),x75071)))
% 173.53/173.41 [7515]P22(f312(f312(f314(x75151),f312(f312(f161(x75151),x75152),x75153)),f312(f168(x75151),x75152)))+~P22(f312(f312(f228(a852),x75153),f312(f190(f853(x75151)),x75152)))
% 173.53/173.41 [7613]~P22(f312(x76132,f663(x76133,x76132,x76131)))+E(f312(f312(f134(x76131),f312(f190(f853(x76131)),f172(x76131,x76132,x76133))),x76133),f127(x76131))
% 173.53/173.41 [7624]P22(f312(f312(f227(f860(f853(x76241),a845)),f157(x76241,x76242)),f157(x76241,x76243)))+~P22(f312(f312(f227(f860(x76241,a845)),x76242),x76243))
% 173.53/173.41 [7625]P22(f312(f312(f227(f860(f853(x76251),a845)),f156(x76251,x76252)),f156(x76251,x76253)))+~P22(f312(f312(f227(f860(x76251,a845)),x76252),x76253))
% 173.53/173.41 [7655]E(f312(f312(f115(f860(x76551,a845)),f48(f860(x76551,a845),x76552)),x76553),f189(f860(x76551,a845)))+P22(f312(f312(f314(f860(x76551,a845)),f677(x76553,x76552,x76551)),x76552))
% 173.53/173.41 [7657]~P22(f312(f312(f314(f860(x76571,a845)),x76573),x76572))+P22(f312(f312(f227(f860(x76571,a845)),f49(f860(x76571,a845),x76572)),x76573))
% 173.53/173.41 [7659]E(f312(f312(f115(f860(x76591,a845)),x76592),x76593),f189(f860(x76591,a845)))+~P22(f312(f312(f227(f860(x76591,a845)),x76592),f312(f88(f860(x76591,a845)),x76593)))
% 173.53/173.41 [7709]E(f312(f312(f21(a852),f312(f312(f89(a852),f312(f162(a852),x77091)),x77092)),f312(f312(f161(a852),x77091),x77093)),f312(f162(a852),f312(f312(f155(a852,x77091),x77093),x77092)))+~P22(f312(f312(f228(a852),x77093),f312(f190(f853(a852)),x77091)))
% 173.53/173.41 [7758]P22(f312(f312(f228(a852),x77581),x77582))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),x77583),x77581)),f312(f312(f89(a852),x77583),x77582)))
% 173.53/173.41 [7759]P22(f312(f312(f228(a852),x77591),x77592))+~P22(f312(f312(f228(a852),f312(f312(f90(a852),x77593),x77591)),f312(f312(f90(a852),x77593),x77592)))
% 173.53/173.42 [7760]P22(f312(f312(f228(a852),x77601),x77602))+~P22(f312(f312(f228(a852),f312(f312(f90(a852),x77601),x77603)),f312(f312(f90(a852),x77602),x77603)))
% 173.53/173.42 [7763]P22(f312(f312(f227(a852),x77631),x77632))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x77633),x77631)),f312(f312(f89(a852),x77633),x77632)))
% 173.53/173.42 [7791]P22(f312(f312(f228(a852),f2(a852)),x77911))+~P22(f312(f312(f228(a852),f312(f312(f90(a852),x77912),x77911)),f312(f312(f90(a852),x77913),x77911)))
% 173.53/173.42 [7792]P22(f312(f312(f228(a852),f2(a852)),x77921))+~P22(f312(f312(f228(a852),f312(f312(f90(a852),x77921),x77922)),f312(f312(f90(a852),x77921),x77923)))
% 173.53/173.42 [7859]E(f242(x78591,x78592,x78593),x78592)+~P22(f312(f312(f227(f860(x78591,a845)),x78593),f312(f312(f289(x78591),x78592),f189(f860(x78591,a845)))))
% 173.53/173.42 [7914]~P22(f312(f133(x79141),x79143))+E(f312(f132(x79141,f312(f312(f8(a845,a845,x79141),a307),f312(a309,x79142))),x79143),f166(x79141,x79142,x79143))
% 173.53/173.42 [7937]E(f312(f312(f134(x79371),f312(f190(f853(x79371)),f172(x79371,x79372,x79373))),x79373),f127(x79371))+P22(f312(f312(f314(x79371),f663(x79373,x79372,x79371)),f312(f168(x79371),x79373)))
% 173.53/173.42 [7941]E(f312(f312(f129(x79411),f312(f312(f169(x79411),x79412),x79413)),f312(f312(f147(x79411),f312(f312(f161(x79411),x79413),x79412)),f127(x79411))),f312(f312(f169(x79411),f312(a126,x79412)),x79413))+~P22(f312(f312(f228(a852),x79412),f312(f190(f853(x79411)),x79413)))
% 173.53/173.42 [8003]E(f312(f132(x80031,f312(f312(f8(a845,a845,x80031),a307),f312(a309,x80032))),x80033),x80033)+P22(f312(f312(f314(x80031),x80032),f312(f168(x80031),x80033)))
% 173.53/173.42 [8013]P22(f312(f312(f227(f860(f860(x80131,a845),a845)),f243(x80131,x80132)),f243(x80131,x80133)))+~P22(f312(f312(f227(f860(x80131,a845)),x80132),x80133))
% 173.53/173.42 [8059]~P22(f312(f133(x80591),x80593))+P22(f312(f133(x80591),f312(f312(f312(f184(f853(x80591),f853(x80591)),x80592),f164(x80591)),x80593)))
% 173.53/173.42 [8064]~P22(f312(f312(f228(a852),x80642),x80643))+P22(f312(f312(f228(a852),f312(f312(f90(a852),f312(a126,x80641)),x80642)),f312(f312(f90(a852),f312(a126,x80641)),x80643)))
% 173.53/173.42 [8085]P22(f312(f312(f227(f860(f860(x80851,a845),a845)),f312(f288(x80851),x80852)),f312(f288(x80851),x80853)))+~P22(f312(f312(f227(f860(x80851,a845)),x80852),x80853))
% 173.53/173.42 [8254]~P22(f312(f312(f227(f860(x82541,a845)),x82543),x82542))+P22(f312(f312(f227(f860(x82541,a845)),f312(f88(f860(x82541,a845)),x82542)),f312(f88(f860(x82541,a845)),x82543)))
% 173.53/173.42 [8284]E(f312(f290(a852,a852,f312(f312(f7(a852,a852,a852),f21(a852)),x82841)),f312(f282(a852,x82842),x82843)),f312(f282(a852,f312(f312(f21(a852),x82842),x82841)),f312(f312(f21(a852),x82843),x82841)))+~P22(f312(f312(f228(a852),x82841),x82843))
% 173.53/173.42 [8303]E(f312(f312(f89(a1),f312(f312(f90(a1),x83031),f54(a1,f312(f47(a1,x83032),x83031),x83033))),f54(a1,x83032,x83031)),f54(a1,x83032,f312(f312(f90(a1),x83031),x83033)))+~P22(f312(f312(f228(a1),f2(a1)),x83033))
% 173.53/173.42 [8313]~P25(x83131)+E(f312(f312(f89(x83131),x83132),f312(f138(x83131,x83131,f89(x83131),f2(x83131)),x83133)),f312(f138(x83131,x83131,f89(x83131),x83132),x83133))
% 173.53/173.42 [8401]~P83(x84011)+P22(f312(f312(f227(x84011),f312(f84(x84011),f312(f312(f89(x84011),x84012),x84013))),f312(f312(f89(x84011),f312(f84(x84011),x84012)),f312(f84(x84011),x84013))))
% 173.53/173.42 [8402]~P83(x84021)+P22(f312(f312(f227(x84021),f312(f84(x84021),f312(f312(f21(x84021),x84022),x84023))),f312(f312(f89(x84021),f312(f84(x84021),x84022)),f312(f84(x84021),x84023))))
% 173.53/173.42 [8417]E(f312(f312(f129(x84171),f312(f312(f169(x84171),x84172),x84173)),f312(f312(f147(x84171),f312(f137(x84171),f312(f312(f134(x84171),x84172),x84173))),f127(x84171))),f312(f312(f169(x84171),f312(a126,x84172)),x84173))+~P22(f312(f312(f228(a852),x84172),f312(f190(f853(x84171)),x84173)))
% 173.53/173.42 [8437]E(f312(f256(x84371,f312(f312(f150(x84371,f859(a113,x84371)),f312(f239(a113,x84371),f87(a113))),x84372)),f312(a3,x84373)),f312(f312(f161(x84371),x84372),x84373))+~P22(f312(f312(f228(a852),x84373),f312(f190(f853(x84371)),x84372)))
% 173.53/173.42 [8506]P22(f312(f312(f314(f859(x85061,x85061)),x85062),f312(f312(f267(x85061,x85061,x85061),x85063),f287(x85061,x85063))))+~P22(f312(f312(f314(f859(x85061,x85061)),x85062),x85063))
% 173.53/173.42 [8522]P22(f312(f312(f227(a852),x85221),x85222))+~P22(f312(f312(f227(a852),f312(f312(f90(a852),f312(a126,x85223)),x85221)),f312(f312(f90(a852),f312(a126,x85223)),x85222)))
% 173.53/173.42 [8536]P22(f312(f312(f227(f860(x85361,a845)),x85362),x85363))+~P22(f312(f312(f227(f860(x85361,a845)),f312(f88(f860(x85361,a845)),x85363)),f312(f88(f860(x85361,a845)),x85362)))
% 173.53/173.42 [8554]P22(f312(f133(x85541),x85542))+~P22(f312(f133(x85541),f312(f312(f312(f184(f853(x85541),f853(x85541)),x85543),f164(x85541)),x85542)))
% 173.53/173.42 [8612]E(f312(f290(f859(x86121,x86122),x86122,f248(x86121,x86122)),f312(f168(f859(x86121,x86122)),x86123)),f181(x86121,x86122,f312(f173(x86121,x86122),x86123)))+~P22(f312(f133(x86121),f312(f312(f150(f859(x86121,x86122),x86121),f246(x86121,x86122)),x86123)))
% 173.53/173.42 [8621]E(f312(f264(x86211,x86211,f287(x86211,x86212)),x86213),x86213)+~P22(f312(f312(f227(f860(x86211,a845)),f312(f264(x86211,x86211,x86212),x86213)),x86213))
% 173.53/173.42 [8665]~P103(x86651)+P33(x86651,f312(f132(x86651,f312(f312(f7(x86651,x86651,a845),a309),f312(x86652,x86653))),x86653))
% 173.53/173.42 [8671]~P22(f312(f312(f227(a852),x86711),x86712))+P22(f312(f312(f227(a852),x86711),f312(f138(a852,a852,f89(a852),x86712),x86713)))
% 173.53/173.42 [8746]~P22(f312(f312(f314(f859(x87461,x87461)),x87462),f287(x87461,x87463)))+P22(f312(f312(f314(f859(x87461,x87461)),x87462),f312(f312(f184(f859(x87461,x87461),a845),f763(x87463,x87462,x87461)),x87463)))
% 173.53/173.42 [8835]~P25(x88351)+E(f312(f312(f89(x88351),x88352),f312(f138(x88351,x88351,f312(f7(x88351,x88351,x88351),f89(x88351)),f2(x88351)),f312(f165(x88351),x88353))),f312(f138(x88351,x88351,f89(x88351),x88352),x88353))
% 173.53/173.42 [9103]P54(x91031,x91032,x91033)+P22(f312(f312(f314(f859(x91031,x91032)),f312(f312(f239(x91031,x91032),f753(x91033,x91032,x91031)),f723(x91033,x91032,x91031))),x91033))
% 173.53/173.42 [9104]P54(x91041,x91042,x91043)+P22(f312(f312(f314(f859(x91041,x91042)),f312(f312(f239(x91041,x91042),f753(x91043,x91042,x91041)),f722(x91043,x91042,x91041))),x91043))
% 173.53/173.42 [9177]~P22(f312(f312(f314(f859(x91771,x91771)),x91772),f312(f312(f267(x91771,x91771,x91771),x91773),f287(x91771,x91773))))+P22(f312(f312(f314(f859(x91771,x91771)),x91772),f312(f312(f184(f859(x91771,x91771),a845),f764(x91773,x91772,x91771)),x91773)))
% 173.53/173.42 [9178]~P22(f312(x91781,f312(f312(f161(x91782),x91783),f312(f190(f853(x91782)),f172(x91782,x91781,x91783)))))+~P22(f312(f312(f228(a852),f312(f190(f853(x91782)),f172(x91782,x91781,x91783))),f312(f190(f853(x91782)),x91783)))
% 173.53/173.42 [9263]~P22(f312(f312(f227(f860(x92631,a845)),x92632),x92633))+P22(f312(f312(f227(f860(x92631,a845)),f312(f312(f7(x92631,f860(x92631,a845),a845),f314(x92631)),x92632)),f312(f312(f7(x92631,f860(x92631,a845),a845),f314(x92631)),x92633)))
% 173.53/173.42 [9317]~P22(f312(f312(f314(f859(f860(x93171,a845),f860(x93171,a845))),f312(f312(f239(f860(x93171,a845),f860(x93171,a845)),x93172),x93173)),f286(x93171)))+P22(f312(f312(f228(f860(x93171,a845)),x93172),x93173))
% 173.53/173.42 [9343]P55(x93431,x93432,x93433)+~P22(f312(f312(f314(f859(x93431,x93431)),f312(f312(f239(x93431,x93431),f756(x93433,x93432,x93431)),f755(x93433,x93432,x93431))),x93433))
% 173.53/173.42 [9344]P55(x93441,x93442,x93443)+~P22(f312(f312(f314(f859(x93441,x93441)),f312(f312(f239(x93441,x93441),f755(x93443,x93442,x93441)),f756(x93443,x93442,x93441))),x93443))
% 173.53/173.42 [9377]~P22(f312(f312(f314(f859(f853(x93771),f853(x93771))),f312(f312(f239(f853(x93771),f853(x93771)),x93772),x93772)),f143(x93771,x93773)))+P22(f312(f312(f314(f859(x93771,x93771)),f312(f312(f239(x93771,x93771),f607(x93772,x93773,x93771)),f607(x93772,x93773,x93771))),x93773))
% 173.53/173.42 [9430]P22(f312(f312(f227(f860(x94301,a845)),x94302),x94303))+~P22(f312(f312(f227(f860(x94301,a845)),f312(f312(f7(x94301,f860(x94301,a845),a845),f314(x94301)),x94302)),f312(f312(f7(x94301,f860(x94301,a845),a845),f314(x94301)),x94303)))
% 173.53/173.42 [9512]E(f312(f312(f21(a852),f312(f312(f6(a852,a852),x95121),f312(f279(a852),x95122))),f312(f312(f6(a852,a852),x95123),f312(f279(a852),x95122))),f312(f312(f6(a852,a852),f312(f312(f18(a852,a852,a852),f312(f312(f8(a852,f860(a852,a852),a852),f21(a852)),x95121)),x95123)),f312(f279(a852),x95122)))+~P22(f312(f312(f227(a852),f312(x95123,f499(x95122,x95121,x95123))),f312(x95121,f499(x95122,x95121,x95123))))
% 173.53/173.42 [9812]E(f312(f233(f859(x98121,x98122)),f312(f249(x98121,x98122,a845),f312(f312(f7(x98121,f860(x98122,f856(x98122)),f860(x98122,a845)),f312(f312(f8(f860(f856(x98122),a845),f860(f860(x98122,f856(x98122)),f860(x98122,a845)),x98121),f8(f856(x98122),a845,x98122)),f312(f312(f8(f856(x98122),f860(f856(x98122),a845),x98121),a309),f312(f173(x98121,x98122),x98123)))),f219(x98122)))),f312(f168(f859(x98121,x98122)),x98123))+~P22(f312(f133(x98121),f312(f312(f150(f859(x98121,x98122),x98121),f246(x98121,x98122)),x98123)))
% 173.53/173.42 [5564]~P71(x55641)+E(f312(f312(f89(x55641),f312(f312(f21(x55641),x55642),x55643)),x55643),x55642)
% 173.53/173.42 [5565]~P71(x55651)+E(f312(f312(f21(x55651),f312(f312(f89(x55651),x55652),x55653)),x55653),x55652)
% 173.53/173.42 [5770]~P71(x57701)+E(f312(f312(f89(x57701),x57702),f312(f312(f89(x57701),f312(f88(x57701),x57702)),x57703)),x57703)
% 173.53/173.42 [5853]~P78(x58531)+E(f312(f312(f90(x58531),f312(f312(f240(x58531),x58532),x58533)),x58532),f312(f312(f240(x58531),x58532),f312(a126,x58533)))
% 173.53/173.42 [5854]~P107(x58541)+E(f312(f312(f90(x58541),f312(f312(f240(x58541),x58542),x58543)),x58542),f312(f312(f240(x58541),x58542),f312(a126,x58543)))
% 173.53/173.42 [6061]~P112(x60611)+E(f312(f84(x60611),f312(f312(f240(x60611),f312(f88(x60611),x60612)),x60613)),f312(f84(x60611),f312(f312(f240(x60611),x60612),x60613)))
% 173.53/173.42 [6119]~P78(x61191)+E(f312(f312(f90(x61191),f312(f312(f240(x61191),x61192),x61193)),x61192),f312(f312(f90(x61191),x61192),f312(f312(f240(x61191),x61192),x61193)))
% 173.53/173.42 [6175]E(f312(f312(f21(a113),f312(f312(f89(a113),x61751),x61752)),x61753),f260(x61751,x61752,x61753))+~P22(f312(f312(f228(a113),x61752),x61753))
% 173.53/173.42 [6197]~E(f312(f312(f134(x61971),x61973),x61972),f127(x61971))+P22(f312(f312(f227(a852),f312(f190(f853(x61971)),x61972)),x61973))
% 173.53/173.42 [6326]E(f312(f312(f90(a852),f312(f117(a852),x63261)),f312(f312(f90(a852),f312(f117(a852),x63262)),x63263)),f2(a852))+~P22(f312(f312(f228(a1),x63261),a92))
% 173.53/173.42 [6342]~P64(x63421)+E(f312(f312(f240(x63421),f312(f312(f268(x63421),f87(x63421)),x63422)),x63423),f312(f312(f268(x63421),f87(x63421)),f312(f312(f240(x63421),x63422),x63423)))
% 173.53/173.42 [6418]E(f312(f312(f21(a852),f312(f312(f89(a852),x64181),x64182)),x64183),f312(f312(f21(a852),x64181),f312(f312(f21(a852),x64183),x64182)))+~P22(f312(f312(f227(a852),x64182),x64183))
% 173.53/173.42 [6419]E(f312(f312(f21(a852),f312(f312(f89(a852),x64191),x64192)),x64193),f312(f312(f89(a852),x64191),f312(f312(f21(a852),x64192),x64193)))+~P22(f312(f312(f227(a852),x64193),x64192))
% 173.53/173.42 [6452]~P87(x64521)+P22(f312(f312(f227(x64521),f312(f312(f115(x64521),x64522),x64523)),x64523))
% 173.53/173.42 [6453]~P99(x64531)+P22(f312(f312(f227(x64531),f312(f312(f115(x64531),x64532),x64533)),x64533))
% 173.53/173.42 [6454]~P87(x64541)+P22(f312(f312(f227(x64541),f312(f312(f115(x64541),x64542),x64543)),x64542))
% 173.53/173.42 [6455]~P99(x64551)+P22(f312(f312(f227(x64551),f312(f312(f115(x64551),x64552),x64553)),x64552))
% 173.53/173.42 [6456]~P103(x64561)+P22(f312(f312(f227(x64561),f312(f312(f225(x64561),x64562),x64563)),x64563))
% 173.53/173.42 [6457]~P103(x64571)+P22(f312(f312(f227(x64571),f312(f312(f225(x64571),x64572),x64573)),x64572))
% 173.53/173.42 [6522]~P107(x65221)+E(f312(f312(f89(x65221),f312(f312(f90(x65221),x65222),x65223)),x65223),f312(f312(f90(x65221),f312(f312(f89(x65221),x65222),f87(x65221))),x65223))
% 173.53/173.42 [6523]~P90(x65231)+E(f312(f312(f90(x65231),f312(f88(x65231),f312(f117(x65231),x65232))),x65233),f312(f312(f90(x65231),f312(f117(x65231),f312(f88(a1),x65232))),x65233))
% 173.53/173.42 [6599]~P25(x65991)+E(f312(f162(x65991),f312(f312(f150(x65992,x65991),f312(f16(x65991,x65992),f2(x65991))),x65993)),f2(x65991))
% 173.53/173.42 [6610]E(f312(f312(f89(a852),f312(f117(a852),x66101)),f312(f312(f89(a852),f312(f117(a852),x66102)),x66103)),f312(f312(f89(a852),f312(f117(a852),x66102)),x66103))+~P22(f312(a194,f312(f117(a1),x66101)))
% 173.53/173.42 [6626]~P31(x66261)+E(f48(x66261,f312(f312(f289(x66261),x66262),f312(f312(f289(x66261),x66263),f189(f860(x66261,a845))))),f312(f312(f124(x66261),x66262),x66263))
% 173.53/173.42 [6627]~P31(x66271)+E(f49(x66271,f312(f312(f289(x66271),x66272),f312(f312(f289(x66271),x66273),f189(f860(x66271,a845))))),f312(f312(f115(x66271),x66272),x66273))
% 173.53/173.42 [6651]E(f312(f312(f169(x66511),x66512),x66513),x66513)+~P22(f312(f312(f227(a852),f312(f190(f853(x66511)),x66513)),x66512))
% 173.53/173.42 [6662]E(f312(f312(f134(x66621),x66622),x66623),f127(x66621))+~P22(f312(f312(f227(a852),f312(f190(f853(x66621)),x66623)),x66622))
% 173.53/173.42 [6673]E(f312(f312(f21(a852),f312(f312(f89(a852),x66731),x66732)),x66733),f312(f312(f89(a852),f312(f312(f21(a852),x66731),x66733)),x66732))+~P22(f312(f312(f227(a852),x66733),x66731))
% 173.53/173.42 [6687]~P22(f312(f312(f228(a852),x66871),x66873))+P22(f312(f312(f228(a852),f312(f312(f21(a852),x66871),x66872)),x66873))
% 173.53/173.42 [6712]~P103(x67121)+E(f166(x67121,x67122,f312(f312(f145(x67121,x67121,f5(x67121)),x67122),x67123)),x67123)
% 173.53/173.42 [6793]E(f312(f312(f21(a852),f312(f312(f89(a852),x67931),x67932)),f312(a126,x67933)),f312(f312(f21(a852),x67931),f312(a126,f312(f312(f21(a852),x67933),x67932))))+~P22(f312(f312(f227(a852),x67932),x67933))
% 173.53/173.42 [6794]~P112(x67941)+P22(f312(f312(f227(x67941),f2(x67941)),f312(f312(f240(x67941),f312(f84(x67941),x67942)),x67943)))
% 173.53/173.42 [6844]P18(x68441,x68442,x68443)+~P22(f312(f312(f227(f860(f851(x68441),a845)),x68443),x68442))
% 173.53/173.42 [6888]~P22(f312(f70(x68881),x68882))+P22(f312(f70(x68881),f312(f312(f21(f860(x68881,a845)),x68882),x68883)))
% 173.53/173.42 [6889]~P22(f312(f70(x68891),x68893))+P22(f312(f70(x68891),f312(f312(f115(f860(x68891,a845)),x68892),x68893)))
% 173.53/173.42 [6890]~P22(f312(f70(x68901),x68902))+P22(f312(f70(x68901),f312(f312(f115(f860(x68901,a845)),x68902),x68903)))
% 173.53/173.42 [6907]~P60(x69071)+E(f312(f312(f89(x69071),f54(x69071,x69072,x69073)),f312(f312(f90(x69071),f312(f47(x69071,x69072),x69073)),x69073)),x69072)
% 173.53/173.42 [7032]~P41(x70321,x70323)+P41(x70321,f312(f312(f115(f860(f859(x70321,x70321),a845)),x70322),x70323))
% 173.53/173.42 [7033]~P41(x70331,x70332)+P41(x70331,f312(f312(f115(f860(f859(x70331,x70331),a845)),x70332),x70333))
% 173.53/173.42 [7150]~P87(x71501)+E(f11(x71501,f312(f168(x71501),f312(f312(f147(x71501),x71502),x71503))),f312(f138(x71501,x71501,f115(x71501),x71502),x71503))
% 173.53/173.42 [7151]~P87(x71511)+E(f10(x71511,f312(f168(x71511),f312(f312(f147(x71511),x71512),x71513))),f312(f138(x71511,x71511,f124(x71511),x71512),x71513))
% 173.53/173.42 [7152]~P103(x71521)+E(f14(x71521,f312(f168(x71521),f312(f312(f147(x71521),x71522),x71523))),f312(f138(x71521,x71521,f226(x71521),x71522),x71523))
% 173.53/173.42 [7153]~P103(x71531)+E(f15(x71531,f312(f168(x71531),f312(f312(f147(x71531),x71532),x71533))),f312(f138(x71531,x71531,f225(x71531),x71532),x71533))
% 173.53/173.42 [7205]~P22(f312(f70(x72051),x72052))+P22(f312(f312(f227(a852),f312(f53(x72051),x72052)),f312(f53(x72051),f312(f312(f289(x72051),x72053),x72052))))
% 173.53/173.42 [7212]E(f312(f312(f124(f860(a852,a845)),f312(f282(a852,x72121),x72122)),f312(f282(a852,x72122),f312(f312(f89(a852),x72122),x72123))),f312(f282(a852,x72121),f312(f312(f89(a852),x72122),x72123)))+~P22(f312(f312(f227(a852),x72121),x72122))
% 173.53/173.42 [7220]P22(f312(f312(f228(a852),x72201),x72202))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),x72201),x72203)),x72202))
% 173.53/173.42 [7223]P22(f312(f312(f227(a852),x72231),x72232))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x72233),x72231)),x72232))
% 173.53/173.42 [7224]P22(f312(f312(f227(a852),x72241),x72242))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x72241),x72243)),x72242))
% 173.53/173.42 [7266]~P103(x72661)+E(f12(x72661,f226(x72661),f312(f168(x72661),f312(f312(f147(x72661),x72662),x72663))),f312(f138(x72661,x72661,f226(x72661),x72662),x72663))
% 173.53/173.42 [7267]~P103(x72671)+E(f13(x72671,f225(x72671),f312(f168(x72671),f312(f312(f147(x72671),x72672),x72673))),f312(f138(x72671,x72671,f225(x72671),x72672),x72673))
% 173.53/173.42 [7271]~E(x72712,f189(f860(f859(x72711,x72711),a845)))+P22(f312(f312(f227(f860(f859(x72711,x72711),a845)),x72712),x72713))
% 173.53/173.42 [7378]E(f312(f312(f124(f860(x73781,a845)),x73782),f312(f312(f21(f860(x73781,a845)),x73783),x73782)),x73783)+~P22(f312(f312(f227(f860(x73781,a845)),x73782),x73783))
% 173.53/173.42 [7379]~P22(f312(f312(f228(a852),x73791),f312(f312(f21(a852),x73793),x73792)))+P22(f312(f312(f228(a852),f312(f312(f89(a852),x73791),x73792)),x73793))
% 173.53/173.42 [7380]~P22(f312(f312(f227(a852),x73801),f312(f312(f89(a852),x73803),x73802)))+P22(f312(f312(f227(a852),f312(f312(f21(a852),x73801),x73802)),x73803))
% 173.53/173.42 [7435]E(x74351,f127(x74352))+E(f312(f137(x74352),f312(f312(f312(f184(f853(x74352),f853(x74352)),x74353),f164(x74352)),x74351)),f312(f312(f161(x74352),x74351),f54(a852,x74353,f312(f190(f853(x74352)),x74351))))
% 173.53/173.42 [7444]E(f312(f312(f289(x74441),x74442),f312(f312(f21(f860(x74441,a845)),x74443),f312(f312(f289(x74441),x74442),f189(f860(x74441,a845))))),x74443)+~P22(f312(f312(f314(x74441),x74442),x74443))
% 173.53/173.42 [7605]P22(f312(f312(f228(a852),x76051),f312(f312(f21(a852),x76052),x76053)))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),x76051),x76053)),x76052))
% 173.53/173.42 [7606]P22(f312(f312(f227(a852),x76061),f312(f312(f89(a852),x76062),x76063)))+~P22(f312(f312(f227(a852),f312(f312(f21(a852),x76061),x76063)),x76062))
% 173.53/173.42 [7629]P22(f312(f70(x76291),x76292))+~P22(f312(f70(x76291),f312(f312(f124(f860(x76291,a845)),x76293),x76292)))
% 173.53/173.42 [7630]P22(f312(f70(x76301),x76302))+~P22(f312(f70(x76301),f312(f312(f124(f860(x76301,a845)),x76302),x76303)))
% 173.53/173.42 [7706]~P48(x77061,x77063)+P22(f312(f312(f314(f859(x77061,x77061)),f312(f312(f239(x77061,x77061),x77062),x77062)),x77063))
% 173.53/173.42 [7833]E(f312(f312(f161(a852),f135(a852,f312(f282(a852,x78331),x78332))),x78333),f312(f312(f89(a852),x78331),x78333))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),x78331),x78333)),x78332))
% 173.53/173.42 [7900]~P22(f312(f312(f195(f312(a27,x79001)),x79002),x79003))+P22(f312(f312(f195(f312(f223(a846),f312(a30,x79001))),x79002),x79003))
% 173.53/173.42 [7903]E(f312(f312(f169(a852),x79031),f135(a852,f312(f282(a852,x79032),x79033))),f135(a852,f312(f282(a852,x79032),f312(f312(f89(a852),x79032),x79031))))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x79032),x79031)),x79033))
% 173.53/173.42 [7956]~P90(x79561)+E(f312(f312(f240(x79561),x79562),f312(f117(a852),f312(f312(f89(a1),x79563),x79563))),f312(f312(f95(x79561,x79561),f312(f312(f240(x79561),x79562),f312(f117(a852),x79563))),f312(f312(f18(x79561,x79561,x79561),f90(x79561)),f5(x79561))))
% 173.53/173.42 [8169]P22(f312(f312(f195(f312(a27,x81691)),x81692),x81693))+~P22(f312(f312(f195(f312(f223(a846),f312(a30,x81691))),x81692),x81693))
% 173.53/173.42 [8232]E(f312(f312(f129(x82321),f312(f312(f169(x82321),x82322),x82323)),f312(f312(f147(x82321),f312(f312(f161(x82321),x82323),x82322)),f312(f312(f134(x82321),f312(a126,x82322)),x82323))),x82323)+~P22(f312(f312(f228(a852),x82322),f312(f190(f853(x82321)),x82323)))
% 173.53/173.42 [8240]P22(f312(f312(f227(f860(x82401,a845)),f300(x82401,x82402)),f300(x82401,x82403)))+~P22(f312(f312(f227(f860(x82401,f860(x82401,a845))),x82403),x82402))
% 173.53/173.42 [8242]~P55(x82421,x82422,x82423)+P55(x82421,x82422,f312(f312(f21(f860(f859(x82421,x82421),a845)),x82423),f287(x82421,f189(f860(f859(x82421,x82421),a845)))))
% 173.53/173.42 [8259]P22(f312(f312(f227(f860(x82591,a845)),f301(x82591,x82592)),f301(x82591,x82593)))+~P22(f312(f312(f227(f860(f859(x82591,x82591),a845)),x82593),x82592))
% 173.53/173.42 [8265]~P119(x82651)+P22(f312(f312(f227(x82651),f2(x82651)),f312(f312(f89(x82651),f312(f312(f90(x82651),x82652),x82652)),f312(f312(f90(x82651),x82653),x82653))))
% 173.53/173.42 [8300]P22(f312(f312(f227(f860(x83001,a845)),f312(f263(x83001),x83002)),f312(f263(x83001),x83003)))+~P22(f312(f312(f227(f860(f859(x83001,x83001),a845)),x83002),x83003))
% 173.53/173.42 [8335]~P51(x83351,x83352)+~P22(f312(f312(f314(f859(x83351,x83351)),f312(f312(f239(x83351,x83351),x83353),x83353)),x83352))
% 173.53/173.42 [8337]~P41(x83371,x83372)+~P22(f312(f312(f314(f859(x83371,x83371)),f312(f312(f239(x83371,x83371),x83373),x83373)),x83372))
% 173.53/173.42 [8403]P22(f312(f312(f227(f860(x84031,a845)),f48(f860(x84031,a845),x84032)),f48(f860(x84031,a845),x84033)))+~P22(f312(f312(f227(f860(f860(x84031,a845),a845)),x84032),x84033))
% 173.53/173.42 [8404]P22(f312(f312(f227(f860(x84041,a845)),f49(f860(x84041,a845),x84042)),f49(f860(x84041,a845),x84043)))+~P22(f312(f312(f227(f860(f860(x84041,a845),a845)),x84043),x84042))
% 173.53/173.42 [8457]~P3(x84571,x84573,x84572)+P22(f312(f312(f227(f860(f859(x84571,x84571),a845)),x84572),f312(f312(f247(x84571,x84571),x84573),f312(f16(f860(x84571,a845),x84571),x84573))))
% 173.53/173.42 [8458]~P50(x84581,x84583,x84582)+P22(f312(f312(f227(f860(f859(x84581,x84581),a845)),x84582),f312(f312(f247(x84581,x84581),x84583),f312(f16(f860(x84581,a845),x84581),x84583))))
% 173.53/173.42 [8507]~P83(x85071)+P22(f312(f312(f227(x85071),f312(f312(f21(x85071),f312(f84(x85071),x85072)),f312(f84(x85071),x85073))),f312(f84(x85071),f312(f312(f21(x85071),x85073),x85072))))
% 173.53/173.42 [8508]~P83(x85081)+P22(f312(f312(f227(x85081),f312(f312(f21(x85081),f312(f84(x85081),x85082)),f312(f84(x85081),x85083))),f312(f84(x85081),f312(f312(f21(x85081),x85082),x85083))))
% 173.53/173.42 [8534]P22(f312(f312(f227(f860(f859(x85341,x85341),a845)),f287(x85341,x85342)),f287(x85341,x85343)))+~P22(f312(f312(f227(f860(f859(x85341,x85341),a845)),x85342),x85343))
% 173.53/173.42 [8688]P55(x86881,x86882,x86883)+~P55(x86881,x86882,f312(f312(f21(f860(f859(x86881,x86881),a845)),x86883),f287(x86881,f189(f860(f859(x86881,x86881),a845)))))
% 173.53/173.42 [8705]P22(f312(f312(f227(f860(f859(f853(x87051),f853(x87051)),a845)),f154(x87051,x87052)),f154(x87051,x87053)))+~P22(f312(f312(f227(f860(f859(x87051,x87051),a845)),x87052),x87053))
% 173.53/173.42 [8706]P22(f312(f312(f227(f860(f859(f853(x87061),f853(x87061)),a845)),f153(x87061,x87062)),f153(x87061,x87063)))+~P22(f312(f312(f227(f860(f859(x87061,x87061),a845)),x87062),x87063))
% 173.53/173.42 [8725]~P50(x87251,x87253,x87252)+P22(f312(f312(f227(f860(f859(x87251,x87251),a845)),x87252),f312(f312(f267(x87251,x87251,x87251),f312(f265(x87251,x87251),x87252)),x87252)))
% 173.53/173.42 [8773]~P22(f312(f133(x87731),x87732))+E(f312(f132(x87731,f312(f312(f7(x87731,f860(x87731,a845),a845),f314(x87731)),f312(f168(x87731),f170(x87731,x87732,x87733)))),x87732),f170(x87731,x87732,x87733))
% 173.53/173.42 [8833]E(x88331,x88332)+~P22(f312(f312(f314(f859(x88333,x88333)),f312(f312(f239(x88333,x88333),x88331),x88332)),f287(x88333,f189(f860(f859(x88333,x88333),a845)))))
% 173.53/173.42 [8923]P22(f312(f312(f314(x89231),x89232),f301(x89231,x89233)))+P22(f312(f312(f314(f859(x89231,x89231)),f312(f312(f239(x89231,x89231),f346(x89233,x89232,x89231)),x89232)),x89233))
% 173.53/173.42 [8924]P22(f312(f312(f314(x89241),x89242),f301(x89241,x89243)))+P22(f312(f312(f314(f859(x89241,x89241)),f312(f312(f239(x89241,x89241),f725(x89243,x89242,x89241)),x89242)),x89243))
% 173.53/173.42 [8925]P22(f312(f312(f314(x89251),x89252),f301(x89251,x89253)))+P22(f312(f312(f314(f859(x89251,x89251)),f312(f312(f239(x89251,x89251),f734(x89253,x89252,x89251)),x89252)),x89253))
% 173.53/173.42 [9007]~P22(f312(f312(f314(f853(x90071)),x90073),f157(x90071,x90072)))+P22(f312(f156(x90071,f312(f312(f7(x90071,f860(x90071,a845),a845),f314(x90071)),x90072)),x90073))
% 173.53/173.42 [9030]P22(f312(x90303,x90302))+E(f312(f233(x90301),f312(f312(f18(x90301,a845,a845),f312(f312(f8(a845,f860(a845,a845),x90301),a310),f312(a309,x90302))),x90303)),f189(f860(x90301,a845)))
% 173.53/173.42 [9049]~P83(x90491)+P22(f312(f312(f227(x90491),f312(f84(x90491),f312(f312(f21(x90491),f312(f84(x90491),x90492)),f312(f84(x90491),x90493)))),f312(f84(x90491),f312(f312(f21(x90491),x90492),x90493))))
% 173.53/173.42 [9062]~P22(f312(x90623,x90622))+E(f312(f233(x90621),f312(f312(f18(x90621,a845,a845),f312(f312(f8(a845,f860(a845,a845),x90621),a310),f312(a309,x90622))),x90623)),f312(f312(f289(x90621),x90622),f189(f860(x90621,a845))))
% 173.53/173.42 [9069]~P22(f312(f312(f314(f860(x90691,a845)),x90693),f312(f288(x90691),x90692)))+P22(f312(f243(x90691,f312(f312(f7(x90691,f860(x90691,a845),a845),f314(x90691)),x90692)),x90693))
% 173.53/173.42 [9102]P41(x91021,x91022)+P22(f312(f312(f314(f859(x91021,x91021)),f312(f312(f239(x91021,x91021),f312(f573(x91022,x91021),f312(a126,x91023))),f312(f573(x91022,x91021),x91023))),x91022))
% 173.53/173.42 [9243]P22(f312(f312(f314(f853(x92431)),x92432),f157(x92431,x92433)))+~P22(f312(f156(x92431,f312(f312(f7(x92431,f860(x92431,a845),a845),f314(x92431)),x92433)),x92432))
% 173.53/173.42 [9255]P22(f312(f312(f314(f860(x92551,a845)),x92552),f312(f288(x92551),x92553)))+~P22(f312(f243(x92551,f312(f312(f7(x92551,f860(x92551,a845),a845),f314(x92551)),x92553)),x92552))
% 173.53/173.42 [9313]P22(f312(f312(f314(x93131),f312(f256(x93131,x93132),x93133)),f312(f168(x93131),f312(f312(f150(f859(a113,x93131),x93131),f248(a113,x93131)),x93132))))+~P22(f312(f312(f228(a113),x93133),f312(f162(a113),f312(f312(f150(f859(a113,x93131),a113),f246(a113,x93131)),x93132))))
% 173.53/173.42 [9360]P22(f312(f312(f227(f860(f859(f853(x93601),f853(x93601)),a845)),f154(x93601,x93602)),f312(f312(f247(f853(x93601),f853(x93601)),f157(x93601,x93603)),f312(f16(f860(f853(x93601),a845),f853(x93601)),f157(x93601,x93603)))))+~P22(f312(f312(f227(f860(f859(x93601,x93601),a845)),x93602),f312(f312(f247(x93601,x93601),x93603),f312(f16(f860(x93601,a845),x93601),x93603))))
% 173.53/173.42 [9381]P22(f312(f312(f314(x93811),f312(f246(x93811,f859(a113,a113)),f312(f254(x93811,x93812),x93813))),f312(f168(x93811),f312(f312(f150(f859(a113,x93811),x93811),f248(a113,x93811)),x93812))))+~P22(f312(f312(f228(a113),f2(a113)),f312(f162(a113),f312(f312(f150(f859(a113,x93811),a113),f246(a113,x93811)),x93812))))
% 173.53/173.42 [9401]~P22(f312(f312(f227(f860(f859(x94011,x94011),a845)),x94012),f312(f312(f247(x94011,x94011),x94013),f312(f16(f860(x94011,a845),x94011),x94013))))+P22(f312(f312(f227(f860(f859(x94011,x94011),a845)),f312(f312(f267(x94011,x94011,x94011),x94012),f287(x94011,x94012))),f312(f312(f247(x94011,x94011),x94013),f312(f16(f860(x94011,a845),x94011),x94013))))
% 173.53/173.42 [9692]~P41(x96921,x96922)+~P22(f312(f312(f314(f859(x96921,x96921)),f312(f312(f239(x96921,x96921),f312(x96923,f312(a126,f572(x96922,x96921,x96923)))),f312(x96923,f572(x96922,x96921,x96923)))),x96922))
% 173.53/173.42 [9693]~P41(x96931,x96932)+~P22(f312(f312(f314(f859(x96931,x96931)),f312(f312(f239(x96931,x96931),f312(x96933,f312(a126,f748(x96933,x96932,x96931)))),f312(x96933,f748(x96933,x96932,x96931)))),x96932))
% 173.53/173.42 [9957]P22(f312(f312(f227(f860(f859(f860(x99571,a845),f860(x99571,a845)),a845)),f312(f312(f267(f860(x99571,a845),f860(x99571,a845),f860(x99571,a845)),f305(x99571,x99572)),f312(f312(f124(f860(f859(f860(x99571,a845),f860(x99571,a845)),a845)),f305(x99571,x99573)),f312(f312(f289(f859(f860(x99571,a845),f860(x99571,a845))),f312(f312(f239(f860(x99571,a845),f860(x99571,a845)),f189(f860(x99571,a845))),f189(f860(x99571,a845)))),f189(f860(f859(f860(x99571,a845),f860(x99571,a845)),a845)))))),f305(x99571,x99572)))+~P22(f312(f312(f227(f860(f859(x99571,x99571),a845)),f312(f312(f267(x99571,x99571,x99571),x99572),x99573)),x99572))
% 173.53/173.42 [9958]P22(f312(f312(f227(f860(f859(f860(x99581,a845),f860(x99581,a845)),a845)),f312(f312(f267(f860(x99581,a845),f860(x99581,a845),f860(x99581,a845)),f303(x99581,x99582)),f312(f312(f124(f860(f859(f860(x99581,a845),f860(x99581,a845)),a845)),f303(x99581,x99583)),f312(f312(f289(f859(f860(x99581,a845),f860(x99581,a845))),f312(f312(f239(f860(x99581,a845),f860(x99581,a845)),f189(f860(x99581,a845))),f189(f860(x99581,a845)))),f189(f860(f859(f860(x99581,a845),f860(x99581,a845)),a845)))))),f303(x99581,x99582)))+~P22(f312(f312(f227(f860(f859(x99581,x99581),a845)),f312(f312(f267(x99581,x99581,x99581),x99582),x99583)),x99582))
% 173.53/173.42 [7149]~P22(f312(f312(f227(a852),x71492),x71491))+E(f312(f312(f21(a852),f312(a126,f312(f312(f21(a852),x71491),x71492))),x71493),f312(f312(f21(a852),f312(a126,x71491)),f312(f312(f89(a852),x71492),x71493)))
% 173.53/173.42 [7384]E(f312(f312(f90(a852),f312(f117(a852),x73841)),f312(f312(f90(a852),f312(f117(a852),x73842)),x73843)),f312(f312(f90(a852),f312(f117(a852),f312(f312(f90(a1),x73841),x73842))),x73843))+P22(f312(f312(f228(a1),x73841),a92))
% 173.53/173.42 [7842]~P22(f312(f312(f227(a852),x78423),x78422))+P22(f312(f312(f227(a852),x78421),f312(f312(f21(a852),f312(f312(f89(a852),x78422),x78421)),x78423)))
% 173.53/173.42 [8048]~P22(f312(f312(f227(a852),x80481),x80482))+E(f312(f312(f129(a852),f135(a852,f312(f282(a852,x80481),x80482))),f135(a852,f312(f282(a852,x80482),f312(f312(f89(a852),x80482),x80483)))),f135(a852,f312(f282(a852,x80481),f312(f312(f89(a852),x80482),x80483))))
% 173.53/173.42 [8310]~P22(f312(f70(x83101),x83102))+E(f312(a126,f312(f53(x83101),f312(f312(f21(f860(x83101,a845)),x83102),f312(f312(f289(x83101),x83103),f189(f860(x83101,a845)))))),f312(f53(x83101),f312(f312(f289(x83101),x83103),x83102)))
% 173.53/173.42 [8361]~P22(f312(f70(x83611),x83612))+E(f312(f312(f89(a852),f87(a852)),f312(f53(x83611),f312(f312(f21(f860(x83611,a845)),x83612),f312(f312(f289(x83611),x83613),f189(f860(x83611,a845)))))),f312(f53(x83611),f312(f312(f289(x83611),x83613),x83612)))
% 173.53/173.42 [8543]E(f312(f312(f21(a852),f312(f53(x85431),x85432)),f312(f53(x85431),f312(f312(f115(f860(x85431,a845)),x85432),x85433))),f312(f53(x85431),f312(f312(f21(f860(x85431,a845)),x85432),x85433)))+~P22(f312(f70(x85431),f312(f312(f115(f860(x85431,a845)),x85432),x85433)))
% 173.53/173.42 [8769]~P32(f312(x87692,f400(x87692,x87693,x87691)))+E(f312(f114(a1),f312(f312(f9(x87691,a852),f312(f312(f8(a1,a852,x87691),a118),x87692)),x87693)),f312(f312(f9(x87691,a1),x87692),x87693))
% 173.53/173.42 [8770]~P32(f312(x87702,f497(x87702,x87703,x87701)))+E(f312(f114(a1),f312(f312(f6(x87701,a852),f312(f312(f8(a1,a852,x87701),a118),x87702)),x87703)),f312(f312(f6(x87701,a1),x87702),x87703))
% 173.53/173.42 [8815]~P22(f312(f70(x88151),x88153))+P22(f312(f312(f227(a852),f312(f312(f21(a852),f312(f53(x88151),x88152)),f312(f53(x88151),x88153))),f312(f53(x88151),f312(f312(f21(f860(x88151,a845)),x88152),x88153))))
% 173.53/173.42 [8842]P22(f312(f312(f314(x88421),f400(x88422,x88423,x88421)),x88423))+E(f312(f114(a1),f312(f312(f9(x88421,a852),f312(f312(f8(a1,a852,x88421),a118),x88422)),x88423)),f312(f312(f9(x88421,a1),x88422),x88423))
% 173.53/173.42 [8843]P22(f312(f312(f314(x88431),f497(x88432,x88433,x88431)),x88433))+E(f312(f114(a1),f312(f312(f6(x88431,a852),f312(f312(f8(a1,a852,x88431),a118),x88432)),x88433)),f312(f312(f6(x88431,a1),x88432),x88433))
% 173.53/173.42 [8915]E(f94(x89151,f312(f312(f7(x89151,f860(x89151,a845),a845),f314(x89151)),f312(f312(f21(f860(x89151,a845)),x89152),f312(f312(f289(x89151),x89153),f189(f860(x89151,a845)))))),f242(x89151,x89153,x89152))+P22(f312(f312(f227(f860(x89151,a845)),x89152),f312(f312(f289(x89151),x89153),f189(f860(x89151,a845)))))
% 173.53/173.42 [9256]E(f312(f312(f150(f853(x92561),x92561),f312(f312(f7(f853(x92561),a852,x92561),f161(x92561)),x92562)),f312(f132(f853(x92561),f312(f312(f8(a852,a845,f853(x92561)),f312(f228(a852),x92562)),f190(f853(x92561)))),x92563)),f312(f312(f161(f853(x92561)),f175(x92561,x92563)),x92562))+~P22(f312(f312(f228(a852),x92562),f312(f190(f853(f853(x92561))),f175(x92561,x92563))))
% 173.53/173.42 [9331]E(f312(f132(x93311,x93312),x93313),f172(x93311,x93312,x93313))+P22(f312(f312(f314(x93311),f670(x93313,x93312,x93311)),f312(f168(x93311),f312(f312(f134(x93311),f312(f190(f853(x93311)),f172(x93311,x93312,x93313))),x93313))))
% 173.53/173.42 [9469]E(f312(f312(f134(x94691),f312(f190(f853(x94691)),f172(x94691,x94692,x94693))),x94693),f127(x94691))+~P22(f312(x94692,f312(f137(x94691),f312(f312(f134(x94691),f312(f190(f853(x94691)),f172(x94691,x94692,x94693))),x94693))))
% 173.53/173.42 [9558]~P22(f312(f312(f314(f859(x95581,x95581)),x95582),f287(x95581,x95583)))+P22(f312(f312(f314(f859(x95581,x95581)),x95582),f312(f312(f50(a852,f860(f859(x95581,x95581),a845)),f235(f860(a852,a845))),f312(f312(f7(a852,f860(f859(x95581,x95581),a845),f860(f859(x95581,x95581),a845)),f184(f859(x95581,x95581),a845)),x95583))))
% 173.53/173.42 [9614]~P22(f312(f312(f227(f860(x96141,a845)),f312(f312(f50(a852,f860(x96141,a845)),f312(f282(a852,f2(a852)),f489(x96143,x96142,x96141))),x96142)),x96143))+P22(f312(f312(f227(f860(x96141,a845)),f312(f312(f50(a852,f860(x96141,a845)),f235(f860(a852,a845))),x96142)),x96143))
% 173.53/173.42 [9671]~P22(f312(f312(f228(a1),f2(a1)),x96713))+P22(f312(f312(f228(a1),x96711),f312(f312(f89(a1),x96712),f312(f312(f90(a1),f312(f312(f89(a1),f312(f84(a1),f312(f312(f21(a1),x96712),x96711))),f87(a1))),x96713))))
% 173.53/173.42 [9681]~P41(x96811,f312(f312(f124(f860(f859(x96811,x96811),a845)),x96812),x96813))+P41(x96811,f312(f312(f124(f860(f859(x96811,x96811),a845)),f312(f312(f124(f860(f859(x96811,x96811),a845)),f312(f312(f267(x96811,x96811,x96811),x96812),x96812)),f312(f312(f267(x96811,x96811,x96811),x96813),x96812))),x96813))
% 173.53/173.42 [9762]P41(x97621,f312(f312(f124(f860(f859(x97621,x97621),a845)),x97622),x97623))+~P41(x97621,f312(f312(f124(f860(f859(x97621,x97621),a845)),f312(f312(f124(f860(f859(x97621,x97621),a845)),f312(f312(f267(x97621,x97621,x97621),x97622),x97622)),f312(f312(f267(x97621,x97621,x97621),x97623),x97622))),x97623))
% 173.53/173.42 [9336]~P111(x93361)+E(f312(f116(x93361),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x93362),x93363)),f189(f860(f859(a852,a852),a845)))))),f312(f312(f21(x93361),f312(f114(x93361),x93362)),f312(f114(x93361),x93363)))
% 173.53/173.42 [9417]P22(f312(x94173,x94172))+E(f312(f233(x94171),f312(f312(f18(x94171,a845,a845),f312(f312(f8(a845,f860(a845,a845),x94171),a310),f312(f312(f7(x94171,x94171,a845),a309),x94172))),x94173)),f189(f860(x94171,a845)))
% 173.53/173.42 [9419]~P22(f312(x94193,x94192))+E(f312(f233(x94191),f312(f312(f18(x94191,a845,a845),f312(f312(f8(a845,f860(a845,a845),x94191),a310),f312(f312(f7(x94191,x94191,a845),a309),x94192))),x94193)),f312(f312(f289(x94191),x94192),f189(f860(x94191,a845))))
% 173.53/173.42 [9790]~P22(f312(f312(f228(a1),f2(a1)),x97903))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x97901),f312(f312(f90(a1),f312(f312(f89(a1),f312(f84(a1),f312(f312(f21(a1),x97901),x97902))),f87(a1))),x97903))),x97902))
% 173.53/173.42 [10020]~P22(f312(f312(f314(x100201),x100203),f301(x100201,x100202)))+P22(f312(f300(x100201,f312(f312(f7(x100201,f860(f859(x100201,x100201),a845),f860(x100201,a845)),f312(f312(f8(f860(x100201,f860(f860(f859(x100201,x100201),a845),a845)),f860(f860(f859(x100201,x100201),a845),f860(x100201,a845)),x100201),f7(x100201,f860(f859(x100201,x100201),a845),a845)),f312(f312(f8(f860(x100201,f859(x100201,x100201)),f860(x100201,f860(f860(f859(x100201,x100201),a845),a845)),x100201),f312(f8(f859(x100201,x100201),f860(f860(f859(x100201,x100201),a845),a845),x100201),f314(f859(x100201,x100201)))),f239(x100201,x100201)))),x100202)),x100203))
% 173.53/173.42 [10032]P22(f312(f312(f314(x100321),x100322),f301(x100321,x100323)))+~P22(f312(f300(x100321,f312(f312(f7(x100321,f860(f859(x100321,x100321),a845),f860(x100321,a845)),f312(f312(f8(f860(x100321,f860(f860(f859(x100321,x100321),a845),a845)),f860(f860(f859(x100321,x100321),a845),f860(x100321,a845)),x100321),f7(x100321,f860(f859(x100321,x100321),a845),a845)),f312(f312(f8(f860(x100321,f859(x100321,x100321)),f860(x100321,f860(f860(f859(x100321,x100321),a845),a845)),x100321),f312(f8(f859(x100321,x100321),f860(f860(f859(x100321,x100321),a845),a845),x100321),f314(f859(x100321,x100321)))),f239(x100321,x100321)))),x100323)),x100322))
% 173.53/173.42 [9612]~P22(f312(f70(x96121),f312(f233(x96121),x96123)))+P22(f312(f70(x96121),f312(f233(x96121),f312(f312(f18(x96121,a845,a845),f312(f312(f8(a845,f860(a845,a845),x96121),a310),x96122)),x96123))))
% 173.53/173.42 [9613]~P22(f312(f70(x96131),f312(f233(x96131),x96132)))+P22(f312(f70(x96131),f312(f233(x96131),f312(f312(f18(x96131,a845,a845),f312(f312(f8(a845,f860(a845,a845),x96131),a310),x96132)),x96133))))
% 173.53/173.42 [9711]P22(f312(f70(x97111),f312(f233(x97111),x97112)))+~P22(f312(f70(x97111),f312(f233(x97111),f312(f312(f18(x97111,a845,a845),f312(f312(f8(a845,f860(a845,a845),x97111),a311),x97113)),x97112))))
% 173.53/173.42 [9712]P22(f312(f70(x97121),f312(f233(x97121),x97122)))+~P22(f312(f70(x97121),f312(f233(x97121),f312(f312(f18(x97121,a845,a845),f312(f312(f8(a845,f860(a845,a845),x97121),a311),x97122)),x97123))))
% 173.53/173.42 [10007]~P22(f312(f70(x100071),x100072))+P22(f312(f70(f853(x100071)),f312(f233(f853(x100071)),f312(f312(f18(f853(x100071),a845,a845),f312(f312(f8(a845,f860(a845,a845),f853(x100071)),a310),f312(f312(f7(f853(x100071),f860(x100071,a845),a845),f312(f312(f8(f860(x100071,a845),f860(f860(x100071,a845),a845),f853(x100071)),f227(f860(x100071,a845))),f168(x100071))),x100072))),f312(f312(f7(f853(x100071),a852,a845),f312(f312(f8(a852,f860(a852,a845),f853(x100071)),a309),f190(f853(x100071)))),x100073)))))
% 173.53/173.42 [10008]~P22(f312(f70(x100081),x100082))+P22(f312(f70(f853(x100081)),f312(f233(f853(x100081)),f312(f312(f18(f853(x100081),a845,a845),f312(f312(f8(a845,f860(a845,a845),f853(x100081)),a310),f312(f312(f7(f853(x100081),f860(x100081,a845),a845),f312(f312(f8(f860(x100081,a845),f860(f860(x100081,a845),a845),f853(x100081)),f227(f860(x100081,a845))),f168(x100081))),x100082))),f312(f312(f7(f853(x100081),a852,a845),f312(f312(f8(a852,f860(a852,a845),f853(x100081)),f227(a852)),f190(f853(x100081)))),x100083)))))
% 173.53/173.42 [9727]~P107(x97271)+E(f312(f312(f240(x97271),x97272),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x97273)),f312(f312(f90(x97271),f312(f312(f240(x97271),x97272),x97273)),f312(f312(f240(x97271),x97272),x97273)))
% 173.53/173.42 [9767]~P78(x97671)+E(f312(f312(f240(x97671),f312(f312(f240(x97671),x97672),x97673)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f240(x97671),x97672),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x97673)))
% 173.53/173.42 [9818]~P111(x98181)+E(f312(f312(f240(x98181),f312(f88(x98181),x98182)),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98183)),f312(f312(f240(x98181),x98182),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98183)))
% 173.53/173.42 [9964]~P112(x99641)+P22(f312(f312(f227(x99641),f2(x99641)),f312(f312(f89(x99641),f312(f312(f240(x99641),x99642),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99641),x99643),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))))
% 173.53/173.42 [9828]~P107(x98281)+E(f312(f312(f240(x98281),x98282),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98283))),f312(f312(f90(x98281),x98282),f312(f312(f90(x98281),f312(f312(f240(x98281),x98282),x98283)),f312(f312(f240(x98281),x98282),x98283))))
% 173.53/173.42 [9881]~P78(x98811)+E(f312(f312(f90(x98811),x98812),f312(f312(f240(x98811),f312(f312(f240(x98811),x98812),x98813)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x98811),x98812),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98813))))
% 173.53/173.42 [9920]~P112(x99201)+P22(f312(f312(f227(x99201),f2(x99201)),f312(f312(f240(x99201),x99202),f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99203))))
% 173.53/173.42 [9985]~P90(x99851)+E(f312(f312(f89(x99851),f312(f312(f89(x99851),f312(f312(f240(x99851),x99852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99851),x99853),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f312(f312(f90(x99851),f312(f312(f90(x99851),f312(f117(x99851),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99852)),x99853)),f312(f312(f240(x99851),f312(f312(f89(x99851),x99852),x99853)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.42 [9986]~P90(x99861)+E(f312(f312(f21(x99861),f312(f312(f89(x99861),f312(f312(f240(x99861),x99862),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99861),x99863),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f312(f312(f90(x99861),f312(f312(f90(x99861),f312(f117(x99861),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x99862)),x99863)),f312(f312(f240(x99861),f312(f312(f21(x99861),x99862),x99863)),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.42 [10089]~P34(x100891,x100892,x100893)+P22(f107(x100891,a845,f312(f312(f8(f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,a845))),f860(a846,f860(f860(x100891,f860(a847,a845)),a845)),f860(x100891,f860(a847,a845))),f312(f8(f860(f860(x100891,f860(a847,a845)),f860(x100891,a845)),f860(f860(x100891,f860(a847,a845)),a845),a846),f312(f8(f860(x100891,a845),a845,f860(x100891,f860(a847,a845))),f97(x100891)))),f312(f312(f8(f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,a845))),f860(x100891,f860(a847,a845))),f312(f8(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,a845)),a846),f312(f8(f860(x100891,f860(a847,a845)),f860(x100891,a845),f860(x100891,f860(a847,a845))),f312(f8(f860(a847,a845),a845,x100891),f97(a847))))),f312(f312(f7(f860(x100891,f860(a847,a845)),f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))))),f312(f312(f8(f860(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f860(f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f860(a846,f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))))),f860(x100891,f860(a847,a845))),f8(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),a846)),f312(f312(f8(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f860(x100891,f860(a847,a845))),f8(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845)))),f312(f312(f8(f860(x100891,f860(f860(a847,a845),f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f860(x100891,f860(a847,a845))),f18(x100891,f860(a847,a845),f860(a847,a845))),f312(f312(f8(f860(x100891,f860(a847,f860(a845,a845))),f860(x100891,f860(f860(a847,a845),f860(a847,a845))),f860(x100891,f860(a847,a845))),f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),x100891),f18(a847,a845,a845))),f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),x100891),f312(f8(a845,f860(a845,a845),a847),a315))))))),f312(f312(f8(f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,f860(a847,a845)))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),a846),f312(f8(f860(x100891,f860(a847,f860(a847,a845))),f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,a845))),f312(f8(f860(a847,f860(a847,a845)),f860(a847,a845),x100891),f312(f8(f860(a847,a845),a845,a847),f97(a847))))),f312(f312(f8(f860(f860(a847,a845),f860(a847,f860(a847,a845))),f860(f860(x100891,f860(a847,a845)),f860(x100891,f860(a847,f860(a847,a845)))),a846),f8(f860(a847,a845),f860(a847,f860(a847,a845)),x100891)),f312(f312(f8(f860(a847,f860(f860(a847,a845),f860(a847,a845))),f860(f860(a847,a845),f860(a847,f860(a847,a845))),a846),f7(a847,f860(a847,a845),f860(a847,a845))),f312(f312(f8(f860(a847,f860(a847,f860(a845,a845))),f860(a847,f860(f860(a847,a845),f860(a847,a845))),a846),f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),a847),f18(a847,a845,a845))),f312(f312(f8(f860(a847,f860(a847,a845)),f860(a847,f860(a847,f860(a845,a845))),a846),f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),a847),f312(f8(a845,f860(a845,a845),a847),a315))),f312(f312(f7(a846,a852,f860(a847,f860(a847,a845))),f312(f312(f8(f860(a847,f860(a852,f860(a847,a845))),f860(a852,f860(a847,f860(a847,a845))),a846),f7(a847,a852,f860(a847,a845))),a198)),x100892))))))))),x100893))
% 173.53/173.42 [10091]P34(x100911,x100912,x100913)+~P22(f107(x100911,a845,f312(f312(f8(f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,a845))),f860(a846,f860(f860(x100911,f860(a847,a845)),a845)),f860(x100911,f860(a847,a845))),f312(f8(f860(f860(x100911,f860(a847,a845)),f860(x100911,a845)),f860(f860(x100911,f860(a847,a845)),a845),a846),f312(f8(f860(x100911,a845),a845,f860(x100911,f860(a847,a845))),f97(x100911)))),f312(f312(f8(f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,a845))),f860(x100911,f860(a847,a845))),f312(f8(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,a845)),a846),f312(f8(f860(x100911,f860(a847,a845)),f860(x100911,a845),f860(x100911,f860(a847,a845))),f312(f8(f860(a847,a845),a845,x100911),f97(a847))))),f312(f312(f7(f860(x100911,f860(a847,a845)),f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))))),f312(f312(f8(f860(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f860(f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f860(a846,f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))))),f860(x100911,f860(a847,a845))),f8(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),a846)),f312(f312(f8(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f860(x100911,f860(a847,a845))),f8(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845)))),f312(f312(f8(f860(x100911,f860(f860(a847,a845),f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f860(x100911,f860(a847,a845))),f18(x100911,f860(a847,a845),f860(a847,a845))),f312(f312(f8(f860(x100911,f860(a847,f860(a845,a845))),f860(x100911,f860(f860(a847,a845),f860(a847,a845))),f860(x100911,f860(a847,a845))),f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),x100911),f18(a847,a845,a845))),f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),x100911),f312(f8(a845,f860(a845,a845),a847),a315))))))),f312(f312(f8(f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,f860(a847,a845)))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),a846),f312(f8(f860(x100911,f860(a847,f860(a847,a845))),f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,a845))),f312(f8(f860(a847,f860(a847,a845)),f860(a847,a845),x100911),f312(f8(f860(a847,a845),a845,a847),f97(a847))))),f312(f312(f8(f860(f860(a847,a845),f860(a847,f860(a847,a845))),f860(f860(x100911,f860(a847,a845)),f860(x100911,f860(a847,f860(a847,a845)))),a846),f8(f860(a847,a845),f860(a847,f860(a847,a845)),x100911)),f312(f312(f8(f860(a847,f860(f860(a847,a845),f860(a847,a845))),f860(f860(a847,a845),f860(a847,f860(a847,a845))),a846),f7(a847,f860(a847,a845),f860(a847,a845))),f312(f312(f8(f860(a847,f860(a847,f860(a845,a845))),f860(a847,f860(f860(a847,a845),f860(a847,a845))),a846),f312(f8(f860(a847,f860(a845,a845)),f860(f860(a847,a845),f860(a847,a845)),a847),f18(a847,a845,a845))),f312(f312(f8(f860(a847,f860(a847,a845)),f860(a847,f860(a847,f860(a845,a845))),a846),f312(f8(f860(a847,a845),f860(a847,f860(a845,a845)),a847),f312(f8(a845,f860(a845,a845),a847),a315))),f312(f312(f7(a846,a852,f860(a847,f860(a847,a845))),f312(f312(f8(f860(a847,f860(a852,f860(a847,a845))),f860(a852,f860(a847,f860(a847,a845))),a846),f7(a847,a852,f860(a847,a845))),a198)),x100912))))))))),x100913))
% 173.53/173.42 [4615]E(x46151,x46152)+~E(f36(x46153,x46151),f36(x46154,x46152))
% 173.53/173.42 [4616]E(x46161,x46162)+~E(f36(x46161,x46163),f36(x46162,x46164))
% 173.53/173.42 [4617]E(x46171,x46172)+~E(f35(x46173,x46171),f35(x46174,x46172))
% 173.53/173.42 [4618]E(x46181,x46182)+~E(f35(x46181,x46183),f35(x46182,x46184))
% 173.53/173.42 [4619]E(x46191,x46192)+~E(f28(x46193,x46191),f28(x46194,x46192))
% 173.53/173.42 [4620]E(x46201,x46202)+~E(f28(x46201,x46203),f28(x46202,x46204))
% 173.53/173.42 [7649]P19(x76491,x76492,x76493,x76494)+~E(f802(x76494,x76493,x76492,x76491),f803(x76494,x76493,x76492,x76491))
% 173.53/173.42 [7935]P39(x79351,x79352,x79353,x79354,f127(x79352))+~E(x79354,f127(x79351))
% 173.53/173.42 [7936]P39(x79361,x79362,x79363,f127(x79361),x79364)+~E(x79364,f127(x79362))
% 173.53/173.42 [8154]~P19(x81541,f856(x81542),x81544,f179(x81541,x81542,x81544))+P19(x81541,f856(x81542),f180(x81541,x81542,x81543,x81544),f179(x81541,x81542,x81544))
% 173.53/173.42 [8243]P36(x82431,x82432,x82433,f180(x82431,x82432,x82433,x82434))+~E(f180(x82431,x82432,x82433,x82434),f180(x82431,x82432,x82434,x82433))
% 173.53/173.42 [8340]~P36(x83401,x83402,x83403,f180(x83401,x83402,x83403,x83404))+E(f180(x83401,x83402,x83403,x83404),f180(x83401,x83402,x83404,x83403))
% 173.53/173.42 [8377]~P19(x83771,f856(x83772),f180(x83771,x83772,x83774,x83773),f179(x83771,x83772,x83773))+P19(x83771,f856(x83772),x83773,f179(x83771,x83772,x83773))
% 173.53/173.42 [8498]~P39(x84982,x84983,x84984,x84981,f127(x84983))+E(x84981,f127(x84982))
% 173.53/173.42 [8499]~P39(x84993,x84992,x84994,f127(x84993),x84991)+E(x84991,f127(x84992))
% 173.53/173.42 [4985]~P12(x49853,x49851,x49854)+E(f312(f312(x49851,x49852),x49852),x49852)
% 173.53/173.42 [5274]~E(x52744,f189(f860(x52741,a845)))+E(f312(f290(x52741,x52742,x52743),x52744),f189(f860(x52742,a845)))
% 173.53/173.42 [5543]~E(f312(f290(x55432,x55433,x55434),x55431),f189(f860(x55433,a845)))+E(x55431,f189(f860(x55432,a845)))
% 173.53/173.42 [5813]~P103(x58132)+E(f312(f312(f145(x58131,x58132,x58133),x58134),f127(x58131)),f312(f312(f147(x58131),x58134),f127(x58131)))
% 173.53/173.42 [5849]E(f312(x58491,x58492),f192(x58493))+P22(f312(f312(f314(x58494),x58492),f179(x58494,x58493,x58491)))
% 173.53/173.42 [6168]~E(x61681,f189(f860(x61682,a845)))+~P22(f312(f71(x61682,x61683,x61681),x61684))
% 173.53/173.42 [6190]~P58(x61901,x61903,x61904,x61902)+P22(f312(f70(x61901),x61902))
% 173.53/173.42 [6191]~P58(x61911,x61913,x61912,x61914)+P22(f312(f70(x61911),x61912))
% 173.53/173.42 [6198]~P58(x61982,x61983,x61984,x61981)+~E(x61981,f189(f860(x61982,a845)))
% 173.53/173.42 [6225]~P105(x62251)+E(f312(f312(f115(f860(x62251,a845)),f312(f282(x62251,x62252),x62253)),f283(x62251,x62253,x62254)),f189(f860(x62251,a845)))
% 173.53/173.42 [6252]~P22(f312(f312(x62523,x62524),x62522))+P22(f312(f312(f314(x62521),x62522),f271(x62521,x62523,x62524)))
% 173.53/173.42 [6253]~P22(f312(f312(x62533,x62534),x62532))+P22(f312(f312(f314(x62531),x62532),f272(x62531,x62533,x62534)))
% 173.53/173.42 [6254]~P22(f312(f312(x62543,x62542),x62544))+P22(f312(f312(f314(x62541),x62542),f273(x62541,x62543,x62544)))
% 173.53/173.42 [6255]~P22(f312(f312(x62553,x62552),x62554))+P22(f312(f312(f314(x62551),x62552),f276(x62551,x62553,x62554)))
% 173.53/173.42 [6393]~P105(x63931)+E(f312(f312(f115(f860(x63931,a845)),f285(x63931,x63932,x63933)),f283(x63931,x63933,x63934)),f189(f860(x63931,a845)))
% 173.53/173.42 [6394]~P105(x63941)+E(f312(f312(f115(f860(x63941,a845)),f284(x63941,x63942,x63943)),f285(x63941,x63943,x63944)),f189(f860(x63941,a845)))
% 173.53/173.42 [6395]~P105(x63951)+E(f312(f312(f115(f860(x63951,a845)),f284(x63951,x63952,x63953)),f284(x63951,x63953,x63954)),f189(f860(x63951,a845)))
% 173.53/173.42 [6396]~P105(x63961)+E(f312(f312(f115(f860(x63961,a845)),f283(x63961,x63962,x63963)),f285(x63961,x63963,x63964)),f189(f860(x63961,a845)))
% 173.53/173.42 [6397]~P105(x63971)+E(f312(f312(f115(f860(x63971,a845)),f283(x63971,x63972,x63973)),f284(x63971,x63973,x63974)),f189(f860(x63971,a845)))
% 173.53/173.42 [6430]P22(f312(f312(x64301,x64302),f570(x64302,x64301)))+~P22(f312(f244(x64303,x64304,x64301),x64302))
% 173.53/173.42 [6479]~E(f312(x64791,x64792),f192(x64793))+~P22(f312(f312(f314(x64794),x64792),f179(x64794,x64793,x64791)))
% 173.53/173.42 [6508]~P103(x65082)+E(f312(f168(x65081),f144(x65081,x65082,x65083,x65084)),f312(f168(x65081),x65084))
% 173.53/173.42 [6560]~P23(x65601)+E(f191(x65601,x65602,f312(a126,x65603),x65604),f191(x65601,x65602,x65603,f312(x65602,x65604)))
% 173.53/173.42 [6619]~P22(f312(f312(f314(x66194),x66193),f271(x66194,x66191,x66192)))+P22(f312(f312(x66191,x66192),x66193))
% 173.53/173.42 [6620]~P22(f312(f312(f314(x66204),x66203),f272(x66204,x66201,x66202)))+P22(f312(f312(x66201,x66202),x66203))
% 173.53/173.42 [6621]~P22(f312(f312(f314(x66214),x66212),f273(x66214,x66211,x66213)))+P22(f312(f312(x66211,x66212),x66213))
% 173.53/173.42 [6622]~P22(f312(f312(f314(x66224),x66222),f276(x66224,x66221,x66223)))+P22(f312(f312(x66221,x66222),x66223))
% 173.53/173.42 [6698]E(f312(f53(f858(x66981,x66982)),f298(x66981,x66982,x66983,x66984)),f2(a852))+P22(f312(f70(x66982),x66984))
% 173.53/173.42 [6699]E(f312(f53(f858(x66991,x66992)),f298(x66991,x66992,x66993,x66994)),f2(a852))+P22(f312(f70(x66991),x66993))
% 173.53/173.42 [6899]~P11(x68994,x68991,x68992)+E(f312(f82(x68991,x68991,x68991,f312(x68992,x68993)),f312(x68992,x68993)),f312(x68992,x68993))
% 173.53/173.42 [7686]~P22(f312(x76861,x76864))+P22(f312(x76861,f104(x76862,a852,x76863,x76861)))
% 173.53/173.42 [7769]~E(x77692,x77693)+P22(f312(f312(f314(f859(x77691,x77691)),f312(f312(f239(x77691,x77691),x77692),x77693)),f287(x77691,x77694)))
% 173.53/173.42 [7797]~P19(x77971,x77972,x77973,f235(f860(x77971,a845)))+E(f312(f86(x77971,x77972,f235(f860(x77971,a845)),x77973),f312(x77973,x77974)),x77974)
% 173.53/173.42 [7883]~P22(f312(f312(f314(f853(x78831)),f312(f312(f147(x78831),x78834),x78832)),f157(x78831,x78833)))+P22(f312(f312(f314(f853(x78831)),x78832),f157(x78831,x78833)))
% 173.53/173.42 [7884]~P22(f312(f312(f314(f853(x78841)),f312(f312(f129(x78841),x78844),x78842)),f157(x78841,x78843)))+P22(f312(f312(f314(f853(x78841)),x78842),f157(x78841,x78843)))
% 173.53/173.42 [7885]~P22(f312(f312(f314(f853(x78851)),f312(f312(f129(x78851),x78852),x78854)),f157(x78851,x78853)))+P22(f312(f312(f314(f853(x78851)),x78852),f157(x78851,x78853)))
% 173.53/173.42 [7901]~P103(x79011)+P33(x79011,f312(f312(f150(x79012,x79011),x79013),f144(x79012,x79011,x79013,x79014)))
% 173.53/173.42 [7996]P19(x79964,x79963,x79961,x79962)+E(f312(x79961,f802(x79962,x79961,x79963,x79964)),f312(x79961,f803(x79962,x79961,x79963,x79964)))
% 173.53/173.42 [8012]E(f180(x80121,x80122,x80123,x80124),f180(x80121,x80122,x80124,x80123))+~E(f312(f312(f115(f860(x80121,a845)),f179(x80121,x80122,x80123)),f179(x80121,x80122,x80124)),f189(f860(x80121,a845)))
% 173.53/173.42 [8050]~P36(x80501,x80502,x80503,x80504)+P22(f312(f312(f227(f860(x80501,a845)),f179(x80501,x80502,x80503)),f179(x80501,x80502,x80504)))
% 173.53/173.42 [8116]~P19(x81162,x81161,x81164,x81163)+P19(x81161,x81162,f86(x81162,x81161,x81163,x81164),f312(f290(x81162,x81161,x81164),x81163))
% 173.53/173.42 [8257]P41(f859(x82572,x82574),f262(x82572,x82574,x82571,x82573))+P22(f312(x82571,f575(x82572,x82573,x82574,x82571)))
% 173.53/173.42 [8384]E(x83841,x83842)+~P22(f312(f312(f314(f859(x83843,x83843)),f312(f312(f239(x83843,x83843),x83841),x83842)),f237(x83843,x83844)))
% 173.53/173.42 [8448]~P22(f312(f70(f858(x84483,x84481)),f298(x84483,x84481,x84484,x84482)))+P22(f312(f70(x84481),x84482))
% 173.53/173.42 [8449]~P22(f312(f70(f858(x84491,x84493)),f298(x84491,x84493,x84492,x84494)))+P22(f312(f70(x84491),x84492))
% 173.53/173.42 [8460]P36(x84601,x84602,x84603,x84604)+~E(f312(x84603,f798(x84604,x84603,x84602,x84601)),f312(x84604,f798(x84604,x84603,x84602,x84601)))
% 173.53/173.42 [8624]P41(f859(x86241,x86242),f262(x86241,x86242,x86243,x86244))+~P41(x86242,f312(x86244,f575(x86241,x86244,x86242,x86243)))
% 173.53/173.42 [8767]P36(x87671,x87672,x87673,x87674)+P22(f312(f312(f314(x87671),f798(x87674,x87673,x87672,x87671)),f179(x87671,x87672,x87673)))
% 173.53/173.42 [9182]E(f312(f312(f155(x91821,x91822),f605(x91823,x91824,x91822,x91821)),f606(x91823,x91824,x91822,x91821)),x91824)+~P22(f312(f312(f314(f859(f853(x91821),f853(x91821))),f312(f312(f239(f853(x91821),f853(x91821)),x91822),x91824)),f153(x91821,x91823)))
% 173.53/173.42 [9183]~P22(f312(x91833,x91834))+P22(f312(f312(f227(a852),f312(x91831,f104(x91832,a852,x91831,x91833))),f312(x91831,x91834)))
% 173.53/173.42 [9189]~P22(f312(f312(f314(f859(f853(x91891),f853(x91891))),f312(f312(f239(f853(x91891),f853(x91891)),x91892),x91893)),f141(x91891,x91894)))+P22(f312(f312(f314(f859(f853(x91891),f853(x91891))),f312(f312(f239(f853(x91891),f853(x91891)),x91892),x91893)),f143(x91891,x91894)))
% 173.53/173.42 [9291]P22(f312(f70(x92911),x92912))+~P22(f312(f312(f314(f859(f860(x92911,a845),f860(x92911,a845))),f312(f312(f239(f860(x92911,a845),f860(x92911,a845)),x92913),x92912)),f303(x92911,x92914)))
% 173.53/173.42 [9292]P22(f312(f70(x92921),x92922))+~P22(f312(f312(f314(f859(f860(x92921,a845),f860(x92921,a845))),f312(f312(f239(f860(x92921,a845),f860(x92921,a845)),x92922),x92923)),f303(x92921,x92924)))
% 173.53/173.42 [9295]~E(x92951,f189(f860(x92952,a845)))+~P22(f312(f312(f314(f859(f860(x92952,a845),f860(x92952,a845))),f312(f312(f239(f860(x92952,a845),f860(x92952,a845)),x92953),x92951)),f303(x92952,x92954)))
% 173.53/173.42 [9932]P9(x99321,x99322,x99323,x99324)+~P22(f312(f312(f249(x99321,x99321,a845),f312(f312(f7(x99321,f860(x99321,x99322),f860(x99321,a845)),f312(f312(f8(f860(x99322,a845),f860(f860(x99321,x99322),f860(x99321,a845)),x99321),f8(x99322,a845,x99321)),f312(f312(f8(x99322,f860(x99322,a845),x99321),a309),x99324))),x99324)),f413(x99324,x99323,x99322,x99321)))
% 173.53/173.42 [4893]~E(x48934,f192(x48931))+E(f312(f312(f193(x48931,x48932),x48933),x48934),f192(x48932))
% 173.53/173.42 [4894]~E(x48944,f127(x48941))+E(f312(f312(f150(x48941,x48942),x48943),x48944),f127(x48942))
% 173.53/173.42 [4895]~E(x48952,f127(x48951))+E(f312(f312(f155(x48951,x48952),x48953),x48954),f127(x48951))
% 173.53/173.42 [5129]E(x51291,f192(x51292))+~E(f312(f312(f193(x51292,x51293),x51294),x51291),f192(x51293))
% 173.53/173.42 [5130]E(x51301,f127(x51302))+~E(f312(f312(f150(x51302,x51303),x51304),x51301),f127(x51303))
% 173.53/173.42 [5131]E(x51311,f127(x51312))+~E(f312(f312(f155(x51312,x51311),x51313),x51314),f127(x51312))
% 173.53/173.42 [5162]E(x51621,x51622)+~E(f312(f312(f129(x51623),x51624),x51621),f312(f312(f129(x51623),x51624),x51622))
% 173.53/173.42 [5163]E(x51631,x51632)+~E(f312(f312(f129(x51633),x51631),x51634),f312(f312(f129(x51633),x51632),x51634))
% 173.53/173.42 [5308]P22(f312(x53083,x53082))+E(f166(x53081,x53082,f312(f132(x53081,x53083),x53084)),f312(f132(x53081,x53083),x53084))
% 173.53/173.42 [5310]~P22(f312(x53102,x53103))+P38(x53101,x53102,f312(f312(f147(x53101),x53103),x53104))
% 173.53/173.42 [5319]E(x53191,x53192)+~E(f135(a852,f312(f282(a852,x53191),x53193)),f312(f312(f147(a852),x53192),x53194))
% 173.53/173.42 [5367]~P20(x53672,x53673)+P20(x53671,f312(f312(f83(x53672,x53671),x53673),x53674))
% 173.53/173.42 [5368]~P41(x53682,x53683)+P41(x53681,f312(f312(f266(x53682,x53681),x53683),x53684))
% 173.53/173.42 [5494]~P38(x54941,x54942,x54944)+P38(x54941,x54942,f312(f312(f147(x54941),x54943),x54944))
% 173.53/173.42 [5495]~P38(x54951,x54952,x54954)+P38(x54951,x54952,f312(f312(f129(x54951),x54953),x54954))
% 173.53/173.42 [5496]~P38(x54961,x54962,x54963)+P38(x54961,x54962,f312(f312(f129(x54961),x54963),x54964))
% 173.53/173.42 [5587]~E(x55871,f127(x55872))+~E(f312(f312(f129(x55872),x55873),f312(f312(f147(x55872),x55874),f127(x55872))),x55871)
% 173.53/173.42 [5617]E(f128(x56171,x56172),x56173)+~E(f312(f312(f129(x56171),x56173),f312(f312(f147(x56171),x56174),f127(x56171))),x56172)
% 173.53/173.42 [5618]E(f140(x56181,x56182),x56183)+~E(f312(f312(f129(x56181),x56184),f312(f312(f147(x56181),x56183),f127(x56181))),x56182)
% 173.53/173.42 [5722]~E(f135(a852,f312(f282(a852,x57221),x57222)),f312(f312(f147(a852),x57223),x57224))+P22(f312(f312(f228(a852),x57221),x57222))
% 173.53/173.42 [5924]E(x59241,f312(f312(f129(x59242),f312(f165(x59242),x59243)),f312(f312(f147(x59242),x59244),f127(x59242))))+~E(f312(f165(x59242),x59241),f312(f312(f147(x59242),x59244),x59243))
% 173.53/173.42 [6087]~P105(x60871)+E(f312(f312(f115(f860(x60871,a845)),f312(f282(x60871,x60872),x60873)),f312(f282(x60871,x60873),x60874)),f189(f860(x60871,a845)))
% 173.53/173.42 [6124]~P26(x61241)+E(f312(f162(x61241),f312(f312(f150(a1,x61241),x61242),f174(x61243,x61244))),f312(f312(f6(a1,x61241),x61242),f312(f168(a1),f174(x61243,x61244))))
% 173.53/173.42 [6125]~P26(x61251)+E(f312(f312(f6(a1,x61251),x61252),f312(f168(a1),f174(x61253,x61254))),f312(f162(x61251),f312(f312(f150(a1,x61251),x61252),f174(x61253,x61254))))
% 173.53/173.42 [6267]~E(x62672,f312(f312(f129(x62671),f312(f165(x62671),x62674)),f312(f312(f147(x62671),x62673),f127(x62671))))+E(f312(f165(x62671),x62672),f312(f312(f147(x62671),x62673),x62674))
% 173.53/173.42 [6283]~P14(x62832,x62833,x62834,x62831)+E(f312(x62831,f189(f860(x62832,a845))),f39(x62833))
% 173.53/173.42 [6304]~P105(x63041)+E(f312(f312(f115(f860(x63041,a845)),f285(x63041,x63042,x63043)),f312(f282(x63041,x63043),x63044)),f189(f860(x63041,a845)))
% 173.53/173.42 [6509]E(x65091,f189(f860(x65092,a845)))+~E(f298(x65093,x65092,x65094,x65091),f189(f860(f858(x65093,x65092),a845)))
% 173.53/173.42 [6510]E(x65101,f189(f860(x65102,a845)))+~E(f298(x65102,x65103,x65101,x65104),f189(f860(f858(x65102,x65103),a845)))
% 173.53/173.42 [6582]~P103(x65822)+E(f312(f190(f853(x65821)),f144(x65821,x65822,x65823,x65824)),f312(f190(f853(x65821)),x65824))
% 173.53/173.42 [6595]~P22(f312(f245(x65953,x65954,x65951),x65952))+P22(f312(f312(x65951,f555(x65952,x65951)),x65952))
% 173.53/173.42 [6632]~P22(f312(f70(x66322),x66324))+P22(f312(f70(x66321),f312(f290(x66322,x66321,x66323),x66324)))
% 173.53/173.42 [6856]~P19(x68562,x68561,x68563,x68564)+E(f312(f53(x68561),f312(f290(x68562,x68561,x68563),x68564)),f312(f53(x68562),x68564))
% 173.53/173.42 [6874]E(f312(f290(x68741,x68742,x68743),f312(f291(x68741,x68742,x68743),x68744)),x68744)+~E(f312(f290(x68741,x68742,x68743),f235(f860(x68741,a845))),f235(f860(x68742,a845)))
% 173.53/173.42 [7279]~P19(x72791,x72792,x72793,f235(f860(x72791,a845)))+E(f312(f291(x72791,x72792,x72793),f312(f290(x72791,x72792,x72793),x72794)),x72794)
% 173.53/173.42 [7607]P22(f312(x76071,x76072))+~P22(f312(f312(f314(x76073),x76072),f312(f168(x76073),f172(x76073,x76071,x76074))))
% 173.53/173.42 [7718]~P22(f312(f312(f314(f853(x77181)),f312(f312(f147(x77181),x77182),x77184)),f157(x77181,x77183)))+P22(f312(f312(f314(x77181),x77182),x77183))
% 173.53/173.42 [7838]~P22(f312(f312(f314(x78381),x78382),f312(f168(x78381),f166(x78381,x78384,x78383))))+P22(f312(f312(f314(x78381),x78382),f312(f168(x78381),x78383)))
% 173.53/173.42 [7840]~P22(f312(f312(f314(x78401),x78402),f312(f168(x78401),f170(x78401,x78403,x78404))))+P22(f312(f312(f314(x78401),x78402),f312(f168(x78401),x78403)))
% 173.53/173.42 [7841]~P22(f312(f312(f314(x78411),x78412),f312(f168(x78411),f172(x78411,x78414,x78413))))+P22(f312(f312(f314(x78411),x78412),f312(f168(x78411),x78413)))
% 173.53/173.42 [7851]E(f312(f190(f853(x78511)),x78512),x78513)+~P22(f312(f312(f314(f853(x78511)),x78512),f312(f168(f853(x78511)),f63(x78511,x78513,x78514))))
% 173.53/173.42 [7947]P22(f312(x79473,x79472))+E(f312(f132(x79471,f312(f312(f8(a845,a845,x79471),a307),f312(a309,x79472))),f312(f132(x79471,x79473),x79474)),f312(f132(x79471,x79473),x79474))
% 173.53/173.42 [8066]E(f312(f312(f161(x80661),f172(x80661,x80662,x80663)),x80664),f312(f312(f161(x80661),x80663),x80664))+~P22(f312(f312(f228(a852),x80664),f312(f190(f853(x80661)),f172(x80661,x80662,x80663))))
% 173.53/173.42 [8152]~P26(x81521)+E(f312(f312(f6(a852,x81521),f312(f312(f8(a852,x81521,a852),x81522),a126)),f312(f282(a852,x81523),x81524)),f312(f312(f6(a852,x81521),x81522),f312(f282(a852,f312(a126,x81523)),f312(a126,x81524))))
% 173.53/173.42 [8161]~P26(x81611)+E(f312(f312(f6(a852,x81611),f312(f312(f8(a852,x81611,a852),x81612),a126)),f283(a852,x81613,x81614)),f312(f312(f6(a852,x81611),x81612),f283(a852,f312(a126,x81613),f312(a126,x81614))))
% 173.53/173.42 [8293]~P19(x82931,x82933,x82934,f235(f860(x82931,a845)))+P19(x82931,f860(x82932,x82933),f312(f312(f8(x82933,f860(x82932,x82933),x82931),f16(x82933,x82932)),x82934),f235(f860(x82931,a845)))
% 173.53/173.42 [8392]~P19(x83922,x83921,x83924,x83923)+E(f312(f290(x83921,x83922,f86(x83922,x83921,x83923,x83924)),f312(f290(x83922,x83921,x83924),x83923)),x83923)
% 173.53/173.42 [8450]~P22(f312(f312(f314(f859(x84501,x84501)),f312(f312(f239(x84501,x84501),x84502),x84504)),f237(x84501,x84503)))+P22(f312(f312(f314(x84501),x84502),x84503))
% 173.53/173.42 [8539]E(f312(f312(f312(f81(x85391,f856(x85392)),f312(f16(f856(x85392),x85391),f192(x85392))),x85393),f312(f219(x85392),f757(x85393,x85394,x85392,x85391))),x85394)+~E(f179(x85391,x85392,x85394),f312(f312(f289(x85391),x85393),f189(f860(x85391,a845))))
% 173.53/173.42 [8661]~E(f312(f312(f6(x86611,a852),x86614),x86613),f312(a126,x86612))+P22(f312(f312(f314(x86611),f719(x86612,x86613,x86614,x86611)),x86613))
% 173.53/173.42 [8680]~E(f312(f312(f6(x86804,a852),x86801),x86803),f312(a126,x86802))+P22(f312(f312(f228(a852),f2(a852)),f312(x86801,f719(x86802,x86803,x86801,x86804))))
% 173.53/173.42 [8691]~P22(f312(f70(x86912),x86914))+P22(f312(f312(f227(a852),f312(f53(x86911),f312(f290(x86912,x86911,x86913),x86914))),f312(f53(x86912),x86914)))
% 173.53/173.42 [8699]P19(x86991,x86992,x86993,x86994)+P22(f312(f312(f314(x86991),f802(x86994,x86993,x86992,x86991)),x86994))
% 173.53/173.42 [8700]P19(x87001,x87002,x87003,x87004)+P22(f312(f312(f314(x87001),f803(x87004,x87003,x87002,x87001)),x87004))
% 173.53/173.42 [8760]P9(x87601,x87602,x87603,x87604)+P22(f312(f312(f314(f859(x87601,x87601)),f413(x87604,x87603,x87602,x87601)),x87603))
% 173.53/173.42 [8819]P22(f312(x88191,x88192))+~P22(f312(x88191,f312(f312(f239(x88193,x88194),f343(x88194,x88193,x88191)),f344(x88194,x88193,x88191))))
% 173.53/173.42 [8836]E(f312(f190(f853(x88361)),x88362),f312(f190(f853(x88361)),x88363))+~P22(f312(f312(f314(f859(f853(x88361),f853(x88361))),f312(f312(f239(f853(x88361),f853(x88361)),x88362),x88363)),f141(x88361,x88364)))
% 173.53/173.42 [8839]E(f312(f190(f853(x88391)),x88392),f312(f190(f853(x88391)),x88393))+~P22(f312(f312(f314(f859(f853(x88391),f853(x88391))),f312(f312(f239(f853(x88391),f853(x88391)),x88392),x88393)),f154(x88391,x88394)))
% 173.53/173.42 [8840]E(f312(f190(f853(x88401)),x88402),f312(f190(f853(x88401)),x88403))+~P22(f312(f312(f314(f859(f853(x88401),f853(x88401))),f312(f312(f239(f853(x88401),f853(x88401)),x88402),x88403)),f153(x88401,x88404)))
% 173.53/173.42 [8919]P22(f312(f312(f227(a852),f151(x89191,x89192,x89193)),f151(x89191,x89194,x89193)))+P22(f312(f312(f314(x89191),f603(x89194,x89192,x89193,x89191)),f312(f168(x89191),x89193)))
% 173.53/173.42 [8922]E(f312(f190(f853(x89221)),x89222),f312(f190(f853(x89221)),x89223))+~P22(f312(f312(f314(f859(f853(x89221),f853(x89221))),f312(f312(f239(f853(x89221),f853(x89221)),x89222),x89223)),f287(f853(x89221),f153(x89221,x89224))))
% 173.53/173.42 [9152]~P19(x91521,x91522,x91523,x91524)+~P22(f312(f312(f228(a852),f312(f53(x91522),f312(f290(x91521,x91522,x91523),x91524))),f312(f53(x91521),x91524)))
% 173.53/173.42 [9200]~P22(f312(f312(f314(f859(f853(x92001),f853(x92001))),f312(f312(f239(f853(x92001),f853(x92001)),x92002),x92003)),f153(x92001,x92004)))+P22(f312(f312(f314(f859(f853(x92001),f853(x92001))),f312(f312(f239(f853(x92001),f853(x92001)),x92002),x92003)),f154(x92001,f287(x92001,x92004))))
% 173.53/173.42 [9204]~P22(f312(f312(f314(f859(f853(x92041),f853(x92041))),f312(f312(f239(f853(x92041),f853(x92041)),x92042),x92043)),f154(x92041,x92044)))+P22(f312(f312(f314(f859(f853(x92041),f853(x92041))),f312(f312(f239(f853(x92041),f853(x92041)),x92042),x92043)),f287(f853(x92041),f153(x92041,x92044))))
% 173.53/173.42 [9220]P22(f312(f312(f314(f859(x92201,x92201)),f312(f312(f239(x92201,x92201),x92202),x92203)),f287(x92201,x92204)))+~P22(f312(f312(f314(f859(x92201,x92201)),f312(f312(f239(x92201,x92201),x92202),x92203)),f312(f312(f267(x92201,x92201,x92201),x92204),f287(x92201,x92204))))
% 173.53/173.42 [9402]E(f312(f312(f129(x94021),f624(x94022,x94023,x94024,x94021)),f312(f312(f147(x94021),f625(x94022,x94023,x94024,x94021)),f627(x94022,x94023,x94024,x94021))),x94024)+~P22(f312(f312(f314(f859(f853(x94021),f853(x94021))),f312(f312(f239(f853(x94021),f853(x94021)),x94024),x94023)),f153(x94021,x94022)))
% 173.53/173.42 [9403]E(f312(f312(f129(x94031),f624(x94032,x94033,x94034,x94031)),f312(f312(f147(x94031),f626(x94032,x94033,x94034,x94031)),f627(x94032,x94033,x94034,x94031))),x94033)+~P22(f312(f312(f314(f859(f853(x94031),f853(x94031))),f312(f312(f239(f853(x94031),f853(x94031)),x94034),x94033)),f153(x94031,x94032)))
% 173.53/173.42 [9476]P22(f312(f312(f314(f859(x94761,x94761)),f312(f312(f239(x94761,x94761),x94762),f778(x94763,x94764,x94762,x94761))),f287(x94761,x94763)))+~P22(f312(f312(f314(f859(x94761,x94761)),f312(f312(f239(x94761,x94761),x94762),x94764)),f312(f312(f267(x94761,x94761,x94761),x94763),f287(x94761,x94763))))
% 173.53/173.42 [9541]P22(f312(f312(f227(a852),f151(x95411,x95412,x95413)),f151(x95411,x95414,x95413)))+~P22(f312(f312(f228(a852),f312(x95412,f603(x95414,x95412,x95413,x95411))),f312(x95414,f603(x95414,x95412,x95413,x95411))))
% 173.53/173.42 [9607]P22(f312(f312(f314(f859(x96071,x96071)),f312(f312(f239(x96071,x96071),f774(x96072,x96073,x96074,x96071)),x96073)),f287(x96071,x96072)))+~P22(f312(f312(f314(f859(x96071,x96071)),f312(f312(f239(x96071,x96071),x96074),x96073)),f312(f312(f267(x96071,x96071,x96071),x96072),f287(x96071,x96072))))
% 173.53/173.42 [5145]~E(x51452,x51453)+E(f166(x51451,x51452,f312(f312(f147(x51451),x51453),x51454)),x51454)
% 173.53/173.42 [5266]P22(f312(x52662,x52663))+E(f172(x52661,x52662,f312(f312(f147(x52661),x52663),x52664)),f127(x52661))
% 173.53/173.42 [5331]~P79(x53312)+E(f312(f312(f88(f860(x53311,x53312)),x53313),x53314),f312(f88(x53312),f312(x53313,x53314)))
% 173.53/173.42 [5343]~E(x53432,f2(a852))+E(f312(f312(f134(x53431),x53432),f312(f312(f147(x53431),x53433),x53434)),f312(f312(f147(x53431),x53433),x53434))
% 173.53/173.42 [5344]P22(f312(x53442,x53443))+E(f312(f132(x53441,x53442),f312(f312(f147(x53441),x53443),x53444)),f312(f132(x53441,x53442),x53444))
% 173.53/173.42 [5477]~E(x54772,x54774)+P22(f312(f312(f312(f289(x54771),x54772),x54773),x54774))
% 173.53/173.42 [5485]E(x54851,f127(x54852))+E(f140(x54853,f312(f312(f150(x54852,x54853),x54854),x54851)),f312(x54854,f140(x54852,x54851)))
% 173.53/173.42 [5499]~E(x54991,f72(x54992,x54994))+E(f312(x54991,f312(f312(f289(x54992),x54993),f189(f860(x54992,a845)))),x54993)
% 173.53/173.42 [5537]E(x55371,f127(x55372))+E(f312(f137(x55373),f312(f312(f150(x55372,x55373),x55374),x55371)),f312(x55374,f312(f137(x55372),x55371)))
% 173.53/173.42 [5637]~P22(f312(x56373,x56374))+P22(f312(f312(f312(f289(x56371),x56372),x56373),x56374))
% 173.53/173.42 [5744]~P13(x57442,x57444,x57441)+E(f312(x57441,f312(f312(f289(x57442),x57443),f189(f860(x57442,a845)))),x57443)
% 173.53/173.42 [5767]~E(x57672,x57673)+P22(f312(f312(f314(x57671),x57672),f312(f312(f289(x57671),x57673),x57674)))
% 173.53/173.42 [5773]~P107(x57731)+E(f312(f312(f89(x57731),x57732),f312(f312(f89(x57731),x57733),x57734)),f312(f312(f89(x57731),x57733),f312(f312(f89(x57731),x57732),x57734)))
% 173.53/173.42 [5774]~P87(x57741)+E(f312(f312(f124(x57741),x57742),f312(f312(f124(x57741),x57743),x57744)),f312(f312(f124(x57741),x57743),f312(f312(f124(x57741),x57742),x57744)))
% 173.53/173.42 [5776]~P98(x57761)+E(f312(f312(f124(x57761),x57762),f312(f312(f124(x57761),x57763),x57764)),f312(f312(f124(x57761),x57763),f312(f312(f124(x57761),x57762),x57764)))
% 173.53/173.42 [5777]~P87(x57771)+E(f312(f312(f115(x57771),x57772),f312(f312(f115(x57771),x57773),x57774)),f312(f312(f115(x57771),x57773),f312(f312(f115(x57771),x57772),x57774)))
% 173.53/173.42 [5779]~P99(x57791)+E(f312(f312(f115(x57791),x57792),f312(f312(f115(x57791),x57793),x57794)),f312(f312(f115(x57791),x57793),f312(f312(f115(x57791),x57792),x57794)))
% 173.53/173.42 [5780]~P107(x57801)+E(f312(f312(f90(x57801),x57802),f312(f312(f90(x57801),x57803),x57804)),f312(f312(f90(x57801),x57803),f312(f312(f90(x57801),x57802),x57804)))
% 173.53/173.42 [5782]~P103(x57821)+E(f312(f312(f225(x57821),x57822),f312(f312(f225(x57821),x57823),x57824)),f312(f312(f225(x57821),x57823),f312(f312(f225(x57821),x57822),x57824)))
% 173.53/173.42 [5784]~P103(x57841)+E(f312(f312(f226(x57841),x57842),f312(f312(f226(x57841),x57843),x57844)),f312(f312(f226(x57841),x57843),f312(f312(f226(x57841),x57842),x57844)))
% 173.53/173.42 [5789]E(x57891,x57892)+E(f166(x57893,x57891,f312(f312(f147(x57893),x57892),x57894)),f312(f312(f147(x57893),x57892),f166(x57893,x57891,x57894)))
% 173.53/173.42 [5802]~P22(f312(x58022,x58023))+E(f312(f132(x58021,x58022),f312(f312(f147(x58021),x58023),x58024)),f312(f312(f147(x58021),x58023),f312(f132(x58021,x58022),x58024)))
% 173.53/173.42 [5943]~P22(f312(x59432,x59433))+E(f172(x59431,x59432,f312(f312(f147(x59431),x59433),x59434)),f312(f312(f147(x59431),x59433),f172(x59431,x59432,x59434)))
% 173.53/173.42 [5989]P18(x59891,x59892,x59893)+~P18(x59891,x59892,f312(f312(f289(f851(x59891)),x59894),x59893))
% 173.53/173.42 [6000]E(x60001,f189(f860(x60002,a845)))+E(f312(f312(f50(x60002,f860(x60003,a845)),x60001),f312(f16(f860(x60003,a845),x60002),x60004)),x60004)
% 173.53/173.42 [6001]E(x60011,f189(f860(x60012,a845)))+E(f312(f312(f51(x60012,f860(x60013,a845)),x60011),f312(f16(f860(x60013,a845),x60012),x60014)),x60014)
% 173.53/173.42 [6009]~E(x60094,f189(f860(x60092,a845)))+E(f312(f312(f247(x60091,x60092),x60093),f312(f16(f860(x60092,a845),x60091),x60094)),f189(f860(f859(x60091,x60092),a845)))
% 173.53/173.42 [6010]~E(x60103,f189(f860(x60101,a845)))+E(f312(f312(f247(x60101,x60102),x60103),f312(f16(f860(x60102,a845),x60101),x60104)),f189(f860(f859(x60101,x60102),a845)))
% 173.53/173.42 [6055]E(x60551,f2(a852))+E(f312(f312(f134(x60552),x60551),f312(f312(f147(x60552),x60553),x60554)),f312(f312(f134(x60552),f312(f312(f21(a852),x60551),f87(a852))),x60554))
% 173.53/173.42 [6081]E(x60811,f189(f860(x60812,a845)))+E(f312(f290(x60812,x60813,f312(f16(x60813,x60812),x60814)),x60811),f312(f312(f289(x60813),x60814),f189(f860(x60813,a845))))
% 173.53/173.42 [6084]E(f312(f291(x60841,x60842,f312(f16(x60842,x60841),x60843)),x60844),f189(f860(x60841,a845)))+P22(f312(f312(f314(x60842),x60843),x60844))
% 173.53/173.42 [6152]~E(x61523,f189(f860(x61521,a845)))+E(f312(f312(f50(x61521,f860(x61522,a845)),x61523),f312(f16(f860(x61522,a845),x61521),x61524)),f189(f860(x61522,a845)))
% 173.53/173.42 [6153]~E(x61533,f189(f860(x61531,a845)))+E(f312(f312(f51(x61531,f860(x61532,a845)),x61533),f312(f16(f860(x61532,a845),x61531),x61534)),f235(f860(x61532,a845)))
% 173.53/173.42 [6155]~P60(x61551)+E(f54(x61551,f312(f312(f90(x61551),x61552),x61553),f312(f312(f90(x61551),x61552),x61554)),f312(f312(f90(x61551),x61552),f54(x61551,x61553,x61554)))
% 173.53/173.42 [6316]E(f312(f291(x63161,x63162,f312(f16(x63162,x63161),x63163)),x63164),f235(f860(x63161,a845)))+~P22(f312(f312(f314(x63162),x63163),x63164))
% 173.53/173.42 [6340]~P22(f312(f312(f314(x63401),x63402),x63404))+P22(f312(f312(f314(x63401),x63402),f312(f312(f289(x63401),x63403),x63404)))
% 173.53/173.42 [6345]P22(f312(x63451,x63452))+~P22(f312(f156(x63453,x63451),f312(f312(f147(x63453),x63452),x63454)))
% 173.53/173.42 [6353]~E(x63533,f312(f312(f21(a852),f312(f190(f853(x63531)),x63532)),f87(a852)))+E(f128(x63531,f312(f312(f155(x63531,x63532),x63533),x63534)),f128(x63531,x63532))
% 173.53/173.42 [6372]~P103(x63721)+E(f312(f312(f115(f860(x63721,a845)),f312(f281(x63721),x63722)),f283(x63721,x63723,x63724)),f283(x63721,x63723,f312(f312(f225(x63721),x63722),x63724)))
% 173.53/173.42 [6373]~P103(x63731)+E(f312(f312(f115(f860(x63731,a845)),f312(f234(x63731),x63732)),f283(x63731,x63733,x63734)),f283(x63731,f312(f312(f226(x63731),x63732),x63733),x63734))
% 173.53/173.42 [6388]E(f312(f312(f115(f860(x63881,a845)),x63882),f312(f312(f289(x63881),x63883),x63884)),f312(f312(f115(f860(x63881,a845)),x63882),x63884))+P22(f312(f312(f314(x63881),x63883),x63882))
% 173.53/173.42 [6400]E(f166(x64001,x64002,f312(f312(f129(x64001),x64003),x64004)),f312(f312(f129(x64001),x64003),f166(x64001,x64002,x64004)))+P22(f312(f312(f314(x64001),x64002),f312(f168(x64001),x64003)))
% 173.53/173.42 [6404]~P78(x64041)+E(f312(f312(f90(x64041),f312(f312(f240(x64041),x64042),x64043)),f312(f312(f240(x64041),x64042),x64044)),f312(f312(f240(x64041),x64042),f312(f312(f89(a852),x64043),x64044)))
% 173.53/173.42 [6405]~P107(x64051)+E(f312(f312(f90(x64051),f312(f312(f240(x64051),x64052),x64053)),f312(f312(f240(x64051),x64052),x64054)),f312(f312(f240(x64051),x64052),f312(f312(f89(a852),x64053),x64054)))
% 173.53/173.42 [6437]~P96(x64371)+E(f312(f312(f115(x64371),f312(f312(f124(x64371),x64372),x64373)),f312(f312(f124(x64371),x64372),x64374)),f312(f312(f124(x64371),x64372),f312(f312(f115(x64371),x64373),x64374)))
% 173.53/173.42 [6438]~P96(x64381)+E(f312(f312(f124(x64381),f312(f312(f115(x64381),x64382),x64383)),f312(f312(f115(x64381),x64382),x64384)),f312(f312(f115(x64381),x64382),f312(f312(f124(x64381),x64383),x64384)))
% 173.53/173.42 [6439]~P107(x64391)+E(f312(f312(f89(x64391),f312(f312(f90(x64391),x64392),x64393)),f312(f312(f90(x64391),x64392),x64394)),f312(f312(f90(x64391),x64392),f312(f312(f89(x64391),x64393),x64394)))
% 173.53/173.42 [6440]~P103(x64401)+E(f312(f312(f226(x64401),f312(f312(f225(x64401),x64402),x64403)),f312(f312(f225(x64401),x64402),x64404)),f312(f312(f225(x64401),x64402),f312(f312(f226(x64401),x64403),x64404)))
% 173.53/173.42 [6441]~P103(x64411)+E(f312(f312(f225(x64411),f312(f312(f226(x64411),x64412),x64413)),f312(f312(f226(x64411),x64412),x64414)),f312(f312(f226(x64411),x64412),f312(f312(f225(x64411),x64413),x64414)))
% 173.53/173.42 [6475]~P60(x64751)+E(f54(x64751,f312(f312(f90(x64751),x64752),x64753),f312(f312(f90(x64751),x64754),x64753)),f312(f312(f90(x64751),f54(x64751,x64752,x64754)),x64753))
% 173.53/173.42 [6476]~E(f312(f190(f853(x64761)),x64763),f312(f190(f853(x64762)),x64764))+E(f312(f312(f150(f859(x64761,x64762),x64762),f248(x64761,x64762)),f312(f312(f177(x64761,x64762),x64763),x64764)),x64764)
% 173.53/173.42 [6477]~E(f312(f190(f853(x64771)),x64773),f312(f190(f853(x64772)),x64774))+E(f312(f312(f150(f859(x64771,x64772),x64771),f246(x64771,x64772)),f312(f312(f177(x64771,x64772),x64773),x64774)),x64773)
% 173.53/173.42 [6483]P22(f312(f156(x64831,x64832),x64833))+~P22(f312(f156(x64831,x64832),f312(f312(f147(x64831),x64834),x64833)))
% 173.53/173.42 [6484]P22(f312(f156(x64841,x64842),x64843))+~P22(f312(f156(x64841,x64842),f312(f312(f129(x64841),x64844),x64843)))
% 173.53/173.42 [6485]P22(f312(f156(x64851,x64852),x64853))+~P22(f312(f156(x64851,x64852),f312(f312(f129(x64851),x64853),x64854)))
% 173.53/173.42 [6491]~P61(x64911)+E(f54(x64911,f312(f312(f21(x64911),x64912),f54(x64911,x64913,x64914)),x64914),f54(x64911,f312(f312(f21(x64911),x64912),x64913),x64914))
% 173.53/173.42 [6492]~P60(x64921)+E(f54(x64921,f312(f312(f90(x64921),x64922),f54(x64921,x64923,x64924)),x64924),f54(x64921,f312(f312(f90(x64921),x64922),x64923),x64924))
% 173.53/173.42 [6493]~P60(x64931)+E(f54(x64931,f312(f312(f89(x64931),x64932),f54(x64931,x64933,x64934)),x64934),f54(x64931,f312(f312(f89(x64931),x64932),x64933),x64934))
% 173.53/173.42 [6572]~P103(x65721)+E(f312(f312(f115(f860(x65721,a845)),f283(x65721,x65722,x65723)),f312(f281(x65721),x65724)),f283(x65721,x65722,f312(f312(f225(x65721),x65723),x65724)))
% 173.53/173.42 [6573]~P103(x65731)+E(f312(f312(f115(f860(x65731,a845)),f283(x65731,x65732,x65733)),f312(f234(x65731),x65734)),f283(x65731,f312(f312(f226(x65731),x65732),x65734),x65733))
% 173.53/173.42 [6578]~E(f312(f190(f853(x65781)),x65783),f312(f190(f853(x65782)),x65784))+E(f312(f312(f177(x65781,x65782),f312(f165(x65781),x65783)),f312(f165(x65782),x65784)),f312(f165(f859(x65781,x65782)),f312(f312(f177(x65781,x65782),x65783),x65784)))
% 173.53/173.42 [6591]E(x65911,f312(f312(f21(a852),f312(f190(f853(x65912)),x65913)),f87(a852)))+E(f128(x65912,f312(f312(f155(x65912,x65913),x65911),x65914)),f312(f312(f155(x65912,f128(x65912,x65913)),x65911),x65914))
% 173.53/173.42 [6602]~P22(f312(f133(x66022),x66024))+P22(f312(f133(f859(x66021,x66022)),f312(f312(f177(x66021,x66022),x66023),x66024)))
% 173.53/173.42 [6603]~P22(f312(f133(x66031),x66033))+P22(f312(f133(f859(x66031,x66032)),f312(f312(f177(x66031,x66032),x66033),x66034)))
% 173.53/173.42 [6692]E(x66921,f312(f312(f312(a201,x66922),x66923),f312(x66924,x66922)))+~P22(f312(f312(f195(f28(x66923,x66924)),x66922),x66921))
% 173.53/173.42 [6838]E(f312(f47(a852,x68381),x68382),x68383)+~P22(f312(f56(x68381,x68382),f312(f312(f239(a852,a852),x68383),x68384)))
% 173.53/173.42 [6884]E(f54(a852,x68841,x68842),x68843)+~P22(f312(f56(x68841,x68842),f312(f312(f239(a852,a852),x68844),x68843)))
% 173.53/173.42 [6887]P22(f312(f133(x68871),x68872))+~P22(f312(f133(x68873),f312(f312(f150(x68871,x68873),x68874),x68872)))
% 173.53/173.42 [6895]~P18(x68951,x68952,f312(f312(f289(f851(x68951)),x68953),x68954))+P18(x68951,x68952,f312(f312(f289(f851(x68951)),x68953),f189(f860(f851(x68951),a845))))
% 173.53/173.42 [6903]P22(f312(f312(f195(x69031),x69032),x69033))+~P22(f312(f312(f312(f312(a198,x69031),x69032),x69034),x69033))
% 173.53/173.42 [6974]E(f166(x69741,x69742,f312(f312(f129(x69741),x69743),x69744)),f312(f312(f129(x69741),f166(x69741,x69742,x69743)),x69744))+~P22(f312(f312(f314(x69741),x69742),f312(f168(x69741),x69743)))
% 173.53/173.42 [7068]~P61(x70681)+E(f54(x70681,f312(f312(f21(x70681),f54(x70681,x70682,x70683)),x70684),x70683),f54(x70681,f312(f312(f21(x70681),x70682),x70684),x70683))
% 173.53/173.42 [7070]~P60(x70701)+E(f54(x70701,f312(f312(f89(x70701),f54(x70701,x70702,x70703)),x70704),x70703),f54(x70701,f312(f312(f89(x70701),x70702),x70704),x70703))
% 173.53/173.42 [7071]~P60(x70711)+E(f54(x70711,f312(f312(f90(x70711),f54(x70711,x70712,x70713)),x70714),x70713),f54(x70711,f312(f312(f90(x70711),x70712),x70714),x70713))
% 173.53/173.42 [7252]~E(x72521,f312(f312(f147(x72522),x72523),x72524))+~P22(f312(f312(f227(a852),f312(f190(f853(x72522)),x72521)),f312(f190(f853(x72522)),x72524)))
% 173.53/173.42 [7325]~E(f312(f173(x73251,x73252),x73253),f312(f173(x73251,x73252),x73254))+E(f312(f290(f859(x73251,x73252),x73251,f246(x73251,x73252)),f312(f168(f859(x73251,x73252)),x73253)),f312(f290(f859(x73251,x73252),x73251,f246(x73251,x73252)),f312(f168(f859(x73251,x73252)),x73254)))
% 173.53/173.42 [7457]P19(x74571,x74572,x74573,f312(f168(x74571),x74574))+~P22(f312(f133(x74572),f312(f312(f150(x74571,x74572),x74573),x74574)))
% 173.53/173.42 [7532]~P22(f312(f312(f227(f860(x75321,a845)),x75322),x75324))+P22(f312(f312(f227(f860(x75321,a845)),x75322),f312(f312(f289(x75321),x75323),x75324)))
% 173.53/173.42 [7563]~P60(x75631)+E(f54(x75631,f312(f312(f89(x75631),f54(x75631,x75632,x75633)),f54(x75631,x75634,x75633)),x75633),f54(x75631,f312(f312(f89(x75631),x75632),x75634),x75633))
% 173.53/173.42 [7564]~P61(x75641)+E(f54(x75641,f312(f312(f21(x75641),f54(x75641,x75642,x75643)),f54(x75641,x75644,x75643)),x75643),f54(x75641,f312(f312(f21(x75641),x75642),x75644),x75643))
% 173.53/173.42 [7565]~P60(x75651)+E(f54(x75651,f312(f312(f90(x75651),f54(x75651,x75652,x75653)),f54(x75651,x75654,x75653)),x75653),f54(x75651,f312(f312(f90(x75651),x75652),x75654),x75653))
% 173.53/173.42 [7664]P22(f312(f312(f312(f312(a198,x76641),x76642),f312(a126,x76643)),x76644))+~P22(f312(f312(f312(f312(a198,x76641),x76642),x76643),x76644))
% 173.53/173.42 [7672]~E(f312(x76724,f399(x76724,x76723,x76721,x76722)),f189(f860(x76722,a845)))+E(f312(f312(f50(x76721,f860(x76722,a845)),x76723),x76724),f189(f860(x76722,a845)))
% 173.53/173.42 [7673]~E(f312(x76734,f633(x76734,x76733,x76731,x76732)),f235(f860(x76732,a845)))+E(f312(f312(f51(x76731,f860(x76732,a845)),x76733),x76734),f235(f860(x76732,a845)))
% 173.53/173.42 [7674]~E(f312(x76744,f412(x76744,x76743,x76742,x76741)),f189(f860(x76742,a845)))+E(f312(f312(f50(x76741,f860(x76742,a845)),x76743),x76744),f189(f860(x76742,a845)))
% 173.53/173.42 [7675]~E(f312(x76754,f634(x76754,x76753,x76752,x76751)),f235(f860(x76752,a845)))+E(f312(f312(f51(x76751,f860(x76752,a845)),x76753),x76754),f235(f860(x76752,a845)))
% 173.53/173.42 [8067]P22(f312(x80671,x80672))+~P22(f312(f312(f314(x80673),x80672),f312(f312(f115(f860(x80673,a845)),x80674),f312(f233(x80673),x80671))))
% 173.53/173.42 [8105]~P22(f312(f312(f227(f860(x81051,a845)),x81053),x81054))+P22(f312(f312(f227(f860(x81051,a845)),f312(f312(f289(x81051),x81052),x81053)),f312(f312(f289(x81051),x81052),x81054)))
% 173.53/173.42 [8275]P22(f312(f312(f195(x82751),x82752),f827(x82753,x82752,x82754,x82751)))+~P22(f312(f312(f195(f36(x82751,x82754)),x82752),x82753))
% 173.53/173.42 [8276]P22(f312(f312(f195(x82761),x82762),f836(x82763,x82762,x82764,x82761)))+~P22(f312(f312(f195(f36(x82761,x82764)),x82762),x82763))
% 173.53/173.42 [8285]P22(f312(x82852,x82853))+E(f312(f312(f134(x82851),f312(f190(f853(x82851)),f172(x82851,x82852,f312(f312(f147(x82851),x82853),x82854)))),f312(f312(f147(x82851),x82853),x82854)),f312(f312(f147(x82851),x82853),x82854))
% 173.53/173.42 [8406]~P22(f312(f312(f228(a852),f312(x84064,x84062)),f312(x84064,x84063)))+P22(f312(f312(f314(f859(x84061,x84061)),f312(f312(f239(x84061,x84061),x84062),x84063)),f312(f312(f266(a852,x84061),a232),x84064)))
% 173.53/173.42 [8501]~P22(f312(x85012,f720(x85014,x85012,x85013,x85011)))+E(f172(x85011,x85012,f312(f312(f129(x85011),x85013),x85014)),f312(f312(f129(x85011),x85013),f172(x85011,x85012,x85014)))
% 173.53/173.42 [8564]P19(f853(x85641),f853(x85642),f312(f150(x85641,x85642),x85643),x85644)+~P19(x85641,x85642,x85643,f48(f860(x85641,a845),f312(f290(f853(x85641),f860(x85641,a845),f168(x85641)),x85644)))
% 173.53/173.42 [8631]~P22(f312(x86312,x86313))+E(f312(f312(f134(x86311),f312(f190(f853(x86311)),f172(x86311,x86312,f312(f312(f147(x86311),x86313),x86314)))),f312(f312(f147(x86311),x86313),x86314)),f312(f312(f134(x86311),f312(f190(f853(x86311)),f172(x86311,x86312,x86314))),x86314))
% 173.53/173.42 [8672]~E(x86722,x86723)+E(f312(f132(x86721,f312(f312(f8(a845,a845,x86721),a307),f312(a309,x86722))),f312(f312(f147(x86721),x86723),x86724)),f312(f132(x86721,f312(f312(f8(a845,a845,x86721),a307),f312(a309,x86722))),x86724))
% 173.53/173.42 [8681]E(f312(f312(f50(x86811,f860(x86812,a845)),x86813),x86814),f189(f860(x86812,a845)))+P22(f312(f312(f314(x86811),f399(x86814,x86813,x86811,x86812)),x86813))
% 173.53/173.42 [8682]E(f312(f312(f51(x86821,f860(x86822,a845)),x86823),x86824),f235(f860(x86822,a845)))+P22(f312(f312(f314(x86821),f633(x86824,x86823,x86821,x86822)),x86823))
% 173.53/173.42 [8683]E(f312(f312(f50(x86831,f860(x86832,a845)),x86833),x86834),f189(f860(x86832,a845)))+P22(f312(f312(f314(x86831),f412(x86834,x86833,x86832,x86831)),x86833))
% 173.53/173.42 [8684]E(f312(f312(f51(x86841,f860(x86842,a845)),x86843),x86844),f235(f860(x86842,a845)))+P22(f312(f312(f314(x86841),f634(x86844,x86843,x86842,x86841)),x86843))
% 173.53/173.42 [8719]P22(f312(f312(f228(a852),f312(x87191,x87192)),f312(x87191,x87193)))+~P22(f312(f312(f314(f859(x87194,x87194)),f312(f312(f239(x87194,x87194),x87192),x87193)),f312(f312(f266(a852,x87194),a232),x87191)))
% 173.53/173.42 [8740]E(f172(x87401,x87402,f312(f312(f129(x87401),x87403),x87404)),f312(f312(f129(x87401),x87403),f172(x87401,x87402,x87404)))+P22(f312(f312(f314(x87401),f720(x87404,x87402,x87403,x87401)),f312(f168(x87401),x87403)))
% 173.53/173.42 [8776]P22(f312(f312(f195(x87761),f827(x87762,x87763,x87761,x87764)),x87762))+~P22(f312(f312(f195(f36(x87764,x87761)),x87763),x87762))
% 173.53/173.42 [8777]P22(f312(f312(f195(x87771),f836(x87772,x87773,x87771,x87774)),x87772))+~P22(f312(f312(f195(f36(x87774,x87771)),x87773),x87772))
% 173.53/173.42 [8886]~P60(x88861)+E(f312(f312(f89(x88861),f312(f312(f89(x88861),f312(f312(f90(x88861),x88862),f312(f47(x88861,x88863),x88862))),f54(x88861,x88863,x88862))),x88864),f312(f312(f89(x88861),x88863),x88864))
% 173.53/173.42 [8908]P22(f312(f312(f314(x89081),f373(x89082,x89083,x89084,x89081)),x89083))+~P22(f312(f312(f314(f860(x89081,a845)),x89084),f312(f312(f69(x89081),x89083),x89082)))
% 173.53/173.42 [8911]E(x89111,x89112)+~P22(f312(f312(f314(f859(x89113,x89113)),f312(f312(f239(x89113,x89113),x89111),x89112)),f312(f312(f184(f859(x89113,x89113),a845),f2(a852)),x89114)))
% 173.53/173.42 [8987]E(f312(f264(x89871,x89871,x89872),f312(f312(f289(x89871),f373(x89872,x89873,x89874,x89871)),f189(f860(x89871,a845)))),x89874)+~P22(f312(f312(f314(f860(x89871,a845)),x89874),f312(f312(f69(x89871),x89873),x89872)))
% 173.53/173.42 [8992]~P22(f312(f312(f314(f859(x89921,x89921)),f312(f312(f239(x89921,x89921),x89923),x89922)),f287(x89921,x89924)))+P22(f312(f312(f314(f859(x89921,x89921)),f312(f312(f239(x89921,x89921),x89922),x89923)),f287(x89921,f312(f265(x89921,x89921),x89924))))
% 173.53/173.42 [9015]~P22(f312(f312(f314(x90151),x90153),x90154))+P22(f312(f312(f314(f860(x90151,a845)),f312(f264(x90151,x90151,x90152),f312(f312(f289(x90151),x90153),f189(f860(x90151,a845))))),f312(f312(f69(x90151),x90154),x90152)))
% 173.53/173.42 [9026]P22(f312(f312(f314(f859(x90261,x90261)),f312(f312(f239(x90261,x90261),x90262),x90263)),f287(x90261,x90264)))+~P22(f312(f312(f314(f859(x90261,x90261)),f312(f312(f239(x90261,x90261),x90263),x90262)),f287(x90261,f312(f265(x90261,x90261),x90264))))
% 173.53/173.42 [9115]E(f312(f312(f155(x91151,f312(f165(x91151),x91152)),f312(f312(f21(a852),f312(f312(f21(a852),f312(f190(f853(x91151)),x91152)),x91153)),f87(a852))),x91154),f312(f165(x91151),f312(f312(f155(x91151,x91152),x91153),x91154)))+~P22(f312(f312(f228(a852),x91153),f312(f190(f853(x91151)),x91152)))
% 173.53/173.42 [9119]~P22(f312(x91192,f711(x91194,x91192,x91193,x91191)))+E(f312(f312(f134(x91191),f312(f190(f853(x91191)),f172(x91191,x91192,f312(f312(f129(x91191),x91193),x91194)))),f312(f312(f129(x91191),x91193),x91194)),f312(f312(f134(x91191),f312(f190(f853(x91191)),f172(x91191,x91192,x91194))),x91194))
% 173.53/173.42 [9158]~P19(x91582,x91581,x91583,f235(f860(x91582,a845)))+P22(f312(f312(f227(f860(x91581,a845)),f312(f290(x91582,x91581,x91583),f312(f88(f860(x91582,a845)),x91584))),f312(f88(f860(x91581,a845)),f312(f290(x91582,x91581,x91583),x91584))))
% 173.53/173.42 [9168]~P60(x91681)+E(f312(f312(f89(x91681),f312(f312(f89(x91681),f312(f312(f90(x91681),f312(f47(x91681,x91682),x91683)),x91683)),f54(x91681,x91682,x91683))),x91684),f312(f312(f89(x91681),x91682),x91684))
% 173.53/173.42 [9173]~P31(x91731)+E(f312(f138(x91731,x91732,f312(f7(x91732,x91731,x91731),f312(f312(f8(x91731,f860(x91731,x91731),x91732),f124(x91731)),x91733)),f189(x91731)),x91734),f312(f312(f50(x91732,x91731),f312(f168(x91732),x91734)),x91733))
% 173.53/173.42 [9174]~P31(x91741)+E(f312(f138(x91741,x91742,f312(f7(x91742,x91741,x91741),f312(f312(f8(x91741,f860(x91741,x91741),x91742),f115(x91741)),x91743)),f235(x91741)),x91744),f312(f312(f51(x91742,x91741),f312(f168(x91742),x91744)),x91743))
% 173.53/173.42 [9186]E(f312(f312(f134(x91861),f312(f190(f853(x91861)),f172(x91861,x91862,f312(f312(f129(x91861),x91863),x91864)))),f312(f312(f129(x91861),x91863),x91864)),f312(f312(f134(x91861),f312(f190(f853(x91861)),f172(x91861,x91862,x91864))),x91864))+P22(f312(f312(f314(x91861),f711(x91864,x91862,x91863,x91861)),f312(f168(x91861),x91863)))
% 173.53/173.42 [9251]~P22(f312(f312(f314(f859(f853(x92514),f853(x92514))),f312(f312(f239(f853(x92514),f853(x92514)),x92513),x92512)),f153(x92514,x92511)))+P22(f312(f312(f228(a852),f605(x92511,x92512,x92513,x92514)),f312(f190(f853(x92514)),x92513)))
% 173.53/173.42 [9279]~P22(f312(f312(f314(f859(f853(x92791),f853(x92791))),f312(f312(f239(f853(x92791),f853(x92791)),x92792),x92793)),f312(f265(f853(x92791),f853(x92791)),f153(x92791,x92794))))+P22(f312(f312(f314(f859(f853(x92791),f853(x92791))),f312(f312(f239(f853(x92791),f853(x92791)),x92792),x92793)),f153(x92791,f312(f265(x92791,x92791),x92794))))
% 173.53/173.42 [9280]P22(f312(f312(f314(f859(f853(x92801),f853(x92801))),f312(f312(f239(f853(x92801),f853(x92801)),x92802),x92803)),f312(f265(f853(x92801),f853(x92801)),f153(x92801,x92804))))+~P22(f312(f312(f314(f859(f853(x92801),f853(x92801))),f312(f312(f239(f853(x92801),f853(x92801)),x92802),x92803)),f153(x92801,f312(f265(x92801,x92801),x92804))))
% 173.53/173.42 [9315]~P22(f312(f312(f314(x93151),x93153),f312(f238(x93151,x93152),x93154)))+P22(f312(f312(f314(f859(x93151,x93152)),f312(f312(f239(x93151,x93152),x93153),f574(x93154,x93152,x93153,x93151))),x93154))
% 173.53/173.42 [9316]~P22(f312(f312(f314(x93161),x93163),f312(f238(x93161,x93162),x93164)))+P22(f312(f312(f314(f859(x93161,x93162)),f312(f312(f239(x93161,x93162),x93163),f576(x93164,x93162,x93163,x93161))),x93164))
% 173.53/173.42 [9426]~P22(f312(f70(f856(x94261)),f312(f290(x94262,f856(x94261),x94263),f235(f860(x94262,a845)))))+P22(f312(f70(f856(x94261)),f312(f290(x94262,f856(x94261),f180(x94262,x94261,x94263,f312(f173(x94262,x94261),x94264))),f235(f860(x94262,a845)))))
% 173.53/173.42 [9471]~P22(f312(f312(f314(f859(x94711,x94711)),f312(f312(f239(x94711,x94711),x94712),x94714)),f312(f312(f267(x94711,x94711,x94711),x94713),f287(x94711,x94713))))+P22(f312(f312(f314(f859(x94711,x94711)),f312(f312(f239(x94711,x94711),x94712),f774(x94713,x94714,x94712,x94711))),x94713))
% 173.53/173.42 [9661]~P22(f312(f312(f314(f859(f853(x96611),f853(x96611))),f312(f312(f239(f853(x96611),f853(x96611)),x96614),x96613)),f153(x96611,x96612)))+P22(f312(f312(f314(f859(x96611,x96611)),f312(f312(f239(x96611,x96611),f625(x96612,x96613,x96614,x96611)),f626(x96612,x96613,x96614,x96611))),x96612))
% 173.53/173.42 [9756]~P22(f312(f312(f314(f859(f853(x97561),f853(x97561))),f312(f312(f239(f853(x97561),f853(x97561)),x97562),x97564)),f153(x97561,x97563)))+P22(f312(f312(f314(f859(x97561,x97561)),f312(f312(f239(x97561,x97561),f312(f312(f161(x97561),x97562),f605(x97563,x97564,x97562,x97561))),f606(x97563,x97564,x97562,x97561))),x97563))
% 173.53/173.42 [9778]~P22(f312(f70(x97782),x97784))+E(f312(f312(f312(f74(f860(x97781,a845),x97782,f124(f860(x97781,a845))),f312(f312(f7(x97782,f860(x97781,a845),f860(x97781,a845)),f312(f312(f8(x97781,f860(f860(x97781,a845),f860(x97781,a845)),x97782),f289(x97781)),x97783)),f189(f860(x97781,a845)))),f189(f860(x97781,a845))),x97784),f312(f290(x97782,x97781,x97783),x97784))
% 173.53/173.42 [9884]~P19(x98841,x98842,x98843,f235(f860(x98841,a845)))+P22(f312(f312(f227(f860(x98841,a845)),f312(f291(x98841,x98842,x98843),f312(f312(f289(x98842),x98844),f189(f860(x98842,a845))))),f312(f312(f289(x98841),f94(x98841,f312(f312(f7(x98841,x98842,a845),f312(f312(f8(x98842,f860(x98842,a845),x98841),a309),x98843)),x98844))),f189(f860(x98841,a845)))))
% 173.53/173.42 [5548]~E(f312(f312(f129(x55481),x55482),x55484),x55483)+E(f312(f312(f169(x55481),f312(f190(f853(x55481)),x55482)),x55483),x55482)
% 173.53/173.42 [5549]~E(f312(f312(f129(x55492),x55493),x55491),x55494)+E(x55491,f312(f312(f134(x55492),f312(f190(f853(x55492)),x55493)),x55494))
% 173.53/173.42 [5560]~E(x55604,f2(a852))+E(f312(f312(f161(x55601),f312(f312(f147(x55601),x55602),x55603)),x55604),x55602)
% 173.53/173.42 [6065]~P107(x60651)+E(f312(f312(f240(x60651),f312(f312(f240(x60651),x60652),x60653)),x60654),f312(f312(f240(x60651),x60652),f312(f312(f90(a852),x60653),x60654)))
% 173.53/173.42 [6066]~P78(x60661)+E(f312(f312(f240(x60661),f312(f312(f240(x60661),x60662),x60663)),x60664),f312(f312(f240(x60661),x60662),f312(f312(f90(a852),x60663),x60664)))
% 173.53/173.42 [6082]E(x60821,f2(a852))+E(f312(f312(f161(x60822),f312(f312(f147(x60822),x60823),x60824)),x60821),f312(f312(f161(x60822),x60824),f312(f312(f21(a852),x60821),f87(a852))))
% 173.53/173.42 [6108]~P114(x61081)+E(f312(f312(f268(x61081),f312(f312(f90(x61081),x61082),x61083)),x61084),f312(f312(f90(x61081),x61082),f312(f312(f268(x61081),x61083),x61084)))
% 173.53/173.42 [6109]~P107(x61091)+E(f312(f312(f89(x61091),f312(f312(f89(x61091),x61092),x61093)),x61094),f312(f312(f89(x61091),x61092),f312(f312(f89(x61091),x61093),x61094)))
% 173.53/173.42 [6110]~P29(x61101)+E(f312(f312(f89(x61101),f312(f312(f89(x61101),x61102),x61103)),x61104),f312(f312(f89(x61101),x61102),f312(f312(f89(x61101),x61103),x61104)))
% 173.53/173.42 [6111]~P87(x61111)+E(f312(f312(f124(x61111),f312(f312(f124(x61111),x61112),x61113)),x61114),f312(f312(f124(x61111),x61112),f312(f312(f124(x61111),x61113),x61114)))
% 173.53/173.42 [6113]~P98(x61131)+E(f312(f312(f124(x61131),f312(f312(f124(x61131),x61132),x61133)),x61134),f312(f312(f124(x61131),x61132),f312(f312(f124(x61131),x61133),x61134)))
% 173.53/173.42 [6114]~P87(x61141)+E(f312(f312(f115(x61141),f312(f312(f115(x61141),x61142),x61143)),x61144),f312(f312(f115(x61141),x61142),f312(f312(f115(x61141),x61143),x61144)))
% 173.53/173.42 [6116]~P99(x61161)+E(f312(f312(f115(x61161),f312(f312(f115(x61161),x61162),x61163)),x61164),f312(f312(f115(x61161),x61162),f312(f312(f115(x61161),x61163),x61164)))
% 173.53/173.42 [6117]~P107(x61171)+E(f312(f312(f90(x61171),f312(f312(f90(x61171),x61172),x61173)),x61174),f312(f312(f90(x61171),x61172),f312(f312(f90(x61171),x61173),x61174)))
% 173.53/173.42 [6118]~P68(x61181)+E(f312(f312(f90(x61181),f312(f312(f90(x61181),x61182),x61183)),x61184),f312(f312(f90(x61181),x61182),f312(f312(f90(x61181),x61183),x61184)))
% 173.53/173.42 [6121]~P103(x61211)+E(f312(f312(f225(x61211),f312(f312(f225(x61211),x61212),x61213)),x61214),f312(f312(f225(x61211),x61212),f312(f312(f225(x61211),x61213),x61214)))
% 173.53/173.42 [6123]~P103(x61231)+E(f312(f312(f226(x61231),f312(f312(f226(x61231),x61232),x61233)),x61234),f312(f312(f226(x61231),x61232),f312(f312(f226(x61231),x61233),x61234)))
% 173.53/173.42 [6138]~P60(x61381)+E(f54(x61381,f312(f312(f89(x61381),x61382),f312(f312(f90(x61381),x61383),x61384)),x61384),f54(x61381,x61382,x61384))
% 173.53/173.42 [6139]~P60(x61391)+E(f54(x61391,f312(f312(f89(x61391),x61392),f312(f312(f90(x61391),x61393),x61394)),x61393),f54(x61391,x61392,x61393))
% 173.53/173.42 [6268]E(f312(f312(f161(x62681),f312(f312(f169(x62681),x62682),x62683)),x62684),f312(f312(f161(x62681),x62683),x62684))+~P22(f312(f312(f228(a852),x62684),x62682))
% 173.53/173.42 [6435]~P107(x64351)+E(f312(f312(f89(x64351),f312(f312(f89(x64351),x64352),x64353)),x64354),f312(f312(f89(x64351),f312(f312(f89(x64351),x64352),x64354)),x64353))
% 173.53/173.42 [6436]~P107(x64361)+E(f312(f312(f90(x64361),f312(f312(f90(x64361),x64362),x64363)),x64364),f312(f312(f90(x64361),f312(f312(f90(x64361),x64362),x64364)),x64363))
% 173.53/173.42 [6496]~P23(x64962)+E(f312(f312(f6(x64961,x64962),f312(f16(x64962,x64961),x64963)),x64964),f312(f312(f90(x64962),f312(f114(x64962),f312(f53(x64961),x64964))),x64963))
% 173.53/173.42 [6665]E(f312(f312(f115(f860(x66651,a845)),f312(f312(f289(x66651),x66652),x66653)),x66654),f312(f312(f115(f860(x66651,a845)),x66653),x66654))+P22(f312(f312(f314(x66651),x66652),x66654))
% 173.53/173.42 [6728]~P81(x67281)+E(f312(f312(f225(x67281),f312(f312(f89(x67281),x67282),x67283)),f312(f312(f89(x67281),x67284),x67283)),f312(f312(f89(x67281),f312(f312(f225(x67281),x67282),x67284)),x67283))
% 173.53/173.42 [6729]~P81(x67291)+E(f312(f312(f226(x67291),f312(f312(f89(x67291),x67292),x67293)),f312(f312(f89(x67291),x67294),x67293)),f312(f312(f89(x67291),f312(f312(f226(x67291),x67292),x67294)),x67293))
% 173.53/173.42 [6730]~P76(x67301)+E(f312(f312(f225(x67301),f312(f312(f21(x67301),x67302),x67303)),f312(f312(f21(x67301),x67304),x67303)),f312(f312(f21(x67301),f312(f312(f225(x67301),x67302),x67304)),x67303))
% 173.53/173.42 [6731]~P76(x67311)+E(f312(f312(f226(x67311),f312(f312(f21(x67311),x67312),x67313)),f312(f312(f21(x67311),x67314),x67313)),f312(f312(f21(x67311),f312(f312(f226(x67311),x67312),x67314)),x67313))
% 173.53/173.42 [6732]~P96(x67321)+E(f312(f312(f115(x67321),f312(f312(f124(x67321),x67322),x67323)),f312(f312(f124(x67321),x67324),x67323)),f312(f312(f124(x67321),f312(f312(f115(x67321),x67322),x67324)),x67323))
% 173.53/173.42 [6733]~P96(x67331)+E(f312(f312(f124(x67331),f312(f312(f115(x67331),x67332),x67333)),f312(f312(f115(x67331),x67334),x67333)),f312(f312(f115(x67331),f312(f312(f124(x67331),x67332),x67334)),x67333))
% 173.53/173.42 [6735]~P110(x67351)+E(f312(f312(f89(x67351),f312(f312(f90(x67351),x67352),x67353)),f312(f312(f90(x67351),x67354),x67353)),f312(f312(f90(x67351),f312(f312(f89(x67351),x67352),x67354)),x67353))
% 173.53/173.42 [6736]~P107(x67361)+E(f312(f312(f90(x67361),f312(f312(f240(x67361),x67362),x67363)),f312(f312(f240(x67361),x67364),x67363)),f312(f312(f240(x67361),f312(f312(f90(x67361),x67362),x67364)),x67363))
% 173.53/173.42 [6737]~P72(x67371)+E(f312(f312(f90(x67371),f312(f312(f240(x67371),x67372),x67373)),f312(f312(f240(x67371),x67374),x67373)),f312(f312(f240(x67371),f312(f312(f90(x67371),x67372),x67374)),x67373))
% 173.53/173.42 [6738]~P64(x67381)+E(f312(f312(f268(x67381),f312(f312(f240(x67381),x67382),x67383)),f312(f312(f240(x67381),x67384),x67383)),f312(f312(f240(x67381),f312(f312(f268(x67381),x67382),x67384)),x67383))
% 173.53/173.42 [6739]~P103(x67391)+E(f312(f312(f226(x67391),f312(f312(f225(x67391),x67392),x67393)),f312(f312(f225(x67391),x67394),x67393)),f312(f312(f225(x67391),f312(f312(f226(x67391),x67392),x67394)),x67393))
% 173.53/173.42 [6740]~P103(x67401)+E(f312(f312(f225(x67401),f312(f312(f226(x67401),x67402),x67403)),f312(f312(f226(x67401),x67404),x67403)),f312(f312(f226(x67401),f312(f312(f225(x67401),x67402),x67404)),x67403))
% 173.53/173.42 [6741]~P114(x67411)+E(f312(f312(f89(x67411),f312(f312(f268(x67411),x67412),x67413)),f312(f312(f268(x67411),x67414),x67413)),f312(f312(f268(x67411),f312(f312(f89(x67411),x67412),x67414)),x67413))
% 173.53/173.42 [6742]~P114(x67421)+E(f312(f312(f21(x67421),f312(f312(f268(x67421),x67422),x67423)),f312(f312(f268(x67421),x67424),x67423)),f312(f312(f268(x67421),f312(f312(f21(x67421),x67422),x67424)),x67423))
% 173.53/173.42 [6743]~P107(x67431)+E(f312(f312(f89(x67431),f312(f312(f90(x67431),x67432),x67433)),f312(f312(f90(x67431),x67434),x67433)),f312(f312(f90(x67431),f312(f312(f89(x67431),x67432),x67434)),x67433))
% 173.53/173.42 [6774]E(f312(f312(f155(x67741,x67742),x67743),x67744),x67742)+~P22(f312(f312(f227(a852),f312(f190(f853(x67741)),x67742)),x67743))
% 173.53/173.42 [6796]~P22(f312(x67963,x67964))+P22(f312(f312(f312(f124(f860(x67961,a845)),x67962),x67963),x67964))
% 173.53/173.42 [6798]~P22(f312(x67982,x67984))+P22(f312(f312(f312(f124(f860(x67981,a845)),x67982),x67983),x67984))
% 173.53/173.42 [6819]E(f312(f312(f161(x68191),f312(f312(f129(x68191),x68192),x68193)),x68194),f312(f312(f161(x68191),x68192),x68194))+~P22(f312(f312(f228(a852),x68194),f312(f190(f853(x68191)),x68192)))
% 173.53/173.42 [6831]E(f312(f312(f21(f860(x68311,a845)),f312(f312(f289(x68311),x68312),x68313)),x68314),f312(f312(f21(f860(x68311,a845)),x68313),x68314))+~P22(f312(f312(f314(x68311),x68312),x68314))
% 173.53/173.42 [6872]~E(f135(a852,f312(f282(a852,x68721),x68722)),f312(f312(f147(a852),x68724),x68723))+E(f135(a852,f312(f282(a852,f312(f312(f89(a852),x68721),f87(a852))),x68722)),x68723)
% 173.53/173.42 [6949]E(x69491,f2(a852))+E(f312(f312(f147(x69492),x69493),f312(f312(f169(x69492),f312(f312(f21(a852),x69491),f87(a852))),x69494)),f312(f312(f169(x69492),x69491),f312(f312(f147(x69492),x69493),x69494)))
% 173.53/173.42 [7048]E(f312(f312(f161(x70481),x70482),f312(f312(f21(a852),x70483),f312(f190(f853(x70481)),x70484))),f312(f312(f161(x70481),f312(f312(f129(x70481),x70484),x70482)),x70483))+P22(f312(f312(f228(a852),x70483),f312(f190(f853(x70481)),x70484)))
% 173.53/173.42 [7081]E(f312(f312(f115(f860(x70811,a845)),x70812),f312(f312(f289(x70811),x70813),x70814)),f312(f312(f289(x70811),x70813),f312(f312(f115(f860(x70811,a845)),x70812),x70814)))+~P22(f312(f312(f314(x70811),x70813),x70812))
% 173.53/173.42 [7116]E(f312(f312(f161(x71161),f312(f312(f155(x71161,x71162),x71163),x71164)),x71163),x71164)+~P22(f312(f312(f228(a852),x71163),f312(f190(f853(x71161)),x71162)))
% 173.53/173.42 [7135]E(x71351,f189(f860(x71352,a845)))+E(f312(f290(f859(x71353,x71352),x71353,f246(x71353,x71352)),f312(f312(f247(x71353,x71352),x71354),f312(f16(f860(x71352,a845),x71353),x71351))),x71354)
% 173.53/173.42 [7136]E(x71361,f189(f860(x71362,a845)))+E(f312(f290(f859(x71362,x71363),x71363,f248(x71362,x71363)),f312(f312(f247(x71362,x71363),x71361),f312(f16(f860(x71363,a845),x71362),x71364))),x71364)
% 173.53/173.42 [7193]E(f312(f312(f21(f860(x71931,a845)),f312(f312(f289(x71931),x71932),x71933)),x71934),f312(f312(f289(x71931),x71932),f312(f312(f21(f860(x71931,a845)),x71933),x71934)))+P22(f312(f312(f314(x71931),x71932),x71934))
% 173.53/173.42 [7229]P22(f312(x72291,x72292))+P22(f312(f312(f312(f312(a198,f35(x72291,x72293)),x72292),x72294),x72292))
% 173.53/173.42 [7236]~E(x72364,f189(f860(x72362,a845)))+E(f312(f290(f859(x72361,x72362),x72361,f246(x72361,x72362)),f312(f312(f247(x72361,x72362),x72363),f312(f16(f860(x72362,a845),x72361),x72364))),f189(f860(x72361,a845)))
% 173.53/173.42 [7237]~E(x72373,f189(f860(x72371,a845)))+E(f312(f290(f859(x72371,x72372),x72372,f248(x72371,x72372)),f312(f312(f247(x72371,x72372),x72373),f312(f16(f860(x72372,a845),x72371),x72374))),f189(f860(x72372,a845)))
% 173.53/173.42 [7292]~P22(f312(f312(f314(x72921),x72922),x72924))+P22(f312(f312(f314(x72921),x72922),f312(f312(f124(f860(x72921,a845)),x72923),x72924)))
% 173.53/173.42 [7295]~P22(f312(f312(f314(x72951),x72952),x72953))+P22(f312(f312(f314(x72951),x72952),f312(f312(f124(f860(x72951,a845)),x72953),x72954)))
% 173.53/173.42 [7313]E(f312(f312(f115(f860(x73131,a845)),f312(f312(f289(x73131),x73132),x73133)),x73134),f312(f312(f289(x73131),x73132),f312(f312(f115(f860(x73131,a845)),x73133),x73134)))+~P22(f312(f312(f314(x73131),x73132),x73134))
% 173.53/173.42 [7587]P22(f312(x75871,x75872))+~P22(f312(f312(f312(f115(f860(x75873,a845)),x75874),x75871),x75872))
% 173.53/173.42 [7588]P22(f312(x75881,x75882))+~P22(f312(f312(f312(f115(f860(x75883,a845)),x75881),x75884),x75882))
% 173.53/173.42 [7591]E(f312(f312(f6(x75911,a852),x75912),f312(f312(f21(f860(x75911,a845)),x75913),f312(f312(f289(x75911),x75914),f189(f860(x75911,a845))))),f312(f312(f6(x75911,a852),x75912),x75913))+P22(f312(f312(f314(x75911),x75914),x75913))
% 173.53/173.42 [7596]~P26(x75961)+E(f312(f162(x75961),f312(f312(f150(a852,x75961),x75962),f135(a852,f312(f282(a852,x75963),x75964)))),f312(f312(f6(a852,x75961),x75962),f312(f168(a852),f135(a852,f312(f282(a852,x75963),x75964)))))
% 173.53/173.42 [7597]~P26(x75971)+E(f312(f312(f6(a852,x75971),x75972),f312(f168(a852),f135(a852,f312(f282(a852,x75973),x75974)))),f312(f162(x75971),f312(f312(f150(a852,x75971),x75972),f135(a852,f312(f282(a852,x75973),x75974)))))
% 173.53/173.42 [7711]~E(x77113,x77114)+P22(f312(f71(x77111,x77112,f312(f312(f289(x77111),x77113),f189(f860(x77111,a845)))),x77114))
% 173.53/173.42 [7803]P22(f312(f312(f314(x78031),x78032),f312(f168(x78031),x78033)))+~P22(f312(f312(f314(x78031),x78032),f312(f168(x78031),f312(f312(f169(x78031),x78034),x78033))))
% 173.53/173.42 [7804]P22(f312(f312(f314(x78041),x78042),f312(f168(x78041),x78043)))+~P22(f312(f312(f314(x78041),x78042),f312(f168(x78041),f312(f312(f134(x78041),x78044),x78043))))
% 173.53/173.42 [7873]P22(f312(f312(f314(x78731),x78732),x78733))+~P22(f312(f312(f314(x78731),x78732),f312(f312(f21(f860(x78731,a845)),x78733),x78734)))
% 173.53/173.42 [7875]P22(f312(f312(f314(x78751),x78752),x78753))+~P22(f312(f312(f314(x78751),x78752),f312(f312(f115(f860(x78751,a845)),x78754),x78753)))
% 173.53/173.42 [7878]P22(f312(f312(f314(x78781),x78782),x78783))+~P22(f312(f312(f314(x78781),x78782),f312(f312(f115(f860(x78781,a845)),x78783),x78784)))
% 173.53/173.42 [7896]E(f312(f312(f129(x78961),f312(f312(f169(x78961),x78962),x78963)),f312(f312(f147(x78961),x78964),f312(f312(f134(x78961),f312(a126,x78962)),x78963))),f312(f312(f155(x78961,x78963),x78962),x78964))+~P22(f312(f312(f228(a852),x78962),f312(f190(f853(x78961)),x78963)))
% 173.53/173.42 [7919]P22(f312(f312(f314(x79191),x79192),x79193))+~P22(f312(f312(f227(f860(x79191,a845)),f312(f312(f289(x79191),x79192),x79194)),x79193))
% 173.53/173.42 [7952]~P22(f312(f312(f314(x79521),x79522),x79523))+~P22(f312(f312(f314(x79521),x79522),f312(f312(f21(f860(x79521,a845)),x79524),x79523)))
% 173.53/173.42 [7985]~P22(f312(f312(f228(a852),x79854),f312(f190(f853(x79851)),x79853)))+P22(f312(f312(f314(x79851),x79852),f312(f168(x79851),f312(f312(f155(x79851,x79853),x79854),x79852))))
% 173.53/173.42 [8043]E(f312(f312(f161(x80431),f312(f312(f134(x80431),x80432),x80433)),x80434),f312(f312(f161(x80431),x80433),f312(f312(f89(a852),x80432),x80434)))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x80432),x80434)),f312(f190(f853(x80431)),x80433)))
% 173.53/173.42 [8054]~P23(x80542)+E(f312(f312(f6(x80541,x80542),f312(f312(f8(a852,x80542,x80541),f114(x80542)),x80543)),x80544),f312(f114(x80542),f312(f312(f6(x80541,a852),x80543),x80544)))
% 173.53/173.42 [8055]~P111(x80552)+E(f312(f312(f6(x80551,x80552),f312(f312(f8(a1,x80552,x80551),f116(x80552)),x80553)),x80554),f312(f116(x80552),f312(f312(f6(x80551,a1),x80553),x80554)))
% 173.53/173.42 [8107]~P67(x81072)+E(f312(f312(f9(x81071,x81072),f312(f312(f8(x81072,x81072,x81071),f84(x81072)),x81073)),x81074),f312(f84(x81072),f312(f312(f9(x81071,x81072),x81073),x81074)))
% 173.53/173.42 [8108]~P30(x81082)+E(f312(f312(f6(x81081,x81082),f312(f312(f8(x81082,x81082,x81081),f88(x81082)),x81083)),x81084),f312(f88(x81082),f312(f312(f6(x81081,x81082),x81083),x81084)))
% 173.53/173.42 [8110]E(f312(f312(f6(x81101,a852),x81102),f312(f312(f21(f860(x81101,a845)),x81103),f312(f312(f289(x81101),x81104),f189(f860(x81101,a845))))),f312(f312(f21(a852),f312(f312(f6(x81101,a852),x81102),x81103)),f312(x81102,x81104)))+~P22(f312(f312(f314(x81101),x81104),x81103))
% 173.53/173.42 [8130]P22(f312(f312(f227(f860(x81301,a845)),x81302),x81303))+~P22(f312(f312(f227(f860(x81301,a845)),f312(f312(f289(x81301),x81304),x81302)),x81303))
% 173.53/173.42 [8345]E(f312(a126,f425(x83451,x83452,x83453,x83454)),x83452)+~P22(f312(f312(f312(f312(a198,f312(a27,x83454)),x83453),x83452),x83451))
% 173.53/173.42 [8347]E(f312(f312(f173(x83471,x83472),x83473),x83474),f192(x83472))+P22(f312(f312(f314(x83471),x83474),f312(f290(f859(x83471,x83472),x83471,f246(x83471,x83472)),f312(f168(f859(x83471,x83472)),x83473))))
% 173.53/173.42 [8348]P41(x83481,x83482)+~P41(x83481,f312(f312(f289(f859(x83481,x83481)),f312(f312(f239(x83481,x83481),x83483),x83484)),x83482))
% 173.53/173.42 [8349]P57(x83491,x83492)+~P57(x83491,f312(f312(f289(f859(x83491,x83491)),f312(f312(f239(x83491,x83491),x83493),x83494)),x83492))
% 173.53/173.42 [8358]~P103(x83581)+E(f312(f312(f145(x83581,x83581,f5(x83581)),x83582),f312(f312(f145(x83581,x83581,f5(x83581)),x83583),x83584)),f312(f312(f145(x83581,x83581,f5(x83581)),x83583),f312(f312(f145(x83581,x83581,f5(x83581)),x83582),x83584)))
% 173.53/173.42 [8367]E(x83671,x83672)+~P22(f312(f71(x83673,x83674,f312(f312(f289(x83673),x83671),f189(f860(x83673,a845)))),x83672))
% 173.53/173.42 [8380]E(f312(f312(f129(x83801),f312(f312(f169(x83801),x83802),x83803)),f312(f312(f169(x83801),x83804),f312(f312(f134(x83801),x83802),x83803))),f312(f312(f169(x83801),f312(f312(f89(a852),x83802),x83804)),x83803))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x83802),x83804)),f312(f190(f853(x83801)),x83803)))
% 173.53/173.42 [8419]P22(f312(f70(x84191),x84192))+~E(x84192,f312(f290(a852,x84191,x84193),f312(f233(a852),f312(f312(f7(a852,a852,a845),f228(a852)),x84194))))
% 173.53/173.42 [8440]~P86(x84401)+E(f312(f138(x84401,x84401,f89(x84401),f312(f312(f89(x84401),x84402),x84403)),x84404),f312(f312(f89(x84401),x84402),f312(f138(x84401,x84401,f89(x84401),x84403),x84404)))
% 173.53/173.42 [8477]P22(f312(f312(f227(f860(x84771,a845)),f312(f238(x84771,x84772),x84773)),f312(f238(x84771,x84772),x84774)))+~P22(f312(f312(f227(f860(f859(x84771,x84772),a845)),x84773),x84774))
% 173.53/173.42 [8492]~P22(f312(f312(f227(a852),x84922),x84924))+P22(f312(f312(f227(f860(x84921,a845)),f312(f168(x84921),f312(f312(f169(x84921),x84922),x84923))),f312(f168(x84921),f312(f312(f169(x84921),x84924),x84923))))
% 173.53/173.42 [8493]~P22(f312(f312(f227(a852),x84934),x84932))+P22(f312(f312(f227(f860(x84931,a845)),f312(f168(x84931),f312(f312(f134(x84931),x84932),x84933))),f312(f168(x84931),f312(f312(f134(x84931),x84934),x84933))))
% 173.53/173.42 [8541]~P22(f312(f70(x85411),f312(f312(f21(f860(x85411,a845)),x85412),x85414)))+P22(f312(f70(x85411),f312(f312(f21(f860(x85411,a845)),x85412),f312(f312(f289(x85411),x85413),x85414))))
% 173.53/173.42 [8575]P22(f312(f312(f314(f859(x85751,x85751)),x85752),f287(x85751,x85753)))+~P22(f312(f312(f314(f859(x85751,x85751)),x85752),f312(f312(f184(f859(x85751,x85751),a845),x85754),x85753)))
% 173.53/173.42 [8654]~P22(f312(f70(x86541),f312(f312(f21(f860(x86541,a845)),x86542),f312(f312(f289(x86541),x86544),x86543))))+P22(f312(f70(x86541),f312(f312(f21(f860(x86541,a845)),x86542),x86543)))
% 173.53/173.42 [8796]~E(f312(f312(f173(x87961,x87962),x87963),x87964),f192(x87962))+~P22(f312(f312(f314(x87961),x87964),f312(f290(f859(x87961,x87962),x87961,f246(x87961,x87962)),f312(f168(f859(x87961,x87962)),x87963))))
% 173.53/173.42 [8863]~P87(x88631)+P22(f312(f312(f227(x88631),f312(f312(f124(x88631),x88632),f312(f312(f115(x88631),x88633),x88634))),f312(f312(f115(x88631),f312(f312(f124(x88631),x88632),x88633)),f312(f312(f124(x88631),x88632),x88634))))
% 173.53/173.42 [8864]~P103(x88641)+P22(f312(f312(f227(x88641),f312(f312(f226(x88641),x88642),f312(f312(f225(x88641),x88643),x88644))),f312(f312(f225(x88641),f312(f312(f226(x88641),x88642),x88643)),f312(f312(f226(x88641),x88642),x88644))))
% 173.53/173.42 [9010]E(x90101,x90102)+~P22(f312(f312(f314(f859(x90103,x90103)),f312(f312(f239(x90103,x90103),x90101),x90102)),f312(f168(f859(x90103,x90103)),f312(f312(f177(x90103,x90103),x90104),x90104))))
% 173.53/173.42 [9044]~P22(f312(f312(f314(f859(x90441,x90441)),f312(f312(f239(x90441,x90441),x90443),x90442)),f287(x90441,x90444)))+~P41(x90441,f312(f312(f289(f859(x90441,x90441)),f312(f312(f239(x90441,x90441),x90442),x90443)),x90444))
% 173.53/173.42 [9045]~P22(f312(f312(f314(f859(x90451,x90451)),f312(f312(f239(x90451,x90451),x90453),x90452)),f287(x90451,x90454)))+~P57(x90451,f312(f312(f289(f859(x90451,x90451)),f312(f312(f239(x90451,x90451),x90452),x90453)),x90454))
% 173.53/173.42 [9048]E(x90481,x90482)+E(f312(f132(x90483,f312(f312(f8(a845,a845,x90483),a307),f312(a309,x90481))),f312(f312(f147(x90483),x90482),x90484)),f312(f312(f147(x90483),x90482),f312(f132(x90483,f312(f312(f8(a845,a845,x90483),a307),f312(a309,x90481))),x90484)))
% 173.53/173.42 [9091]~P87(x90911)+P22(f312(f312(f227(x90911),f312(f312(f124(x90911),f312(f312(f115(x90911),x90912),x90913)),f312(f312(f115(x90911),x90912),x90914))),f312(f312(f115(x90911),x90912),f312(f312(f124(x90911),x90913),x90914))))
% 173.53/173.42 [9092]~P103(x90921)+P22(f312(f312(f227(x90921),f312(f312(f226(x90921),f312(f312(f225(x90921),x90922),x90923)),f312(f312(f225(x90921),x90922),x90924))),f312(f312(f225(x90921),x90922),f312(f312(f226(x90921),x90923),x90924))))
% 173.53/173.42 [9167]~E(f312(f290(x91672,x91671,x91673),f235(f860(x91672,a845))),f235(f860(x91671,a845)))+P22(f312(f312(f227(f860(x91671,a845)),f312(f88(f860(x91671,a845)),f312(f290(x91672,x91671,x91673),x91674))),f312(f290(x91672,x91671,x91673),f312(f88(f860(x91672,a845)),x91674))))
% 173.53/173.42 [9244]P22(f312(f312(f312(f312(a198,f312(f223(a846),f312(a30,x92441))),x92442),f425(x92443,x92444,x92442,x92441)),x92443))+~P22(f312(f312(f312(f312(a198,f312(a27,x92441)),x92442),x92444),x92443))
% 173.53/173.42 [9486]P22(f312(f312(f314(f859(x94861,x94861)),f312(f312(f239(x94861,x94861),x94862),x94863)),f312(f265(x94861,x94861),f312(f312(f267(x94861,x94861,x94861),x94864),f287(x94861,x94864)))))+~P22(f312(f312(f314(f859(x94861,x94861)),f312(f312(f239(x94861,x94861),x94862),x94863)),f312(f312(f267(x94861,x94861,x94861),f312(f265(x94861,x94861),x94864)),f287(x94861,f312(f265(x94861,x94861),x94864)))))
% 173.53/173.42 [9487]~P22(f312(f312(f314(f859(x94871,x94871)),f312(f312(f239(x94871,x94871),x94872),x94873)),f312(f265(x94871,x94871),f312(f312(f267(x94871,x94871,x94871),x94874),f287(x94871,x94874)))))+P22(f312(f312(f314(f859(x94871,x94871)),f312(f312(f239(x94871,x94871),x94872),x94873)),f312(f312(f267(x94871,x94871,x94871),f312(f265(x94871,x94871),x94874)),f287(x94871,f312(f265(x94871,x94871),x94874)))))
% 173.53/173.42 [9509]~P22(f312(f312(f314(x95092),x95094),f312(f236(x95091,x95092),x95093)))+P22(f312(f312(f314(f859(x95091,x95092)),f312(f312(f239(x95091,x95092),f567(x95093,x95091,x95094,x95092)),x95094)),x95093))
% 173.53/173.42 [9510]~P22(f312(f312(f314(x95102),x95104),f312(f236(x95101,x95102),x95103)))+P22(f312(f312(f314(f859(x95101,x95102)),f312(f312(f239(x95101,x95102),f568(x95103,x95101,x95104,x95102)),x95104)),x95103))
% 173.53/173.42 [9529]~P22(f312(f312(f314(x95291),x95294),f312(f312(f124(f860(x95291,a845)),x95292),x95293)))+P22(f312(f312(f312(f124(f860(x95291,a845)),f312(f312(f7(x95291,f860(x95291,a845),a845),f314(x95291)),x95292)),f312(f312(f7(x95291,f860(x95291,a845),a845),f314(x95291)),x95293)),x95294))
% 173.53/173.42 [9530]~P22(f312(f312(f314(x95301),x95304),f312(f312(f115(f860(x95301,a845)),x95302),x95303)))+P22(f312(f312(f312(f115(f860(x95301,a845)),f312(f312(f7(x95301,f860(x95301,a845),a845),f314(x95301)),x95302)),f312(f312(f7(x95301,f860(x95301,a845),a845),f314(x95301)),x95303)),x95304))
% 173.53/173.42 [9605]~P22(f312(f312(f314(f859(x96051,x96051)),f312(f312(f239(x96051,x96051),x96054),x96053)),f312(f312(f267(x96051,x96051,x96051),x96052),f287(x96051,x96052))))+P22(f312(f312(f314(f859(x96051,x96051)),f312(f312(f239(x96051,x96051),f778(x96052,x96053,x96054,x96051)),x96053)),x96052))
% 173.53/173.42 [9650]P22(f312(f312(f314(x96501),x96502),f312(f312(f124(f860(x96501,a845)),x96503),x96504)))+~P22(f312(f312(f312(f124(f860(x96501,a845)),f312(f312(f7(x96501,f860(x96501,a845),a845),f314(x96501)),x96503)),f312(f312(f7(x96501,f860(x96501,a845),a845),f314(x96501)),x96504)),x96502))
% 173.53/173.42 [9651]P22(f312(f312(f314(x96511),x96512),f312(f312(f115(f860(x96511,a845)),x96513),x96514)))+~P22(f312(f312(f312(f115(f860(x96511,a845)),f312(f312(f7(x96511,f860(x96511,a845),a845),f314(x96511)),x96513)),f312(f312(f7(x96511,f860(x96511,a845),a845),f314(x96511)),x96514)),x96512))
% 173.53/173.42 [9937]P37(x99371,f312(f312(f7(x99371,f860(f859(x99371,x99371),a845),f860(x99371,a845)),f312(f312(f8(f860(x99371,f860(f860(f859(x99371,x99371),a845),a845)),f860(f860(f859(x99371,x99371),a845),f860(x99371,a845)),x99371),f7(x99371,f860(f859(x99371,x99371),a845),a845)),f312(f312(f8(f860(x99371,f859(x99371,x99371)),f860(x99371,f860(f860(f859(x99371,x99371),a845),a845)),x99371),f312(f8(f859(x99371,x99371),f860(f860(f859(x99371,x99371),a845),a845),x99371),f314(f859(x99371,x99371)))),f239(x99371,x99371)))),x99372),x99373,x99374)+~P22(f312(f312(f314(f859(f853(x99371),f853(x99371))),f312(f312(f239(f853(x99371),f853(x99371)),x99373),x99374)),f154(x99371,x99372)))
% 173.53/173.42 [9941]P58(x99411,f312(f312(f7(x99411,f860(f859(x99411,x99411),a845),f860(x99411,a845)),f312(f312(f8(f860(x99411,f860(f860(f859(x99411,x99411),a845),a845)),f860(f860(f859(x99411,x99411),a845),f860(x99411,a845)),x99411),f7(x99411,f860(f859(x99411,x99411),a845),a845)),f312(f312(f8(f860(x99411,f859(x99411,x99411)),f860(x99411,f860(f860(f859(x99411,x99411),a845),a845)),x99411),f312(f8(f859(x99411,x99411),f860(f860(f859(x99411,x99411),a845),a845),x99411),f314(f859(x99411,x99411)))),f239(x99411,x99411)))),x99412),x99413,x99414)+~P22(f312(f312(f314(f859(f860(x99411,a845),f860(x99411,a845))),f312(f312(f239(f860(x99411,a845),f860(x99411,a845)),x99413),x99414)),f303(x99411,x99412)))
% 173.53/173.42 [9969]E(x99691,x99692)+~E(f312(f312(f7(x99693,f860(f859(x99693,x99694),a845),f860(x99694,a845)),f312(f312(f8(f860(x99694,f860(f860(f859(x99693,x99694),a845),a845)),f860(f860(f859(x99693,x99694),a845),f860(x99694,a845)),x99693),f7(x99694,f860(f859(x99693,x99694),a845),a845)),f312(f312(f8(f860(x99694,f859(x99693,x99694)),f860(x99694,f860(f860(f859(x99693,x99694),a845),a845)),x99693),f312(f8(f859(x99693,x99694),f860(f860(f859(x99693,x99694),a845),a845),x99694),f314(f859(x99693,x99694)))),f239(x99693,x99694)))),x99691),f312(f312(f7(x99693,f860(f859(x99693,x99694),a845),f860(x99694,a845)),f312(f312(f8(f860(x99694,f860(f860(f859(x99693,x99694),a845),a845)),f860(f860(f859(x99693,x99694),a845),f860(x99694,a845)),x99693),f7(x99694,f860(f859(x99693,x99694),a845),a845)),f312(f312(f8(f860(x99694,f859(x99693,x99694)),f860(x99694,f860(f860(f859(x99693,x99694),a845),a845)),x99693),f312(f8(f859(x99693,x99694),f860(f860(f859(x99693,x99694),a845),a845),x99694),f314(f859(x99693,x99694)))),f239(x99693,x99694)))),x99692))
% 173.53/173.42 [9973]~P37(x99731,f312(f312(f7(x99731,f860(f859(x99731,x99731),a845),f860(x99731,a845)),f312(f312(f8(f860(x99731,f860(f860(f859(x99731,x99731),a845),a845)),f860(f860(f859(x99731,x99731),a845),f860(x99731,a845)),x99731),f7(x99731,f860(f859(x99731,x99731),a845),a845)),f312(f312(f8(f860(x99731,f859(x99731,x99731)),f860(x99731,f860(f860(f859(x99731,x99731),a845),a845)),x99731),f312(f8(f859(x99731,x99731),f860(f860(f859(x99731,x99731),a845),a845),x99731),f314(f859(x99731,x99731)))),f239(x99731,x99731)))),x99734),x99732,x99733)+P22(f312(f312(f314(f859(f853(x99731),f853(x99731))),f312(f312(f239(f853(x99731),f853(x99731)),x99732),x99733)),f154(x99731,x99734)))
% 173.53/173.42 [9974]~P58(x99741,f312(f312(f7(x99741,f860(f859(x99741,x99741),a845),f860(x99741,a845)),f312(f312(f8(f860(x99741,f860(f860(f859(x99741,x99741),a845),a845)),f860(f860(f859(x99741,x99741),a845),f860(x99741,a845)),x99741),f7(x99741,f860(f859(x99741,x99741),a845),a845)),f312(f312(f8(f860(x99741,f859(x99741,x99741)),f860(x99741,f860(f860(f859(x99741,x99741),a845),a845)),x99741),f312(f8(f859(x99741,x99741),f860(f860(f859(x99741,x99741),a845),a845),x99741),f314(f859(x99741,x99741)))),f239(x99741,x99741)))),x99744),x99742,x99743)+P22(f312(f312(f314(f859(f860(x99741,a845),f860(x99741,a845))),f312(f312(f239(f860(x99741,a845),f860(x99741,a845)),x99742),x99743)),f303(x99741,x99744)))
% 173.53/173.42 [7364]~P90(x73641)+E(f312(f312(f89(x73641),f312(f117(x73641),x73642)),f312(f312(f89(x73641),f312(f117(x73641),x73643)),x73644)),f312(f312(f89(x73641),f312(f117(x73641),f312(f312(f89(a1),x73642),x73643))),x73644))
% 173.53/173.42 [7365]~P90(x73651)+E(f312(f312(f89(x73651),f312(f117(x73651),x73652)),f312(f312(f21(x73651),f312(f117(x73651),x73653)),x73654)),f312(f312(f21(x73651),f312(f117(x73651),f312(f312(f89(a1),x73652),x73653))),x73654))
% 173.53/173.42 [7366]~P90(x73661)+E(f312(f312(f90(x73661),f312(f117(x73661),x73662)),f312(f312(f90(x73661),f312(f117(x73661),x73663)),x73664)),f312(f312(f90(x73661),f312(f117(x73661),f312(f312(f90(a1),x73662),x73663))),x73664))
% 173.53/173.42 [7408]~P23(x74081)+E(f312(f162(x74081),f312(f312(f150(x74082,x74081),f312(f16(x74081,x74082),x74083)),x74084)),f312(f312(f90(x74081),f312(f114(x74081),f312(f190(f853(x74082)),x74084))),x74083))
% 173.53/173.42 [7643]E(f312(f256(x76431,f312(f312(f147(f859(a113,x76431)),x76432),x76433)),x76434),f312(f248(a113,x76431),x76432))+~P22(f312(f312(f228(a113),x76434),f312(f246(a113,x76431),x76432)))
% 173.53/173.42 [7688]~P90(x76881)+E(f312(f312(f89(x76881),f312(f117(x76881),x76882)),f312(f312(f21(x76881),x76883),f312(f117(x76881),x76884))),f312(f312(f89(x76881),f312(f117(x76881),f312(f312(f89(a1),x76882),f312(f88(a1),x76884)))),x76883))
% 173.53/173.42 [7814]E(f312(f256(x78141,x78142),f312(f312(f21(a113),x78143),f312(f246(a113,x78141),x78144))),f312(f256(x78141,f312(f312(f147(f859(a113,x78141)),x78144),x78142)),x78143))+P22(f312(f312(f228(a113),x78143),f312(f246(a113,x78141),x78144)))
% 173.53/173.42 [8260]~P22(f312(f312(f314(x82601),x82602),f312(f168(x82601),f128(x82601,x82604))))+P22(f312(f312(f314(x82601),x82602),f312(f168(x82601),f128(x82601,f312(f312(f129(x82601),x82603),x82604)))))
% 173.53/173.42 [8261]~P22(f312(f312(f314(x82611),x82612),f312(f168(x82611),f128(x82611,x82613))))+P22(f312(f312(f314(x82611),x82612),f312(f168(x82611),f128(x82611,f312(f312(f129(x82611),x82613),x82614)))))
% 173.53/173.42 [8280]E(f312(f312(f124(f860(x82801,a845)),f312(f312(f115(f860(x82801,a845)),x82802),x82803)),x82804),f312(f312(f115(f860(x82801,a845)),x82802),f312(f312(f124(f860(x82801,a845)),x82803),x82804)))+~P22(f312(f312(f227(f860(x82801,a845)),x82804),x82802))
% 173.53/173.42 [8588]~E(f312(f312(f124(f860(x85881,a845)),f312(f312(f115(f860(x85881,a845)),x85883),x85884)),x85882),f312(f312(f115(f860(x85881,a845)),x85883),f312(f312(f124(f860(x85881,a845)),x85884),x85882)))+P22(f312(f312(f227(f860(x85881,a845)),x85882),x85883))
% 173.53/173.42 [8870]~P22(f312(f312(f227(f860(x88701,a845)),x88702),f312(f312(f124(f860(x88701,a845)),x88703),x88704)))+P22(f312(f312(f227(f860(x88701,a845)),f312(f312(f21(f860(x88701,a845)),x88702),x88703)),x88704))
% 173.53/173.42 [8932]~P22(f312(f312(f312(f312(a198,f312(a27,x89321)),x89322),f312(a126,x89323)),x89324))+P22(f312(f312(f312(f312(a198,f312(f223(a846),f312(a30,x89321))),x89322),x89323),x89324))
% 173.53/173.42 [8989]P22(f312(f312(f227(f860(x89891,a845)),x89892),f312(f312(f124(f860(x89891,a845)),x89893),x89894)))+~P22(f312(f312(f227(f860(x89891,a845)),f312(f312(f21(f860(x89891,a845)),x89892),x89893)),x89894))
% 173.53/173.42 [9043]P22(f312(f312(f312(f312(a198,f312(a27,x90431)),x90432),f312(a126,x90433)),x90434))+~P22(f312(f312(f312(f312(a198,f312(f223(a846),f312(a30,x90431))),x90432),x90433),x90434))
% 173.53/173.42 [9072]~P83(x90721)+E(f312(f84(x90721),f312(f312(f6(x90722,x90721),f312(f312(f8(x90721,x90721,x90722),f84(x90721)),x90723)),x90724)),f312(f312(f6(x90722,x90721),f312(f312(f8(x90721,x90721,x90722),f84(x90721)),x90723)),x90724))
% 173.53/173.42 [9242]~P83(x92421)+P22(f312(f312(f227(x92421),f2(x92421)),f312(f312(f6(x92422,x92421),f312(f312(f8(x92421,x92421,x92422),f84(x92421)),x92423)),x92424)))
% 173.53/173.42 [9247]~P30(x92471)+E(f312(f162(x92471),f312(f312(f150(x92472,x92471),f312(f82(x92471,x92471,x92472,f88(x92471)),x92473)),x92474)),f312(f88(x92471),f312(f162(x92471),f312(f312(f150(x92472,x92471),x92473),x92474))))
% 173.53/173.42 [9380]~P83(x93801)+P22(f312(f312(f227(x93801),f312(f84(x93801),f312(f312(f6(x93802,x93801),x93803),x93804))),f312(f312(f6(x93802,x93801),f312(f312(f8(x93801,x93801,x93802),f84(x93801)),x93803)),x93804)))
% 173.53/173.42 [9411]~E(f312(f312(f89(a852),x94111),x94114),f312(f312(f89(a852),x94113),x94112))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x94111),x94112)),f312(f312(f239(a852,a852),x94113),x94114))),a122))
% 173.53/173.42 [9412]~P22(f312(f312(f228(a852),x94121),x94123))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x94121),x94122)),f312(f312(f239(a852,a852),x94123),x94124))),a45))
% 173.53/173.42 [9413]~P22(f312(f312(f228(a852),x94131),x94133))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x94131),x94132)),f312(f312(f239(a852,a852),x94133),x94134))),a79))
% 173.53/173.42 [9554]E(f312(f312(f89(a852),x95541),x95542),f312(f312(f89(a852),x95543),x95544))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x95541),x95544)),f312(f312(f239(a852,a852),x95543),x95542))),a122))
% 173.53/173.42 [9579]E(f312(f312(f161(x95791),f312(f312(f134(x95791),f312(f190(f853(x95791)),f172(x95791,x95792,x95793))),x95793)),x95794),f312(f312(f161(x95791),x95793),f312(f312(f89(a852),x95794),f312(f190(f853(x95791)),f172(x95791,x95792,x95793)))))+~P22(f312(f312(f228(a852),x95794),f312(f190(f853(x95791)),f312(f312(f134(x95791),f312(f190(f853(x95791)),f172(x95791,x95792,x95793))),x95793))))
% 173.53/173.42 [9596]~P22(f312(f312(f314(x95962),x95964),f312(f312(f50(x95961,f860(x95962,a845)),f235(f860(x95961,a845))),x95963)))+P22(f312(f312(f312(f50(x95961,f860(x95962,a845)),f235(f860(x95961,a845))),f312(f312(f8(f860(x95962,a845),f860(x95962,a845),x95961),f312(f7(x95962,f860(x95962,a845),a845),f314(x95962))),x95963)),x95964))
% 173.53/173.42 [9597]~P22(f312(f312(f314(x95972),x95974),f312(f312(f51(x95971,f860(x95972,a845)),f235(f860(x95971,a845))),x95973)))+P22(f312(f312(f312(f51(x95971,f860(x95972,a845)),f235(f860(x95971,a845))),f312(f312(f8(f860(x95972,a845),f860(x95972,a845),x95971),f312(f7(x95972,f860(x95972,a845),a845),f314(x95972))),x95973)),x95974))
% 173.53/173.42 [9677]~P22(f312(f57(x96771,x96772),f312(f312(f239(a1,a1),x96774),x96773)))+P22(f312(f57(f312(f88(a1),x96771),x96772),f312(f312(f239(a1,a1),f312(f312(f312(f108(a1),f312(f312(a309,x96773),f2(a1))),f312(f88(a1),x96774)),f312(f312(f21(a1),f312(f88(a1),x96774)),f87(a1)))),f312(f312(f312(f108(a1),f312(f312(a309,x96773),f2(a1))),f2(a1)),f312(f312(f21(a1),x96772),x96773)))))
% 173.53/173.42 [9686]P22(f312(f312(f314(x96861),x96862),f312(f312(f50(x96863,f860(x96861,a845)),f235(f860(x96863,a845))),x96864)))+~P22(f312(f312(f312(f50(x96863,f860(x96861,a845)),f235(f860(x96863,a845))),f312(f312(f8(f860(x96861,a845),f860(x96861,a845),x96863),f312(f7(x96861,f860(x96861,a845),a845),f314(x96861))),x96864)),x96862))
% 173.53/173.42 [9687]P22(f312(f312(f314(x96871),x96872),f312(f312(f51(x96873,f860(x96871,a845)),f235(f860(x96873,a845))),x96874)))+~P22(f312(f312(f312(f51(x96873,f860(x96871,a845)),f235(f860(x96873,a845))),f312(f312(f8(f860(x96871,a845),f860(x96871,a845),x96873),f312(f7(x96871,f860(x96871,a845),a845),f314(x96871))),x96874)),x96872))
% 173.53/173.42 [9697]E(f312(f312(f50(a852,f860(x96971,a845)),f235(f860(a852,a845))),x96972),f312(f312(f50(a852,f860(x96971,a845)),f235(f860(a852,a845))),x96973))+~E(f312(f312(f50(a852,f860(x96971,a845)),f312(f282(a852,f2(a852)),f490(x96972,x96974,x96973,x96971))),x96973),f312(f312(f50(a852,f860(x96971,a845)),f312(f282(a852,f2(a852)),f312(f312(f89(a852),f490(x96972,x96974,x96973,x96971)),x96974))),x96972))
% 173.53/173.42 [10030]~P22(f312(f312(f227(f860(f859(x100301,x100302),a845)),x100303),x100304))+P22(f312(f312(f227(f860(x100301,f860(x100302,a845))),f312(f312(f7(x100301,f860(f859(x100301,x100302),a845),f860(x100302,a845)),f312(f312(f8(f860(x100302,f860(f860(f859(x100301,x100302),a845),a845)),f860(f860(f859(x100301,x100302),a845),f860(x100302,a845)),x100301),f7(x100302,f860(f859(x100301,x100302),a845),a845)),f312(f312(f8(f860(x100302,f859(x100301,x100302)),f860(x100302,f860(f860(f859(x100301,x100302),a845),a845)),x100301),f312(f8(f859(x100301,x100302),f860(f860(f859(x100301,x100302),a845),a845),x100302),f314(f859(x100301,x100302)))),f239(x100301,x100302)))),x100303)),f312(f312(f7(x100301,f860(f859(x100301,x100302),a845),f860(x100302,a845)),f312(f312(f8(f860(x100302,f860(f860(f859(x100301,x100302),a845),a845)),f860(f860(f859(x100301,x100302),a845),f860(x100302,a845)),x100301),f7(x100302,f860(f859(x100301,x100302),a845),a845)),f312(f312(f8(f860(x100302,f859(x100301,x100302)),f860(x100302,f860(f860(f859(x100301,x100302),a845),a845)),x100301),f312(f8(f859(x100301,x100302),f860(f860(f859(x100301,x100302),a845),a845),x100302),f314(f859(x100301,x100302)))),f239(x100301,x100302)))),x100304)))
% 173.53/173.42 [10046]P22(f312(f312(f227(f860(f859(x100461,x100462),a845)),x100463),x100464))+~P22(f312(f312(f227(f860(x100461,f860(x100462,a845))),f312(f312(f7(x100461,f860(f859(x100461,x100462),a845),f860(x100462,a845)),f312(f312(f8(f860(x100462,f860(f860(f859(x100461,x100462),a845),a845)),f860(f860(f859(x100461,x100462),a845),f860(x100462,a845)),x100461),f7(x100462,f860(f859(x100461,x100462),a845),a845)),f312(f312(f8(f860(x100462,f859(x100461,x100462)),f860(x100462,f860(f860(f859(x100461,x100462),a845),a845)),x100461),f312(f8(f859(x100461,x100462),f860(f860(f859(x100461,x100462),a845),a845),x100462),f314(f859(x100461,x100462)))),f239(x100461,x100462)))),x100463)),f312(f312(f7(x100461,f860(f859(x100461,x100462),a845),f860(x100462,a845)),f312(f312(f8(f860(x100462,f860(f860(f859(x100461,x100462),a845),a845)),f860(f860(f859(x100461,x100462),a845),f860(x100462,a845)),x100461),f7(x100462,f860(f859(x100461,x100462),a845),a845)),f312(f312(f8(f860(x100462,f859(x100461,x100462)),f860(x100462,f860(f860(f859(x100461,x100462),a845),a845)),x100461),f312(f8(f859(x100461,x100462),f860(f860(f859(x100461,x100462),a845),a845),x100462),f314(f859(x100461,x100462)))),f239(x100461,x100462)))),x100464)))
% 173.53/173.42 [9122]~P22(f312(f312(f314(f859(x91221,x91221)),x91222),f287(x91221,x91224)))+P22(f312(f312(f314(f859(x91221,x91221)),x91222),f287(x91221,f312(f312(f124(f860(f859(x91221,x91221),a845)),x91223),x91224))))
% 173.53/173.42 [9123]~P22(f312(f312(f314(f859(x91231,x91231)),x91232),f287(x91231,x91233)))+P22(f312(f312(f314(f859(x91231,x91231)),x91232),f287(x91231,f312(f312(f124(f860(f859(x91231,x91231),a845)),x91233),x91234))))
% 173.53/173.42 [9477]~E(f312(f168(x94771),x94774),f179(x94771,x94772,x94773))+E(f312(f173(x94771,x94772),f312(f312(f150(x94771,f859(x94771,x94772)),f312(f312(f18(x94771,x94772,f859(x94771,x94772)),f239(x94771,x94772)),f312(f312(f8(f856(x94772),x94772,x94771),f223(x94772)),x94773))),x94774)),x94773)
% 173.53/173.42 [9796]~P22(f312(f312(f228(a852),f312(f312(f89(a852),x97961),x97964)),f312(f312(f89(a852),x97963),x97962)))+P22(f312(f312(f228(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x97961),x97962)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x97963),x97964)),f189(f860(f859(a852,a852),a845)))))))
% 173.53/173.42 [9797]~P22(f312(f312(f227(a852),f312(f312(f89(a852),x97971),x97974)),f312(f312(f89(a852),x97973),x97972)))+P22(f312(f312(f227(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x97971),x97972)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x97973),x97974)),f189(f860(f859(a852,a852),a845)))))))
% 173.53/173.42 [9879]P22(f312(f312(f228(a852),f312(f312(f89(a852),x98791),x98792)),f312(f312(f89(a852),x98793),x98794)))+~P22(f312(f312(f228(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x98791),x98794)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x98793),x98792)),f189(f860(f859(a852,a852),a845)))))))
% 173.53/173.42 [9880]P22(f312(f312(f227(a852),f312(f312(f89(a852),x98801),x98802)),f312(f312(f89(a852),x98803),x98804)))+~P22(f312(f312(f227(a1),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x98801),x98804)),f189(f860(f859(a852,a852),a845)))))),f312(a98,f312(f264(f859(a852,a852),f859(a852,a852),a122),f312(f312(f289(f859(a852,a852)),f312(f312(f239(a852,a852),x98803),x98802)),f189(f860(f859(a852,a852),a845)))))))
% 173.53/173.42 [9922]P22(f312(f312(f227(f860(x99221,a845)),f312(f312(f50(a852,f860(x99221,a845)),f235(f860(a852,a845))),x99222)),f312(f312(f50(a852,f860(x99221,a845)),f235(f860(a852,a845))),x99223)))+~P22(f312(f312(f227(f860(x99221,a845)),f312(f312(f50(a852,f860(x99221,a845)),f312(f282(a852,f2(a852)),f491(x99223,x99224,x99222,x99221))),x99222)),f312(f312(f50(a852,f860(x99221,a845)),f312(f282(a852,f2(a852)),f312(f312(f89(a852),f491(x99223,x99224,x99222,x99221)),x99224))),x99223)))
% 173.53/173.42 [10021]~P22(f312(f312(f314(x100212),x100214),f312(f236(x100211,x100212),x100213)))+P22(f312(f245(x100211,x100212,f312(f312(f7(x100211,f860(f859(x100211,x100212),a845),f860(x100212,a845)),f312(f312(f8(f860(x100212,f860(f860(f859(x100211,x100212),a845),a845)),f860(f860(f859(x100211,x100212),a845),f860(x100212,a845)),x100211),f7(x100212,f860(f859(x100211,x100212),a845),a845)),f312(f312(f8(f860(x100212,f859(x100211,x100212)),f860(x100212,f860(f860(f859(x100211,x100212),a845),a845)),x100211),f312(f8(f859(x100211,x100212),f860(f860(f859(x100211,x100212),a845),a845),x100212),f314(f859(x100211,x100212)))),f239(x100211,x100212)))),x100213)),x100214))
% 173.53/173.42 [10022]~P22(f312(f312(f314(x100221),x100224),f312(f238(x100221,x100222),x100223)))+P22(f312(f244(x100221,x100222,f312(f312(f7(x100221,f860(f859(x100221,x100222),a845),f860(x100222,a845)),f312(f312(f8(f860(x100222,f860(f860(f859(x100221,x100222),a845),a845)),f860(f860(f859(x100221,x100222),a845),f860(x100222,a845)),x100221),f7(x100222,f860(f859(x100221,x100222),a845),a845)),f312(f312(f8(f860(x100222,f859(x100221,x100222)),f860(x100222,f860(f860(f859(x100221,x100222),a845),a845)),x100221),f312(f8(f859(x100221,x100222),f860(f860(f859(x100221,x100222),a845),a845),x100222),f314(f859(x100221,x100222)))),f239(x100221,x100222)))),x100223)),x100224))
% 173.53/173.42 [10033]P22(f312(f312(f314(x100331),x100332),f312(f236(x100333,x100331),x100334)))+~P22(f312(f245(x100333,x100331,f312(f312(f7(x100333,f860(f859(x100333,x100331),a845),f860(x100331,a845)),f312(f312(f8(f860(x100331,f860(f860(f859(x100333,x100331),a845),a845)),f860(f860(f859(x100333,x100331),a845),f860(x100331,a845)),x100333),f7(x100331,f860(f859(x100333,x100331),a845),a845)),f312(f312(f8(f860(x100331,f859(x100333,x100331)),f860(x100331,f860(f860(f859(x100333,x100331),a845),a845)),x100333),f312(f8(f859(x100333,x100331),f860(f860(f859(x100333,x100331),a845),a845),x100331),f314(f859(x100333,x100331)))),f239(x100333,x100331)))),x100334)),x100332))
% 173.53/173.42 [10034]P22(f312(f312(f314(x100341),x100342),f312(f238(x100341,x100343),x100344)))+~P22(f312(f244(x100341,x100343,f312(f312(f7(x100341,f860(f859(x100341,x100343),a845),f860(x100343,a845)),f312(f312(f8(f860(x100343,f860(f860(f859(x100341,x100343),a845),a845)),f860(f860(f859(x100341,x100343),a845),f860(x100343,a845)),x100341),f7(x100343,f860(f859(x100341,x100343),a845),a845)),f312(f312(f8(f860(x100343,f859(x100341,x100343)),f860(x100343,f860(f860(f859(x100341,x100343),a845),a845)),x100341),f312(f8(f859(x100341,x100343),f860(f860(f859(x100341,x100343),a845),a845),x100343),f314(f859(x100341,x100343)))),f239(x100341,x100343)))),x100344)),x100342))
% 173.53/173.42 [9707]P22(f312(f156(x97071,x97072),x97073))+~P22(f312(f156(x97071,f312(f312(f18(x97071,a845,a845),f312(f312(f8(a845,f860(a845,a845),x97071),a310),x97074)),x97072)),x97073))
% 173.53/173.42 [9708]P22(f312(f156(x97081,x97082),x97083))+~P22(f312(f156(x97081,f312(f312(f18(x97081,a845,a845),f312(f312(f8(a845,f860(a845,a845),x97081),a310),x97082)),x97084)),x97083))
% 173.53/173.42 [9799]~P107(x97991)+E(f312(f312(f90(x97991),f312(f312(f89(x97991),f87(x97991)),f87(x97991))),f312(f312(f6(a852,x97991),f312(f312(f8(x97991,x97991,a852),f312(f89(x97991),x97992)),f312(f312(f7(a852,x97991,x97991),f312(f312(f8(x97991,f860(x97991,x97991),a852),f90(x97991)),f114(x97991))),x97993))),f312(f279(a852),x97994))),f312(f312(f90(x97991),f312(f114(x97991),x97994)),f312(f312(f89(x97991),x97992),f312(f312(f89(x97991),x97992),f312(f312(f90(x97991),f312(f114(x97991),f312(f312(f21(a852),x97994),f87(a852)))),x97993)))))
% 173.53/173.42 [9944]P22(f312(x99441,f577(x99442,x99443,x99444,x99441)))+P41(x99442,f312(f233(f859(x99442,x99442)),f312(f249(x99442,x99442,a845),f312(f312(f8(f860(x99442,a845),f860(x99442,a845),x99442),f312(f18(x99442,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99442),a310),x99441))),f312(f312(f7(x99442,f860(x99442,x99442),f860(x99442,a845)),f312(f312(f8(f860(x99442,a845),f860(f860(x99442,x99442),f860(x99442,a845)),x99442),f8(x99442,a845,x99442)),a309)),x99443)))))
% 173.53/173.42 [9959]~P22(f312(f312(f228(a852),f312(x99594,f312(x99593,f577(x99591,x99593,x99594,x99592)))),f312(x99594,f577(x99591,x99593,x99594,x99592))))+P41(x99591,f312(f233(f859(x99591,x99591)),f312(f249(x99591,x99591,a845),f312(f312(f8(f860(x99591,a845),f860(x99591,a845),x99591),f312(f18(x99591,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99591),a310),x99592))),f312(f312(f7(x99591,f860(x99591,x99591),f860(x99591,a845)),f312(f312(f8(f860(x99591,a845),f860(f860(x99591,x99591),f860(x99591,a845)),x99591),f8(x99591,a845,x99591)),a309)),x99593)))))
% 173.53/173.42 [10063]~P22(f312(f312(f314(f859(x100631,x100631)),f312(f312(f239(x100631,x100631),x100633),x100634)),f312(f312(f124(f860(f859(x100631,x100631),a845)),x100632),f287(x100631,f189(f860(f859(x100631,x100631),a845))))))+P22(f312(f312(f312(f312(f124(f860(x100631,f860(x100631,a845))),f312(f312(f7(x100631,f860(f859(x100631,x100631),a845),f860(x100631,a845)),f312(f312(f8(f860(x100631,f860(f860(f859(x100631,x100631),a845),a845)),f860(f860(f859(x100631,x100631),a845),f860(x100631,a845)),x100631),f7(x100631,f860(f859(x100631,x100631),a845),a845)),f312(f312(f8(f860(x100631,f859(x100631,x100631)),f860(x100631,f860(f860(f859(x100631,x100631),a845),a845)),x100631),f312(f8(f859(x100631,x100631),f860(f860(f859(x100631,x100631),a845),a845),x100631),f314(f859(x100631,x100631)))),f239(x100631,x100631)))),x100632)),a309),x100633),x100634))
% 173.53/173.42 [10073]P22(f312(f312(f314(f859(x100731,x100731)),f312(f312(f239(x100731,x100731),x100732),x100733)),f312(f312(f124(f860(f859(x100731,x100731),a845)),x100734),f287(x100731,f189(f860(f859(x100731,x100731),a845))))))+~P22(f312(f312(f312(f312(f124(f860(x100731,f860(x100731,a845))),f312(f312(f7(x100731,f860(f859(x100731,x100731),a845),f860(x100731,a845)),f312(f312(f8(f860(x100731,f860(f860(f859(x100731,x100731),a845),a845)),f860(f860(f859(x100731,x100731),a845),f860(x100731,a845)),x100731),f7(x100731,f860(f859(x100731,x100731),a845),a845)),f312(f312(f8(f860(x100731,f859(x100731,x100731)),f860(x100731,f860(f860(f859(x100731,x100731),a845),a845)),x100731),f312(f8(f859(x100731,x100731),f860(f860(f859(x100731,x100731),a845),a845),x100731),f314(f859(x100731,x100731)))),f239(x100731,x100731)))),x100734)),a309),x100732),x100733))
% 173.53/173.42 [9930]~P104(x99303)+E(f99(x99301,f312(f312(f18(x99301,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99301),a310),x99302)),f312(f312(f8(f860(x99301,a845),a845,x99301),f97(x99301)),f312(f312(f8(f860(x99301,a845),f860(x99301,a845),x99301),f312(f18(x99301,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99301),a315),x99302))),f312(f312(f8(x99303,f860(x99301,a845),x99301),f312(f7(x99301,x99303,a845),f312(f312(f8(x99303,f860(x99303,a845),x99301),f227(x99303)),x99304))),x99304))))),f312(f101(x99301,x99303,x99304),x99302))
% 173.53/173.42 [9972]~P104(x99723)+E(f99(x99721,f312(f312(f18(x99721,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99721),a310),x99722)),f312(f312(f8(f860(x99721,a845),a845,x99721),f97(x99721)),f312(f312(f8(f860(x99721,a845),f860(x99721,a845),x99721),f312(f18(x99721,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99721),a315),x99722))),f312(f312(f7(x99721,f860(x99721,x99723),f860(x99721,a845)),f312(f312(f8(f860(x99723,a845),f860(f860(x99721,x99723),f860(x99721,a845)),x99721),f8(x99723,a845,x99721)),f312(f312(f8(x99723,f860(x99723,a845),x99721),f227(x99723)),x99724))),x99724))))),f104(x99721,x99723,x99724,x99722))
% 173.53/173.42 [10019]E(f312(f312(f147(f853(x100191)),f312(f312(f147(x100191),x100192),f312(f138(f853(x100191),f853(x100191),f129(x100191),f127(x100191)),f312(f312(f150(f853(x100191),f853(x100191)),f152(f853(x100191),x100191,f127(x100191),f312(f312(f8(f853(x100191),f860(f853(x100191),f853(x100191)),x100191),f16(f853(x100191),f853(x100191))),f312(f312(f7(x100191,f853(x100191),f853(x100191)),f147(x100191)),f127(x100191))))),x100193)))),f175(x100191,f312(f312(f147(f853(x100191)),x100194),f312(f138(f853(f853(x100191)),f853(f853(x100191)),f129(f853(x100191)),f127(f853(x100191))),f312(f312(f150(f853(x100191),f853(f853(x100191))),f152(f853(f853(x100191)),x100191,f127(f853(x100191)),f312(f16(f860(f853(x100191),f853(f853(x100191))),x100191),f312(f312(f7(f853(x100191),f853(f853(x100191)),f853(f853(x100191))),f147(f853(x100191))),f127(f853(x100191)))))),x100193))))),f175(x100191,f312(f312(f147(f853(x100191)),f312(f312(f147(x100191),x100192),x100194)),x100193)))+~P22(f312(f300(f853(f853(x100191)),f176(x100191)),f312(f312(f147(f853(x100191)),f312(f312(f147(x100191),x100192),x100194)),x100193)))
% 173.53/173.42 [10062]~P22(f312(f70(x100622),f312(f233(x100622),x100624)))+P22(f312(f70(x100621),f312(f233(x100621),f312(f312(f8(f860(x100622,a845),a845,x100621),f96(x100622)),f312(f312(f7(x100621,f860(x100622,a845),f860(x100622,a845)),f312(f312(f8(f860(x100622,f860(a845,a845)),f860(f860(x100622,a845),f860(x100622,a845)),x100621),f18(x100622,a845,a845)),f312(f312(f8(f860(x100622,a845),f860(x100622,f860(a845,a845)),x100621),f312(f8(a845,f860(a845,a845),x100622),a310)),f312(f312(f7(x100621,f860(x100622,x100621),f860(x100622,a845)),f312(f312(f8(f860(x100621,a845),f860(f860(x100622,x100621),f860(x100622,a845)),x100621),f8(x100621,a845,x100622)),a309)),x100623)))),x100624)))))
% 173.53/173.42 [8150]P36(x81501,x81502,x81503,x81504)+~P36(x81501,x81502,f180(x81501,x81502,x81505,x81503),x81504)
% 173.53/173.42 [5575]E(f312(f312(f289(x55751),x55752),f179(x55751,x55753,x55754)),f179(x55751,x55753,x55754))+~E(f312(x55754,x55752),f312(f219(x55753),x55755))
% 173.53/173.42 [5968]P22(f312(f245(x59681,x59682,x59683),x59684))+~P22(f312(f312(x59683,x59685),x59684))
% 173.53/173.42 [5970]P22(f312(f244(x59701,x59702,x59703),x59704))+~P22(f312(f312(x59703,x59704),x59705))
% 173.53/173.42 [5973]~E(f312(x59734,x59732),f312(f219(x59733),x59735))+P22(f312(f312(f314(x59731),x59732),f179(x59731,x59733,x59734)))
% 173.53/173.42 [5974]~E(f312(x59744,x59745),f312(f219(x59741),x59742))+P22(f312(f312(f314(x59741),x59742),f181(x59743,x59741,x59744)))
% 173.53/173.42 [6561]~E(x65613,f2(a113))+E(f312(f259(x65611,x65612,x65613,x65614),x65615),f312(f239(x65611,x65612),x65615))
% 173.53/173.42 [6635]~E(f312(x66354,x66355),f192(x66352))+E(f312(f221(f856(x66351),x66352,f192(x66351),x66353),f312(x66354,x66355)),f192(x66351))
% 173.53/173.42 [7248]E(f312(x72481,x72482),f192(x72483))+~E(f312(f180(x72484,x72483,x72485,x72481),x72482),f192(x72483))
% 173.53/173.42 [7249]E(f312(x72491,x72492),f192(x72493))+~E(f312(f180(x72494,x72493,x72491,x72495),x72492),f192(x72493))
% 173.53/173.42 [7284]E(f312(f180(x72841,x72842,x72843,x72844),x72845),f312(x72843,x72845))+P22(f312(f312(f314(x72841),x72845),f179(x72841,x72842,x72844)))
% 173.53/173.42 [7285]E(f312(f180(x72851,x72852,x72853,x72854),x72855),f312(x72854,x72855))+P22(f312(f312(f314(x72851),x72855),f179(x72851,x72852,x72853)))
% 173.53/173.42 [7601]~P15(x76014,x76011,x76012,x76015)+E(f312(f82(x76011,x76011,x76011,f312(x76012,x76013)),f312(x76012,x76013)),f312(x76012,x76013))
% 173.53/173.42 [7648]E(f312(f180(x76481,x76482,x76483,x76484),x76485),f312(x76484,x76485))+~P22(f312(f312(f314(x76481),x76485),f179(x76481,x76482,x76484)))
% 173.53/173.42 [8324]P22(f312(f312(f314(f859(x83241,x83241)),f312(f312(f239(x83241,x83241),x83242),x83243)),f306(x83241,x83244,x83245)))+~P22(f312(f312(f228(a852),f312(x83244,x83242)),f312(x83244,x83243)))
% 173.53/173.42 [8425]~P22(f312(f312(f314(x84254),x84253),f277(x84254,x84251,x84252,x84255)))+P22(f312(f312(x84251,x84252),x84253))
% 173.53/173.42 [8426]~P22(f312(f312(f314(x84264),x84263),f274(x84264,x84261,x84262,x84265)))+P22(f312(f312(x84261,x84262),x84263))
% 173.53/173.42 [8427]~P22(f312(f312(f314(x84274),x84272),f277(x84274,x84271,x84275,x84273)))+P22(f312(f312(x84271,x84272),x84273))
% 173.53/173.42 [8428]~P22(f312(f312(f314(x84284),x84282),f274(x84284,x84281,x84285,x84283)))+P22(f312(f312(x84281,x84282),x84283))
% 173.53/173.42 [8565]~P56(x85652,x85651,x85655,x85653,x85654)+E(f312(f290(x85651,x85652,x85653),x85654),f235(f860(x85652,a845)))
% 173.53/173.42 [9000]~P39(x90001,x90002,x90003,x90004,x90005)+P39(x90001,x90002,x90003,f312(f165(x90001),x90004),f312(f165(x90002),x90005))
% 173.53/173.42 [9002]~P39(x90021,x90022,x90023,f312(f165(x90021),x90024),x90025)+P39(x90021,x90022,x90023,x90024,f312(f165(x90022),x90025))
% 173.53/173.42 [9003]~P39(x90031,x90032,x90033,x90034,f312(f165(x90032),x90035))+P39(x90031,x90032,x90033,f312(f165(x90031),x90034),x90035)
% 173.53/173.42 [9008]P39(x90081,x90082,x90083,x90084,x90085)+~P39(x90081,x90082,x90083,f312(f165(x90081),x90084),f312(f165(x90082),x90085))
% 173.53/173.42 [9404]P22(f312(f312(f314(f859(f853(x94041),f853(x94041))),f312(f312(f239(f853(x94041),f853(x94041)),f312(f312(f147(x94041),x94042),x94043)),f312(f312(f147(x94041),x94042),x94044))),f153(x94041,x94045)))+~P22(f312(f312(f314(f859(f853(x94041),f853(x94041))),f312(f312(f239(f853(x94041),f853(x94041)),x94043),x94044)),f153(x94041,x94045)))
% 173.53/173.42 [9405]P22(f312(f312(f314(f859(f853(x94051),f853(x94051))),f312(f312(f239(f853(x94051),f853(x94051)),f312(f312(f129(x94051),x94052),x94053)),f312(f312(f129(x94051),x94052),x94054))),f143(x94051,x94055)))+~P22(f312(f312(f314(f859(f853(x94051),f853(x94051))),f312(f312(f239(f853(x94051),f853(x94051)),x94053),x94054)),f143(x94051,x94055)))
% 173.53/173.42 [9584]E(f312(f312(f147(x95841),f591(x95842,x95843,x95844,x95845,x95841)),f592(x95842,x95843,x95844,x95845,x95841)),x95845)+~P22(f312(f312(f314(f859(f853(x95841),f853(x95841))),f312(f312(f239(f853(x95841),f853(x95841)),x95845),f312(f312(f147(x95841),x95844),x95843))),f154(x95841,x95842)))
% 173.53/173.42 [9608]E(f312(f312(f147(x96081),f593(x96082,x96083,x96084,x96085,x96081)),f594(x96082,x96083,x96084,x96085,x96081)),x96083)+~P22(f312(f312(f314(f859(f853(x96081),f853(x96081))),f312(f312(f239(f853(x96081),f853(x96081)),f312(f312(f147(x96081),x96085),x96084)),x96083)),f154(x96081,x96082)))
% 173.53/173.42 [9768]~P22(f312(f312(f314(f859(f853(x97681),f853(x97681))),f312(f312(f239(f853(x97681),f853(x97681)),f312(f312(f147(x97681),x97685),x97682)),x97684)),f154(x97681,x97683)))+P22(f312(f312(f314(f859(f853(x97681),f853(x97681))),f312(f312(f239(f853(x97681),f853(x97681)),x97682),f594(x97683,x97684,x97682,x97685,x97681))),f154(x97681,x97683)))
% 173.53/173.42 [9843]~P22(f312(f312(f314(f859(f853(x98431),f853(x98431))),f312(f312(f239(f853(x98431),f853(x98431)),x98435),f312(f312(f147(x98431),x98434),x98433))),f154(x98431,x98432)))+P22(f312(f312(f314(f859(f853(x98431),f853(x98431))),f312(f312(f239(f853(x98431),f853(x98431)),f592(x98432,x98433,x98434,x98435,x98431)),x98433)),f154(x98431,x98432)))
% 173.53/173.42 [10013]P22(f312(f312(f314(f859(x100131,x100131)),f312(f312(f239(x100131,x100131),f312(x100132,f312(f312(f89(a852),x100133),x100134))),f312(x100132,x100133))),f287(x100131,x100135)))+~P22(f312(f312(f314(f859(x100131,x100131)),f312(f312(f239(x100131,x100131),f312(x100132,f312(a126,f754(x100134,x100133,x100135,x100132,x100131)))),f312(x100132,f754(x100134,x100133,x100135,x100132,x100131)))),f287(x100131,x100135)))
% 173.53/173.42 [10036]E(x100361,f2(a113))+E(f312(f221(f859(f853(x100362),x100363),f859(x100362,x100363),f312(f312(f239(f853(x100362),x100363),f127(x100362)),x100364),f312(f249(x100362,x100363,f859(f853(x100362),x100363)),f312(f312(f7(x100362,f860(x100363,f859(f853(x100362),x100363)),f860(x100363,f859(f853(x100362),x100363))),f312(f312(f8(f860(f859(f853(x100362),x100363),f859(f853(x100362),x100363)),f860(f860(x100363,f859(f853(x100362),x100363)),f860(x100363,f859(f853(x100362),x100363))),x100362),f8(f859(f853(x100362),x100363),f859(f853(x100362),x100363),x100363)),f312(f312(f8(f860(f853(x100362),f860(x100363,f859(f853(x100362),x100363))),f860(f859(f853(x100362),x100363),f859(f853(x100362),x100363)),x100362),f249(f853(x100362),x100363,f859(f853(x100362),x100363))),f312(f312(f8(f860(f853(x100362),f853(x100362)),f860(f853(x100362),f860(x100363,f859(f853(x100362),x100363))),x100362),f312(f8(f853(x100362),f860(x100363,f859(f853(x100362),x100363)),f853(x100362)),f239(f853(x100362),x100363))),f147(x100362))))),f131(x100363,x100362,x100365,f312(f312(f21(a113),x100361),f87(a113)))))),f312(x100365,x100364)),f312(f131(x100363,x100362,x100365,x100361),x100364))
% 173.53/173.42 [5164]E(x51641,x51642)+~E(f312(f312(f147(x51643),x51644),x51641),f312(f312(f147(x51643),x51645),x51642))
% 173.53/173.42 [5165]E(x51651,x51652)+~E(f312(f312(f147(x51653),x51651),x51654),f312(f312(f147(x51653),x51652),x51655))
% 173.53/173.42 [5215]P22(f312(x52151,x52152))+~E(f312(f132(x52153,x52151),x52154),f312(f312(f147(x52153),x52152),x52155))
% 173.53/173.42 [5216]P22(f312(x52161,x52162))+~E(f312(f312(f147(x52163),x52162),x52164),f312(f132(x52163,x52161),x52165))
% 173.53/173.42 [5364]~E(f312(f312(f134(x53641),x53643),x53642),f312(f312(f147(x53641),x53644),x53645))+E(f312(f312(f161(x53641),x53642),x53643),x53644)
% 173.53/173.42 [5498]~P11(x54984,x54985,x54981)+E(f312(f312(x54981,x54982),f312(f312(x54981,x54982),x54983)),f312(f312(x54981,x54982),x54983))
% 173.53/173.42 [6090]~P103(x60902)+~E(f312(f312(f145(x60901,x60902,x60903),x60904),x60905),f127(x60901))
% 173.53/173.42 [6464]E(x64641,x64642)+~E(f312(f312(f129(x64643),x64644),f312(f312(f147(x64643),x64641),f127(x64643))),f312(f312(f129(x64643),x64645),f312(f312(f147(x64643),x64642),f127(x64643))))
% 173.53/173.42 [6465]E(x64651,x64652)+~E(f312(f312(f129(x64653),x64651),f312(f312(f147(x64653),x64654),f127(x64653))),f312(f312(f129(x64653),x64652),f312(f312(f147(x64653),x64655),f127(x64653))))
% 173.53/173.42 [6714]E(f312(f183(x67141,x67142,x67143,x67144),x67145),f192(x67142))+P22(f312(f312(f314(x67141),x67145),x67144))
% 173.53/173.42 [6772]E(f312(f312(f289(x67721),f312(x67722,x67723)),f312(f290(x67724,x67721,x67722),x67725)),f312(f290(x67724,x67721,x67722),x67725))+~P22(f312(f312(f314(x67724),x67723),x67725))
% 173.53/173.42 [6779]~P22(f312(x67794,f312(x67793,x67795)))+P22(f312(f312(f291(x67791,x67792,x67793),x67794),x67795))
% 173.53/173.42 [6783]~E(x67834,f2(a113))+E(f312(f131(x67831,x67832,x67833,x67834),x67835),f312(f312(f239(f853(x67832),x67831),f127(x67832)),x67835))
% 173.53/173.42 [6876]~E(f312(f290(x68761,x68762,x68763),x68764),x68765)+E(f312(f290(f860(x68761,a845),f860(x68762,a845),f290(x68761,x68762,x68763)),f312(f288(x68761),x68764)),f312(f288(x68762),x68765))
% 173.53/173.42 [6913]E(f312(f183(x69131,x69132,x69133,x69134),x69135),f312(x69133,x69135))+~P22(f312(f312(f314(x69131),x69135),x69134))
% 173.53/173.42 [7204]P19(x72041,x72042,x72043,x72044)+~P19(x72041,x72042,x72043,f312(f312(f289(x72041),x72045),x72044))
% 173.53/173.42 [7273]P22(f312(x72731,x72732))+~P22(f312(f312(f103(x72733,x72734,x72731),x72735),x72732))
% 173.53/173.42 [7316]~P22(f312(f312(f314(x73164),x73163),x73165))+P22(f312(f312(f314(x73161),f312(x73162,x73163)),f312(f290(x73164,x73161,x73162),x73165)))
% 173.53/173.42 [7339]~P103(x73392)+E(f144(x73391,x73392,x73393,f312(f132(x73391,x73394),x73395)),f312(f132(x73391,x73394),f144(x73391,x73392,x73393,x73395)))
% 173.53/173.42 [7373]P22(f312(x73731,f312(x73732,x73733)))+~P22(f312(f312(f291(x73734,x73735,x73732),x73731),x73733))
% 173.53/173.42 [7374]P22(f312(f312(x73741,x73742),x73743))+~P22(f312(f312(f103(x73744,x73741,x73745),x73742),x73743))
% 173.53/173.42 [7437]~P22(f312(f312(f314(x74373),f312(x74374,x74372)),x74375))+P22(f312(f312(f314(x74371),x74372),f312(f291(x74371,x74373,x74374),x74375)))
% 173.53/173.42 [7828]~P22(f312(f312(f314(x78285),x78283),f312(f291(x78285,x78281,x78282),x78284)))+P22(f312(f312(f314(x78281),f312(x78282,x78283)),x78284))
% 173.53/173.42 [8056]~E(x80563,f312(f312(f312(f81(x80561,f856(x80562)),f312(f16(f856(x80562),x80561),f192(x80562))),x80564),f312(f219(x80562),x80565)))+E(f179(x80561,x80562,x80563),f312(f312(f289(x80561),x80564),f189(f860(x80561,a845))))
% 173.53/173.42 [8155]E(f312(x81551,f797(x81552,x81551,x81553,x81554)),x81554)+~P22(f312(f312(f314(x81555),x81554),f312(f290(x81553,x81555,x81551),x81552)))
% 173.53/173.42 [8475]~E(x84752,f312(f312(f147(x84751),x84754),x84755))+P22(f312(f312(f314(f859(f853(x84751),f853(x84751))),f312(f312(f239(f853(x84751),f853(x84751)),f127(x84751)),x84752)),f143(x84751,x84753)))
% 173.53/173.42 [8525]~P39(x85251,x85253,x85255,x85252,x85254)+E(f312(f190(f853(x85251)),x85252),f312(f190(f853(x85253)),x85254))
% 173.53/173.42 [8535]P22(f312(f312(f227(f860(x85351,a845)),f312(f312(f51(x85352,f860(x85351,a845)),x85353),x85354)),f312(x85354,x85355)))+~P22(f312(f312(f314(x85352),x85355),x85353))
% 173.53/173.42 [8581]~P56(x85811,x85812,x85813,x85815,x85814)+E(f312(f290(x85811,x85812,x85813),f235(f860(x85811,a845))),x85814)
% 173.53/173.42 [8785]E(f312(f312(f312(f81(x87851,f856(x87852)),f183(x87851,x87852,x87853,x87854)),x87855),f192(x87852)),f183(x87851,x87852,x87853,x87854))+P22(f312(f312(f314(x87851),x87855),x87854))
% 173.53/173.42 [8787]E(f312(f132(x87871,x87872),f726(x87873,x87874,x87875,x87872,x87871)),x87873)+~E(f312(f132(x87871,x87872),x87875),f312(f312(f147(x87871),x87874),x87873))
% 173.53/173.42 [8788]E(f312(f132(x87881,x87882),f728(x87883,x87882,x87884,x87885,x87881)),x87884)+~E(f312(f312(f147(x87881),x87885),x87884),f312(f132(x87881,x87882),x87883))
% 173.53/173.42 [8789]E(f312(x87891,f739(x87892,x87893,x87891,x87894,x87895)),x87892)+~E(f312(f312(f193(x87895,x87894),x87891),x87893),f312(f219(x87894),x87892))
% 173.53/173.42 [8793]E(f312(f219(x87931),f739(x87932,x87933,x87934,x87935,x87931)),x87933)+~E(f312(f312(f193(x87931,x87935),x87934),x87933),f312(f219(x87935),x87932))
% 173.53/173.42 [8895]E(f312(f190(f853(x88951)),x88952),x88953)+~P22(f312(f312(f314(f859(f853(x88951),f853(x88951))),f312(f312(f239(f853(x88951),f853(x88951)),x88954),x88952)),f312(f139(x88951,x88955),x88953)))
% 173.53/173.42 [8896]E(f312(f190(f853(x88961)),x88962),x88963)+~P22(f312(f312(f314(f859(f853(x88961),f853(x88961))),f312(f312(f239(f853(x88961),f853(x88961)),x88962),x88964)),f312(f139(x88961,x88965),x88963)))
% 173.53/173.42 [8962]P22(f312(f312(f314(x89621),f797(x89622,x89623,x89621,x89624)),x89622))+~P22(f312(f312(f314(x89625),x89624),f312(f290(x89621,x89625,x89623),x89622)))
% 173.53/173.42 [9118]~P49(f860(x91183,a845),f860(x91181,a845),x91182)+P22(f312(f312(f227(f860(x91181,a845)),f312(x91182,f312(f312(f115(f860(x91183,a845)),x91184),x91185))),f312(f312(f115(f860(x91181,a845)),f312(x91182,x91184)),f312(x91182,x91185))))
% 173.53/173.42 [9120]E(f312(f290(x91201,x91202,x91203),f815(x91204,x91203,x91201,x91205,x91202)),x91205)+~P22(f312(f312(f227(f860(x91202,a845)),x91205),f312(f290(x91201,x91202,x91203),x91204)))
% 173.53/173.42 [9370]E(f312(x93701,f799(x93702,x93701,x93703,x93704,x93705)),f312(f219(x93705),x93704))+~P22(f312(f312(f314(x93705),x93704),f181(x93703,x93705,f183(x93703,x93705,x93701,x93702))))
% 173.53/173.42 [9418]P22(f312(f312(f314(f859(f853(x94181),f853(x94181))),f312(f312(f239(f853(x94181),f853(x94181)),f312(f312(f147(x94181),x94182),x94183)),f312(f312(f147(x94181),x94182),x94184))),f287(f853(x94181),f153(x94181,x94185))))+~P22(f312(f312(f314(f859(f853(x94181),f853(x94181))),f312(f312(f239(f853(x94181),f853(x94181)),x94183),x94184)),f287(f853(x94181),f153(x94181,x94185))))
% 173.53/173.42 [9448]~E(f312(x94483,f585(x94485,x94484,x94483,x94482,x94481)),f312(x94485,f585(x94485,x94484,x94483,x94482,x94481)))+E(f312(f312(f150(x94481,x94482),x94483),x94484),f312(f312(f150(x94481,x94482),x94485),x94484))
% 173.53/173.42 [9524]~E(f312(f132(x95241,x95245),x95244),f312(f312(f147(x95241),x95243),x95242))+E(f312(f312(f129(x95241),f727(x95242,x95243,x95244,x95245,x95241)),f312(f312(f147(x95241),x95243),f726(x95242,x95243,x95244,x95245,x95241))),x95244)
% 173.53/173.42 [9525]~E(f312(f312(f147(x95251),x95255),x95254),f312(f132(x95251,x95253),x95252))+E(f312(f312(f129(x95251),f729(x95252,x95253,x95254,x95255,x95251)),f312(f312(f147(x95251),x95255),f728(x95252,x95253,x95254,x95255,x95251))),x95252)
% 173.53/173.42 [9526]E(f312(f312(f150(x95261,x95262),x95263),x95264),f312(f312(f150(x95261,x95262),x95265),x95264))+P22(f312(f312(f314(x95261),f585(x95263,x95264,x95265,x95262,x95261)),f312(f168(x95261),x95264)))
% 173.53/173.42 [9555]~P22(f312(f312(f314(x95555),x95554),f312(f264(x95551,x95555,x95553),x95552)))+P22(f312(f312(f314(x95551),f359(x95552,x95553,x95551,x95554,x95555)),x95552))
% 173.53/173.42 [9556]~P22(f312(f312(f314(x95565),x95564),f312(f264(x95561,x95565,x95563),x95562)))+P22(f312(f312(f314(x95561),f369(x95562,x95563,x95561,x95564,x95565)),x95562))
% 173.53/173.42 [9580]~P22(f312(f312(f227(f860(x95805,a845)),x95804),f312(f290(x95801,x95805,x95803),x95802)))+P22(f312(f312(f227(f860(x95801,a845)),f815(x95802,x95803,x95801,x95804,x95805)),x95802))
% 173.53/173.42 [9632]~P22(f312(f312(f314(x96325),x96324),f181(x96321,x96325,f183(x96321,x96325,x96323,x96322))))+P22(f312(f312(f314(x96321),f799(x96322,x96323,x96321,x96324,x96325)),x96322))
% 173.53/173.42 [5378]~E(f312(x53783,x53784),x53785)+E(f312(f312(f312(f81(x53781,x53782),x53783),x53784),x53785),x53783)
% 173.53/173.42 [5812]E(f312(x58121,x58122),x58123)+~E(f312(f312(f312(f81(x58124,x58125),x58121),x58122),x58123),x58121)
% 173.53/173.42 [5910]E(x59101,x59102)+~E(f312(f248(x59103,x59104),f312(f312(f239(x59103,x59104),x59105),x59101)),x59102)
% 173.53/173.42 [5911]E(x59111,x59112)+~E(f312(f246(x59113,x59114),f312(f312(f239(x59113,x59114),x59111),x59115)),x59112)
% 173.53/173.42 [6167]~E(x61673,f312(f312(f129(x61671),x61674),f312(f312(f147(x61671),x61672),x61675)))+P22(f312(f312(f314(x61671),x61672),f312(f168(x61671),x61673)))
% 173.53/173.42 [6548]E(f312(f290(x65481,x65482,f312(f16(x65482,x65481),x65483)),x65484),f312(f312(f289(x65482),x65483),f189(f860(x65482,a845))))+~P22(f312(f312(f314(x65481),x65485),x65484))
% 173.53/173.42 [6618]E(f312(f312(f124(f860(x66181,a845)),f312(f168(x66181),x66182)),f312(f168(x66181),x66183)),f312(f168(x66181),x66184))+~E(f163(x66181,x66185,x66184),f312(f312(f239(f853(x66181),f853(x66181)),x66182),x66183))
% 173.53/173.42 [6718]~P103(x67182)+E(f312(f190(f853(x67181)),f312(f312(f145(x67181,x67182,x67183),x67184),x67185)),f312(a126,f312(f190(f853(x67181)),x67185)))
% 173.53/173.42 [6727]~P103(x67272)+E(f312(f168(x67271),f312(f312(f145(x67271,x67272,x67273),x67274),x67275)),f312(f312(f289(x67271),x67274),f312(f168(x67271),x67275)))
% 173.53/173.42 [7005]~P107(x70051)+E(f312(f312(f89(x70051),f312(f312(f89(x70051),x70052),x70053)),f312(f312(f89(x70051),x70054),x70055)),f312(f312(f89(x70051),f312(f312(f89(x70051),x70052),x70054)),f312(f312(f89(x70051),x70053),x70055)))
% 173.53/173.42 [7006]~P107(x70061)+E(f312(f312(f90(x70061),f312(f312(f90(x70061),x70062),x70063)),f312(f312(f90(x70061),x70064),x70065)),f312(f312(f90(x70061),f312(f312(f90(x70061),x70062),x70064)),f312(f312(f90(x70061),x70063),x70065)))
% 173.53/173.42 [7007]~P64(x70071)+E(f312(f312(f268(x70071),f312(f312(f90(x70071),x70072),x70073)),f312(f312(f90(x70071),x70074),x70075)),f312(f312(f90(x70071),f312(f312(f268(x70071),x70072),x70074)),f312(f312(f268(x70071),x70073),x70075)))
% 173.53/173.42 [7019]~P103(x70191)+E(f285(x70191,f312(f312(f226(x70191),x70192),x70193),f312(f312(f225(x70191),x70194),x70195)),f312(f312(f115(f860(x70191,a845)),f285(x70191,x70192,x70194)),f285(x70191,x70193,x70195)))
% 173.53/173.42 [7020]~P103(x70201)+E(f284(x70201,f312(f312(f226(x70201),x70202),x70203),f312(f312(f225(x70201),x70204),x70205)),f312(f312(f115(f860(x70201,a845)),f284(x70201,x70202,x70204)),f284(x70201,x70203,x70205)))
% 173.53/173.42 [7021]~P103(x70211)+E(f283(x70211,f312(f312(f226(x70211),x70212),x70213),f312(f312(f225(x70211),x70214),x70215)),f312(f312(f115(f860(x70211,a845)),f283(x70211,x70212,x70214)),f283(x70211,x70213,x70215)))
% 173.53/173.42 [7022]~P103(x70221)+E(f312(f312(f115(f860(x70221,a845)),f312(f282(x70221,x70222),x70223)),f312(f282(x70221,x70224),x70225)),f312(f282(x70221,f312(f312(f226(x70221),x70222),x70224)),f312(f312(f225(x70221),x70223),x70225)))
% 173.53/173.42 [7137]~P22(f312(x71371,f340(x71373,x71372,x71371)))+P22(f312(x71371,f312(f312(f239(x71372,x71373),x71374),x71375)))
% 173.53/173.42 [7216]~E(f312(x72163,x72164),f192(x72162))+E(f181(x72161,x72162,f312(f312(f312(f81(x72161,f856(x72162)),x72163),x72164),f312(f219(x72162),x72165))),f312(f312(f289(x72162),x72165),f181(x72161,x72162,x72163)))
% 173.53/173.42 [7239]~E(x72392,f312(x72394,x72395))+P22(f312(f312(f314(x72391),x72392),f312(f290(x72393,x72391,x72394),f235(f860(x72393,a845)))))
% 173.53/173.42 [7296]~E(f312(x72963,x72964),f192(x72962))+E(f312(f312(f21(f860(x72961,a845)),f179(x72961,x72962,x72963)),f312(f312(f289(x72961),x72964),x72965)),f312(f312(f21(f860(x72961,a845)),f179(x72961,x72962,x72963)),x72965))
% 173.53/173.42 [7314]~P11(x73143,x73142,x73144)+P11(x73141,x73142,f312(f312(f8(x73143,f860(x73142,x73142),x73141),x73144),x73145))
% 173.53/173.42 [7454]~P19(x74541,x74542,x74543,x74544)+P19(x74541,x74542,x74543,f312(f312(f21(f860(x74541,a845)),x74544),x74545))
% 173.53/173.42 [7609]~P22(f312(f312(x76093,x76094),x76095))+P22(f312(f312(f249(x76091,x76092,a845),x76093),f312(f312(f239(x76091,x76092),x76094),x76095)))
% 173.53/173.42 [7724]~P22(f312(x77242,x77244))+~E(f312(f312(f134(x77241),f312(f190(f853(x77241)),f172(x77241,x77242,x77243))),x77243),f312(f312(f147(x77241),x77244),x77245))
% 173.53/173.42 [7745]P19(x77451,x77452,x77453,x77454)+~P19(x77451,x77452,x77453,f312(f312(f124(f860(x77451,a845)),x77455),x77454))
% 173.53/173.42 [7746]P19(x77461,x77462,x77463,x77464)+~P19(x77461,x77462,x77463,f312(f312(f124(f860(x77461,a845)),x77464),x77465))
% 173.53/173.42 [7790]~P103(x77902)+E(f312(f312(f145(x77901,x77902,x77903),x77904),f144(x77901,x77902,x77903,x77905)),f144(x77901,x77902,x77903,f312(f312(f147(x77901),x77904),x77905)))
% 173.53/173.42 [7945]~P34(x79451,f312(a126,x79452),f312(f312(f312(f100(x79451),x79453),f312(a27,x79454)),x79455))+P34(x79451,x79452,f312(f312(f312(f100(x79451),x79453),f312(f223(a846),f312(a30,x79454))),x79455))
% 173.53/173.42 [8082]P34(x80821,f312(a126,x80822),f312(f312(f312(f100(x80821),x80823),f312(a27,x80824)),x80825))+~P34(x80821,x80822,f312(f312(f312(f100(x80821),x80823),f312(f223(a846),f312(a30,x80824))),x80825))
% 173.53/173.42 [8111]~P11(x81112,x81111,x81113)+E(f312(f138(x81111,x81112,f312(f7(x81112,x81111,x81111),x81113),x81114),x81115),f312(f312(f73(x81112,x81111,x81113),x81114),f312(f168(x81112),x81115)))
% 173.53/173.42 [8141]~E(f312(f312(f134(x81411),f312(f190(f853(x81411)),f172(x81411,x81412,x81413))),x81413),f312(f312(f147(x81411),x81414),x81415))+E(f312(f312(f129(x81411),f172(x81411,x81412,x81413)),f312(f312(f147(x81411),x81414),x81415)),x81413)
% 173.53/173.42 [8165]P22(f312(f312(x81651,x81652),x81653))+~P22(f312(f312(f249(x81654,x81655,a845),x81651),f312(f312(f239(x81654,x81655),x81652),x81653)))
% 173.53/173.42 [8231]~E(f312(f312(f173(x82311,x82312),x82315),x82313),f312(f219(x82312),x82314))+P22(f312(f312(f314(f859(x82311,x82312)),f312(f312(f239(x82311,x82312),x82313),x82314)),f312(f168(f859(x82311,x82312)),x82315)))
% 173.53/173.42 [8637]P22(f312(f312(f227(f860(x86371,a845)),f312(f290(x86372,x86371,x86373),x86374)),f312(f290(x86372,x86371,x86373),x86375)))+~P22(f312(f312(f227(f860(x86372,a845)),x86374),x86375))
% 173.53/173.42 [8638]P22(f312(f312(f227(f860(x86381,a845)),f312(f291(x86381,x86382,x86383),x86384)),f312(f291(x86381,x86382,x86383),x86385)))+~P22(f312(f312(f227(f860(x86382,a845)),x86384),x86385))
% 173.53/173.42 [8712]E(x87121,f2(a113))+E(f312(f312(f251(x87122,x87123,x87122,f859(x87123,x87122)),f312(x87124,x87125)),f259(x87123,x87122,f312(f312(f21(a113),x87121),f87(a113)),x87124)),f312(f259(x87123,x87122,x87121,x87124),x87125))
% 173.53/173.42 [9031]P34(x90311,x90312,f312(f312(f312(f100(x90311),x90313),x90314),x90315))+P22(f312(f312(x90313,f562(x90315,x90314,x90313,x90312)),f571(x90315,x90314,x90313,x90312)))
% 173.53/173.42 [9039]~P22(f312(f312(f195(x90393),f312(f312(f312(a201,x90394),f40(x90391)),f312(x90392,x90394))),x90395))+P22(f312(f312(f195(f32(x90391,x90392,x90393)),x90394),f312(f312(f312(a201,x90395),f40(x90391)),f312(f312(a202,x90394),x90391))))
% 173.53/173.42 [9230]E(f312(f219(x92301),f588(x92302,x92303,x92304,x92301,x92305)),f312(f312(f173(x92305,x92301),x92302),x92304))+~P22(f312(f312(f314(f859(x92305,x92301)),f312(f312(f239(x92305,x92301),x92304),x92303)),f312(f168(f859(x92305,x92301)),x92302)))
% 173.53/173.42 [9272]P34(x92721,x92722,f312(f312(f312(f100(x92721),x92723),x92724),x92725))+~P22(f312(f312(x92725,f562(x92725,x92724,x92723,x92722)),f584(x92725,x92724,x92723,x92722)))
% 173.53/173.42 [9334]P34(x93341,x93342,f312(f312(f312(f100(x93341),x93343),x93344),x93345))+P22(f312(f312(f312(f312(a198,x93344),f571(x93345,x93344,x93343,x93342)),x93342),f584(x93345,x93344,x93343,x93342)))
% 173.53/173.42 [9337]~P18(x93371,x93372,f312(f312(f289(f851(x93371)),f312(f312(f312(f100(x93371),x93373),f312(f223(a846),f312(a30,x93374))),x93375)),f189(f860(f851(x93371),a845))))+P18(x93371,x93372,f312(f312(f289(f851(x93371)),f312(f312(f312(f100(x93371),x93373),f312(a27,x93374)),x93375)),f189(f860(f851(x93371),a845))))
% 173.53/173.42 [9362]~P22(f312(f70(x93623),f312(f290(x93622,x93623,x93625),f235(f860(x93622,a845)))))+P22(f312(f70(x93621),f312(f290(x93622,x93621,f312(f312(f8(x93623,x93621,x93622),x93624),x93625)),f235(f860(x93622,a845)))))
% 173.53/173.42 [9383]P22(f312(f312(f227(f860(f860(x93831,a845),a845)),f312(f290(f860(x93832,a845),f860(x93831,a845),f290(x93832,x93831,x93833)),f312(f288(x93832),x93834))),f312(f288(x93831),x93835)))+~P22(f312(f312(f227(f860(x93831,a845)),f312(f290(x93832,x93831,x93833),x93834)),x93835))
% 173.53/173.42 [9400]~P22(f312(f70(f856(x94001)),f312(f290(x94002,f856(x94001),x94003),f235(f860(x94002,a845)))))+P22(f312(f70(f856(x94001)),f312(f290(x94002,f856(x94001),f312(f312(f312(f81(x94002,f856(x94001)),x94003),x94004),f312(f219(x94001),x94005))),f235(f860(x94002,a845)))))
% 173.53/173.42 [9432]P22(f312(f312(f195(x94321),f312(f312(f312(a201,x94322),f40(x94323)),f312(x94324,x94322))),f477(x94325,x94322,x94321,x94324,x94323)))+~P22(f312(f312(f195(f32(x94323,x94324,x94321)),x94322),x94325))
% 173.53/173.42 [9457]E(x94571,x94572)+~P22(f312(f75(x94573,x94574,x94575,x94571,f189(f860(x94573,a845))),x94572))
% 173.53/173.42 [9472]E(f312(f312(f239(x94721,x94722),f532(x94723,x94724,x94725,x94722,x94721)),f533(x94723,x94724,x94725,x94722,x94721)),x94725)+~P22(f312(f312(f314(f859(x94721,x94722)),x94725),f312(f312(f247(x94721,x94722),x94724),x94723)))
% 173.53/173.42 [9483]P22(f312(f312(f195(x94831),f312(f312(f312(a201,x94832),f40(x94833)),f312(x94834,x94832))),f444(x94835,x94832,x94831,x94834,x94833)))+~P22(f312(f312(f195(f32(x94833,x94834,x94831)),x94832),f312(f312(f312(a201,x94835),f40(x94833)),f312(f312(a202,x94832),x94833))))
% 173.53/173.42 [9489]~P22(f312(f312(f195(f312(a27,x94892)),f312(f312(f312(a201,f312(f312(a203,x94894),a204)),f40(a26)),f312(x94893,x94894))),x94895))+P22(f312(f312(f195(f31(x94891,x94892,x94893)),x94894),f312(f312(f312(a201,f312(f312(a203,x94895),f312(a202,x94894))),x94891),f312(f312(a202,x94895),a25))))
% 173.53/173.42 [9519]P22(f312(f312(f195(f312(a27,x95191)),f312(f312(f312(a201,f312(f312(a203,x95192),a204)),f40(a26)),f312(x95193,x95192))),f608(x95194,x95192,x95193,x95191,x95195)))+~P22(f312(f312(f195(f31(x95195,x95191,x95193)),x95192),x95194))
% 173.53/173.42 [9560]P22(f312(f312(f314(x95601),f532(x95602,x95603,x95604,x95605,x95601)),x95603))+~P22(f312(f312(f314(f859(x95601,x95605)),x95604),f312(f312(f247(x95601,x95605),x95603),x95602)))
% 173.53/173.42 [9586]E(f312(f312(f312(a201,f477(x95861,x95862,x95863,x95864,x95865)),f40(x95865)),f312(f312(a202,x95862),x95865)),x95861)+~P22(f312(f312(f195(f32(x95865,x95864,x95863)),x95862),x95861))
% 173.53/173.42 [9609]E(f312(f312(f312(a201,f444(x96091,x96092,x96093,x96094,x96095)),f40(x96095)),f312(f312(a202,x96092),x96095)),f312(f312(f312(a201,x96091),f40(x96095)),f312(f312(a202,x96092),x96095)))+~P22(f312(f312(f195(f32(x96095,x96094,x96093)),x96092),f312(f312(f312(a201,x96091),f40(x96095)),f312(f312(a202,x96092),x96095))))
% 173.53/173.42 [9637]P22(f312(f312(f195(f312(a27,x96371)),f312(f312(f312(a201,f312(f312(a203,x96372),a204)),f40(a26)),f312(x96373,x96372))),f517(x96374,x96372,x96373,x96371,x96375)))+~P22(f312(f312(f195(f31(x96375,x96371,x96373)),x96372),f312(f312(f312(a201,f312(f312(a203,x96374),f312(a202,x96372))),x96375),f312(f312(a202,x96374),a25))))
% 173.53/173.42 [9667]P18(x96675,x96674,f312(f312(f289(f851(x96675)),f312(f312(f312(f100(x96675),x96671),x96673),x96672)),f189(f860(f851(x96675),a845))))+P22(f312(f312(x96671,f672(x96672,x96673,x96674,x96675,x96671)),f684(x96672,x96673,x96674,x96675,x96671)))
% 173.53/173.42 [9715]P22(f312(f312(f314(x97151),f533(x97152,x97153,x97154,x97151,x97155)),f312(x97152,f532(x97152,x97153,x97154,x97151,x97155))))+~P22(f312(f312(f314(f859(x97155,x97151)),x97154),f312(f312(f247(x97155,x97151),x97153),x97152)))
% 173.53/173.42 [9745]P22(f312(f312(f314(f859(x97451,x97451)),f312(f312(f239(x97451,x97451),x97452),f775(x97453,x97454,x97455,x97452,x97451))),x97453))+~P22(f312(f312(f314(f859(x97451,x97451)),f312(f312(f239(x97451,x97451),x97452),x97455)),f312(f312(f184(f859(x97451,x97451),a845),f312(a126,x97454)),x97453)))
% 173.53/173.42 [9746]P22(f312(f312(f314(f859(x97461,x97461)),f312(f312(f239(x97461,x97461),x97462),f777(x97463,x97464,x97465,x97462,x97461))),x97463))+~P22(f312(f312(f314(f859(x97461,x97461)),f312(f312(f239(x97461,x97461),x97462),x97465)),f312(f312(f184(f859(x97461,x97461),a845),f312(a126,x97464)),x97463)))
% 173.53/173.42 [9763]~P22(f312(f312(f314(f859(f853(x97631),f853(x97631))),f312(f312(f239(f853(x97631),f853(x97631)),f312(f312(f147(x97631),x97632),x97635)),x97634)),f154(x97631,x97633)))+P22(f312(f312(f314(f859(x97631,x97631)),f312(f312(f239(x97631,x97631),x97632),f593(x97633,x97634,x97635,x97632,x97631))),x97633))
% 173.53/173.42 [9765]~P18(x97651,x97652,f312(f312(f289(f851(x97651)),f312(f312(f312(f100(x97651),f103(x97651,x97653,x97654)),x97655),x97653)),f189(f860(f851(x97651),a845))))+P18(x97651,x97652,f312(f312(f289(f851(x97651)),f312(f312(f312(f100(x97651),x97653),f35(x97654,x97655)),f103(x97651,x97653,f312(f82(a845,a845,a847,a307),x97654)))),f189(f860(f851(x97651),a845))))
% 173.53/173.42 [9766]~P21(x97661,x97662,f312(f312(f289(f851(x97661)),f312(f312(f312(f100(x97661),f103(x97661,x97663,x97664)),x97665),x97663)),f189(f860(f851(x97661),a845))))+P21(x97661,x97662,f312(f312(f289(f851(x97661)),f312(f312(f312(f100(x97661),x97663),f35(x97664,x97665)),f103(x97661,x97663,f312(f82(a845,a845,a847,a307),x97664)))),f189(f860(f851(x97661),a845))))
% 173.53/173.42 [9874]E(f312(f312(f312(a201,f312(f312(a203,f608(x98741,x98742,x98743,x98744,x98745)),f312(a202,x98742))),x98745),f312(f312(a202,f608(x98741,x98742,x98743,x98744,x98745)),a25)),x98741)+~P22(f312(f312(f195(f31(x98745,x98744,x98743)),x98742),x98741))
% 173.53/173.42 [9883]E(f312(f312(f312(a201,f312(f312(a203,f517(x98831,x98832,x98833,x98834,x98835)),f312(a202,x98832))),x98835),f312(f312(a202,f517(x98831,x98832,x98833,x98834,x98835)),a25)),f312(f312(f312(a201,f312(f312(a203,x98831),f312(a202,x98832))),x98835),f312(f312(a202,x98831),a25)))+~P22(f312(f312(f195(f31(x98835,x98834,x98833)),x98832),f312(f312(f312(a201,f312(f312(a203,x98831),f312(a202,x98832))),x98835),f312(f312(a202,x98831),a25))))
% 173.53/173.42 [10037]P18(x100371,x100372,f312(f312(f289(f851(x100371)),f312(f312(f312(f100(x100371),x100373),x100374),x100375)),f189(f860(f851(x100371),a845))))+~P18(x100371,x100372,f312(f312(f289(f851(x100371)),f312(f312(f312(f100(x100371),f312(f16(f860(a847,a845),x100371),f312(f312(f7(a847,a847,a845),a309),f684(x100375,x100374,x100372,x100371,x100373)))),x100374),f312(f16(f860(a847,a845),x100371),f312(x100375,f672(x100375,x100374,x100372,x100371,x100373))))),f189(f860(f851(x100371),a845))))
% 173.53/173.42 [6238]P22(f312(x62382,x62384))+E(f172(x62381,x62382,f312(f312(f129(x62381),x62383),f312(f312(f147(x62381),x62384),x62385))),f172(x62381,x62382,x62383))
% 173.53/173.42 [6288]~P73(x62882)+E(f312(f312(f312(f21(f860(x62881,x62882)),x62883),x62884),x62885),f312(f312(f21(x62882),f312(x62883,x62885)),f312(x62884,x62885)))
% 173.53/173.42 [6290]~P87(x62902)+E(f312(f312(f312(f124(f860(x62901,x62902)),x62903),x62904),x62905),f312(f312(f124(x62902),f312(x62903,x62905)),f312(x62904,x62905)))
% 173.53/173.42 [6292]~P87(x62922)+E(f312(f312(f312(f115(f860(x62921,x62922)),x62923),x62924),x62925),f312(f312(f115(x62922),f312(x62923,x62925)),f312(x62924,x62925)))
% 173.53/173.42 [6305]E(x63051,x63052)+E(f312(f312(f161(x63053),f312(f312(f155(x63053,x63054),x63051),x63055)),x63052),f312(f312(f161(x63053),x63054),x63052))
% 173.53/173.42 [6565]~E(x65654,f189(f860(x65653,a845)))+E(f312(f312(f21(f860(x65651,a845)),x65652),f312(f312(f50(x65653,f860(x65651,a845)),x65654),x65655)),x65652)
% 173.53/173.42 [6566]~E(x65664,f189(f860(x65663,a845)))+E(f312(f312(f124(f860(x65661,a845)),x65662),f312(f312(f50(x65663,f860(x65661,a845)),x65664),x65665)),x65662)
% 173.53/173.42 [6567]~E(x65674,f189(f860(x65673,a845)))+E(f312(f312(f115(f860(x65671,a845)),x65672),f312(f312(f51(x65673,f860(x65671,a845)),x65674),x65675)),x65672)
% 173.53/173.42 [6585]~E(x65854,f189(f860(x65853,a845)))+E(f312(f312(f289(x65851),x65852),f312(f312(f50(x65853,f860(x65851,a845)),x65854),x65855)),f312(f312(f289(x65851),x65852),f189(f860(x65851,a845))))
% 173.53/173.42 [7361]E(f312(f312(f161(x73611),f312(f312(f150(x73612,x73611),x73613),x73614)),x73615),f312(x73613,f312(f312(f161(x73612),x73614),x73615)))+~P22(f312(f312(f228(a852),x73615),f312(f190(f853(x73612)),x73614)))
% 173.53/173.42 [7425]E(f312(f312(f124(f860(x74251,a845)),f312(x74252,x74253)),f312(f312(f50(x74254,f860(x74251,a845)),x74255),x74252)),f312(f312(f50(x74254,f860(x74251,a845)),x74255),x74252))+~P22(f312(f312(f314(x74254),x74253),x74255))
% 173.53/173.42 [7426]E(f312(f312(f115(f860(x74261,a845)),f312(x74262,x74263)),f312(f312(f51(x74264,f860(x74261,a845)),x74265),x74262)),f312(f312(f51(x74264,f860(x74261,a845)),x74265),x74262))+~P22(f312(f312(f314(x74264),x74263),x74265))
% 173.53/173.42 [8027]~E(x80273,f189(f860(x80271,a845)))+E(f312(f312(f50(x80271,f860(x80272,a845)),x80273),f312(f312(f8(f860(x80272,a845),f860(x80272,a845),x80271),f312(f289(x80272),x80274)),x80275)),f189(f860(x80272,a845)))
% 173.53/173.42 [8033]~P22(f312(f312(f314(x80334),x80333),x80335))+P22(f312(f312(f227(f860(x80331,a845)),f312(x80332,x80333)),f312(f312(f50(x80334,f860(x80331,a845)),x80335),x80332)))
% 173.53/173.42 [8093]E(x80931,f312(f312(f312(a201,x80932),x80933),f312(x80934,x80932)))+~P22(f312(f312(f312(f312(a198,f28(x80933,x80934)),x80932),x80935),x80931))
% 173.53/173.42 [8164]~E(f312(x81644,x81642),x81645)+P22(f312(f312(f314(x81641),x81642),f312(f291(x81641,x81643,x81644),f312(f312(f289(x81643),x81645),f189(f860(x81643,a845))))))
% 173.53/173.42 [8211]~P54(x82111,x82112,f312(f265(x82112,x82111),x82113))+E(f312(f312(f115(f860(x82111,a845)),f312(f264(x82112,x82111,x82113),x82114)),f312(f264(x82112,x82111,x82113),x82115)),f312(f264(x82112,x82111,x82113),f312(f312(f115(f860(x82112,a845)),x82114),x82115)))
% 173.53/173.42 [8334]E(x83341,f189(f860(x83342,a845)))+E(f312(f312(f50(x83342,f860(x83343,a845)),x83341),f312(f312(f8(f860(x83343,a845),f860(x83343,a845),x83342),f312(f289(x83343),x83344)),x83345)),f312(f312(f289(x83343),x83344),f312(f312(f50(x83342,f860(x83343,a845)),x83341),x83345)))
% 173.53/173.42 [8393]~P19(x83932,x83931,x83933,f235(f860(x83932,a845)))+E(f312(f312(f21(f860(x83931,a845)),f312(f290(x83932,x83931,x83933),x83934)),f312(f290(x83932,x83931,x83933),x83935)),f312(f290(x83932,x83931,x83933),f312(f312(f21(f860(x83932,a845)),x83934),x83935)))
% 173.53/173.42 [8394]~P19(x83942,x83941,x83943,f235(f860(x83942,a845)))+E(f312(f312(f115(f860(x83941,a845)),f312(f290(x83942,x83941,x83943),x83944)),f312(f290(x83942,x83941,x83943),x83945)),f312(f290(x83942,x83941,x83943),f312(f312(f115(f860(x83942,a845)),x83944),x83945)))
% 173.53/173.42 [8461]~P22(f312(f312(f76(x84611,x84612,x84615),x84613),x84614))+P22(f312(f312(f314(f859(x84611,x84612)),f312(f312(f239(x84611,x84612),x84613),x84614)),x84615))
% 173.53/173.42 [8495]P22(f312(f312(f314(x84951),x84952),f312(f236(x84953,x84951),x84954)))+~P22(f312(f312(f314(f859(x84953,x84951)),f312(f312(f239(x84953,x84951),x84955),x84952)),x84954))
% 173.53/173.42 [8497]P22(f312(f312(f314(x84971),x84972),f312(f238(x84971,x84973),x84974)))+~P22(f312(f312(f314(f859(x84971,x84973)),f312(f312(f239(x84971,x84973),x84972),x84975)),x84974))
% 173.53/173.42 [8623]P22(f312(f312(f76(x86231,x86232,x86233),x86234),x86235))+~P22(f312(f312(f314(f859(x86231,x86232)),f312(f312(f239(x86231,x86232),x86234),x86235)),x86233))
% 173.53/173.42 [8660]E(f312(x86601,x86602),x86603)+~P22(f312(f312(f314(x86604),x86602),f312(f291(x86604,x86605,x86601),f312(f312(f289(x86605),x86603),f189(f860(x86605,a845))))))
% 173.53/173.42 [8892]P22(f312(f312(f314(f859(x88921,x88922)),f312(f312(f239(x88921,x88922),x88923),x88924)),f312(f265(x88922,x88921),x88925)))+~P22(f312(f312(f314(f859(x88922,x88921)),f312(f312(f239(x88922,x88921),x88924),x88923)),x88925))
% 173.53/173.42 [8910]~P22(f312(f312(x89101,x89105),x89104))+P22(f312(f312(x89101,f312(f248(x89102,x89103),f312(f312(f239(x89102,x89103),x89104),x89105))),f312(f246(x89102,x89103),f312(f312(f239(x89102,x89103),x89104),x89105))))
% 173.53/173.42 [8940]~P22(f312(f312(f314(f859(x89402,x89401)),f312(f312(f239(x89402,x89401),x89404),x89403)),f312(f265(x89401,x89402),x89405)))+P22(f312(f312(f314(f859(x89401,x89402)),f312(f312(f239(x89401,x89402),x89403),x89404)),x89405))
% 173.53/173.42 [8968]~P22(f312(f312(f314(f859(x89683,x89681)),f312(f312(f239(x89683,x89681),x89685),x89682)),x89684))+P22(f312(f312(f314(x89681),x89682),f312(f264(x89683,x89681,x89684),f312(f312(f289(x89683),x89685),f189(f860(x89683,a845))))))
% 173.53/173.42 [9013]P22(f312(f312(f314(f859(x90131,x90132)),f312(f312(f239(x90131,x90132),x90133),x90134)),x90135))+~P22(f312(f312(f314(x90132),x90134),f312(f264(x90131,x90132,x90135),f312(f312(f289(x90131),x90133),f189(f860(x90131,a845))))))
% 173.53/173.42 [9034]E(f312(f312(f312(f81(x90341,f856(x90342)),f183(x90341,x90342,x90343,x90344)),x90345),f192(x90342)),f183(x90341,x90342,x90343,f312(f312(f21(f860(x90341,a845)),x90344),f312(f312(f289(x90341),x90345),f189(f860(x90341,a845))))))+~P22(f312(f312(f314(x90341),x90345),x90344))
% 173.53/173.42 [9099]~P26(x90991)+E(f312(f312(f6(a852,x90991),x90992),f283(a852,f312(f312(f89(a852),x90993),x90994),f312(f312(f89(a852),x90995),x90994))),f312(f312(f6(a852,x90991),f312(f312(f8(a852,x90991,a852),x90992),f312(f312(f7(a852,a852,a852),f89(a852)),x90994))),f283(a852,x90993,x90995)))
% 173.53/173.42 [9124]~P26(x91241)+E(f312(f312(f6(a852,x91241),x91242),f312(f282(a852,f312(f312(f89(a852),x91243),x91244)),f312(f312(f89(a852),x91245),x91244))),f312(f312(f6(a852,x91241),f312(f312(f8(a852,x91241,a852),x91242),f312(f312(f7(a852,a852,a852),f89(a852)),x91244))),f312(f282(a852,x91243),x91245)))
% 173.53/173.42 [9179]~P19(x91791,x91792,x91793,f235(f860(x91791,a845)))+E(f312(f312(f150(x91791,x91792),x91793),f312(f132(x91791,f312(f312(f8(a845,a845,x91791),a307),f312(a309,x91794))),x91795)),f312(f132(x91792,f312(f312(f8(a845,a845,x91792),a307),f312(a309,f312(x91793,x91794)))),f312(f312(f150(x91791,x91792),x91793),x91795)))
% 173.53/173.42 [9197]~P19(x91971,x91972,x91973,f312(f312(f289(x91971),x91974),f312(f168(x91971),x91975)))+E(f312(f312(f150(x91971,x91972),x91973),f312(f132(x91971,f312(f312(f8(a845,a845,x91971),a307),f312(a309,x91974))),x91975)),f312(f132(x91972,f312(f312(f8(a845,a845,x91972),a307),f312(a309,f312(x91973,x91974)))),f312(f312(f150(x91971,x91972),x91973),x91975)))
% 173.53/173.42 [9351]P22(f312(f312(f314(f859(f853(x93511),f853(x93511))),f312(f312(f239(f853(x93511),f853(x93511)),f312(f312(f147(x93511),x93512),x93513)),f312(f312(f147(x93511),x93514),x93513))),f153(x93511,x93515)))+~P22(f312(f312(f314(f859(x93511,x93511)),f312(f312(f239(x93511,x93511),x93512),x93514)),x93515))
% 173.53/173.42 [9384]P22(f312(f312(f312(f312(a198,x93841),x93842),x93843),f361(x93844,x93843,x93842,x93845,x93841)))+~P22(f312(f312(f312(f312(a198,f36(x93841,x93845)),x93842),x93843),x93844))
% 173.53/173.42 [9385]P22(f312(f312(f312(f312(a198,x93851),x93852),x93853),f376(x93854,x93853,x93852,x93855,x93851)))+~P22(f312(f312(f312(f312(a198,f36(x93851,x93855)),x93852),x93853),x93854))
% 173.53/173.42 [9455]P18(x94551,x94552,f312(f312(f289(f851(x94551)),f312(f312(f312(f100(x94551),x94553),f312(a27,x94554)),x94555)),f189(f860(f851(x94551),a845))))+~P18(x94551,f312(f312(f289(f851(x94551)),f312(f312(f312(f100(x94551),x94553),f312(a27,x94554)),x94555)),x94552),f312(f312(f289(f851(x94551)),f312(f312(f312(f100(x94551),x94553),f312(f223(a846),f312(a30,x94554))),x94555)),f189(f860(f851(x94551),a845))))
% 173.53/173.42 [9467]E(f312(f312(f289(x94671),f518(x94672,x94673,x94674,x94675,x94671)),f519(x94672,x94673,x94674,x94675,x94671)),f312(f312(f289(x94671),x94674),x94673))+~P22(f312(f71(x94671,x94675,f312(f312(f289(x94671),x94674),x94673)),x94672))
% 173.53/173.42 [9468]E(f312(f312(f289(x94681),f520(x94682,x94683,x94684,x94685,x94681)),f521(x94682,x94683,x94684,x94685,x94681)),f312(f312(f289(x94681),x94684),x94683))+~P22(f312(f71(x94681,x94685,f312(f312(f289(x94681),x94684),x94683)),x94682))
% 173.53/173.42 [9546]P22(f312(f312(f314(x95461),f639(x95462,x95463,x95464,x95465,x95461)),x95464))+P22(f312(f312(f312(f51(x95461,f860(x95465,a845)),x95464),x95463),x95462))
% 173.53/173.42 [9550]P22(f312(f312(f314(x95501),f636(x95502,x95503,x95501,x95504,x95505)),x95503))+P22(f312(f312(f314(x95505),x95504),f312(f312(f51(x95501,f860(x95505,a845)),x95503),x95502)))
% 173.53/173.42 [9559]P22(f312(f312(f314(x95591),f637(x95592,x95593,x95591,x95594,x95595)),x95593))+P22(f312(f312(f227(f860(x95595,a845)),x95594),f312(f312(f51(x95591,f860(x95595,a845)),x95593),x95592)))
% 173.53/173.42 [9562]P22(f312(f312(x95621,f405(x95622,x95621,x95623,x95624,x95625)),x95622))+~P22(f312(f312(f312(f50(x95625,f860(x95624,a845)),x95623),x95621),x95622))
% 173.53/173.42 [9565]P22(f312(f312(f314(x95651),f405(x95652,x95653,x95654,x95655,x95651)),x95654))+~P22(f312(f312(f312(f50(x95651,f860(x95655,a845)),x95654),x95653),x95652))
% 173.53/173.42 [9573]P22(f312(f312(f314(x95731),f411(x95732,x95733,x95731,x95734,x95735)),x95733))+~P22(f312(f312(f314(x95735),x95734),f312(f312(f50(x95731,f860(x95735,a845)),x95733),x95732)))
% 173.53/173.42 [9578]P22(f312(f312(f314(x95781),x95782),f312(x95783,f411(x95783,x95784,x95785,x95782,x95781))))+~P22(f312(f312(f314(x95781),x95782),f312(f312(f50(x95785,f860(x95781,a845)),x95784),x95783)))
% 173.53/173.42 [9672]~P22(f312(f312(x96724,f639(x96725,x96724,x96723,x96722,x96721)),x96725))+P22(f312(f312(f312(f51(x96721,f860(x96722,a845)),x96723),x96724),x96725))
% 173.53/173.42 [9675]~P22(f312(f312(f314(x96751),x96752),f312(x96755,f636(x96755,x96754,x96753,x96752,x96751))))+P22(f312(f312(f314(x96751),x96752),f312(f312(f51(x96753,f860(x96751,a845)),x96754),x96755)))
% 173.53/173.42 [9678]~P22(f312(f312(f227(f860(x96781,a845)),x96782),f312(x96785,f637(x96785,x96784,x96783,x96782,x96781))))+P22(f312(f312(f227(f860(x96781,a845)),x96782),f312(f312(f51(x96783,f860(x96781,a845)),x96784),x96785)))
% 173.53/173.42 [9721]P22(f312(f312(f312(f312(a198,x97211),f361(x97212,x97213,x97214,x97211,x97215)),x97213),x97212))+~P22(f312(f312(f312(f312(a198,f36(x97215,x97211)),x97214),x97213),x97212))
% 173.53/173.42 [9722]P22(f312(f312(f312(f312(a198,x97221),f376(x97222,x97223,x97224,x97221,x97225)),x97223),x97222))+~P22(f312(f312(f312(f312(a198,f36(x97225,x97221)),x97224),x97223),x97222))
% 173.53/173.42 [9749]~P22(f312(f312(f314(x97491),f518(x97495,x97494,x97493,x97492,x97491)),f519(x97495,x97494,x97493,x97492,x97491)))+~P22(f312(f71(x97491,x97492,f312(f312(f289(x97491),x97493),x97494)),x97495))
% 173.53/173.42 [9750]~P22(f312(f312(f314(x97501),f520(x97505,x97504,x97503,x97502,x97501)),f521(x97505,x97504,x97503,x97502,x97501)))+~P22(f312(f71(x97501,x97502,f312(f312(f289(x97501),x97503),x97504)),x97505))
% 173.53/173.42 [9751]~P22(f312(f312(f314(f859(x97511,x97511)),f312(f312(f239(x97511,x97511),x97512),x97515)),f312(f312(f184(f859(x97511,x97511),a845),f312(a126,x97514)),x97513)))+P22(f312(f312(f314(f859(x97511,x97511)),f312(f312(f239(x97511,x97511),x97512),f776(x97513,x97514,x97515,x97512,x97511))),f312(f312(f184(f859(x97511,x97511),a845),x97514),x97513)))
% 173.53/173.42 [9757]P22(f312(f75(x97571,x97571,x97572,f518(x97573,x97574,x97575,x97572,x97571),f519(x97573,x97574,x97575,x97572,x97571)),x97573))+~P22(f312(f71(x97571,x97572,f312(f312(f289(x97571),x97575),x97574)),x97573))
% 173.53/173.42 [9758]P22(f312(f75(x97581,x97581,x97582,f520(x97583,x97584,x97585,x97582,x97581),f521(x97583,x97584,x97585,x97582,x97581)),x97583))+~P22(f312(f71(x97581,x97582,f312(f312(f289(x97581),x97585),x97584)),x97583))
% 173.53/173.42 [9770]~P103(x97701)+P33(x97701,f312(f312(f150(x97702,x97701),x97703),f312(f132(x97702,f312(f312(f7(x97702,x97701,a845),f312(f312(f8(x97701,f860(x97701,a845),x97702),a309),x97703)),f312(x97704,x97705))),x97705)))
% 173.53/173.42 [9815]~P22(f312(f312(f314(x98152),x98155),f312(f264(x98151,x98152,x98154),x98153)))+P22(f312(f312(f314(f859(x98151,x98152)),f312(f312(f239(x98151,x98152),f359(x98153,x98154,x98151,x98155,x98152)),x98155)),x98154))
% 173.53/173.42 [9816]~P22(f312(f312(f314(x98162),x98165),f312(f264(x98161,x98162,x98164),x98163)))+P22(f312(f312(f314(f859(x98161,x98162)),f312(f312(f239(x98161,x98162),f369(x98163,x98164,x98161,x98165,x98162)),x98165)),x98164))
% 173.53/173.42 [9836]~P22(f312(f312(f314(f859(x98361,x98361)),f312(f312(f239(x98361,x98361),x98365),x98364)),f312(f312(f184(f859(x98361,x98361),a845),f312(a126,x98363)),x98362)))+P22(f312(f312(f314(f859(x98361,x98361)),f312(f312(f239(x98361,x98361),f776(x98362,x98363,x98364,x98365,x98361)),x98364)),x98362))
% 173.53/173.42 [9839]~P22(f312(f312(f314(f859(x98391,x98391)),f312(f312(f239(x98391,x98391),x98395),x98394)),f312(f312(f184(f859(x98391,x98391),a845),f312(a126,x98393)),x98392)))+P22(f312(f312(f314(f859(x98391,x98391)),f312(f312(f239(x98391,x98391),f775(x98392,x98393,x98394,x98395,x98391)),x98394)),f312(f312(f184(f859(x98391,x98391),a845),x98393),x98392)))
% 173.53/173.42 [9840]~P22(f312(f312(f314(f859(x98401,x98401)),f312(f312(f239(x98401,x98401),x98405),x98404)),f312(f312(f184(f859(x98401,x98401),a845),f312(a126,x98403)),x98402)))+P22(f312(f312(f314(f859(x98401,x98401)),f312(f312(f239(x98401,x98401),f777(x98402,x98403,x98404,x98405,x98401)),x98404)),f312(f312(f184(f859(x98401,x98401),a845),x98403),x98402)))
% 173.53/173.42 [9841]~P22(f312(f312(f314(f859(f853(x98411),f853(x98411))),f312(f312(f239(f853(x98411),f853(x98411)),x98415),f312(f312(f147(x98411),x98414),x98413))),f154(x98411,x98412)))+P22(f312(f312(f314(f859(x98411,x98411)),f312(f312(f239(x98411,x98411),f591(x98412,x98413,x98414,x98415,x98411)),x98414)),x98412))
% 173.53/173.42 [6964]E(x69641,f192(x69642))+E(f179(x69643,x69642,f312(f312(f312(f81(x69643,f856(x69642)),x69644),x69645),x69641)),f312(f312(f289(x69643),x69645),f179(x69643,x69642,x69644)))
% 173.53/173.42 [7446]~E(x74463,f189(f860(x74462,a845)))+E(f312(f312(f124(f860(x74461,a845)),f312(f312(f50(x74462,f860(x74461,a845)),x74463),x74464)),x74465),x74465)
% 173.53/173.42 [7447]~E(x74473,f189(f860(x74472,a845)))+E(f312(f312(f115(f860(x74471,a845)),f312(f312(f51(x74472,f860(x74471,a845)),x74473),x74474)),x74475),x74475)
% 173.53/173.42 [7802]~E(x78025,f192(x78022))+E(f179(x78021,x78022,f312(f312(f312(f81(x78021,f856(x78022)),x78023),x78024),x78025)),f312(f312(f21(f860(x78021,a845)),f179(x78021,x78022,x78023)),f312(f312(f289(x78021),x78024),f189(f860(x78021,a845)))))
% 173.53/173.42 [7867]~E(x78673,f189(f860(x78672,a845)))+E(f312(f312(f21(f860(x78671,a845)),f312(f312(f51(x78672,f860(x78671,a845)),x78673),x78674)),x78675),f312(f312(f21(f860(x78671,a845)),f235(f860(x78671,a845))),x78675))
% 173.53/173.42 [7995]E(f312(f312(f155(x79951,f312(f312(f129(x79951),x79952),x79953)),x79954),x79955),f312(f312(f129(x79951),f312(f312(f155(x79951,x79952),x79954),x79955)),x79953))+~P22(f312(f312(f228(a852),x79954),f312(f190(f853(x79951)),x79952)))
% 173.53/173.42 [8115]P22(f312(f312(f314(x81151),x81155),f312(f168(x81151),x81153)))+E(f312(f312(f173(x81151,x81152),f312(f312(f177(x81151,x81152),x81153),f312(f312(f150(x81151,x81152),x81154),x81153))),x81155),f192(x81152))
% 173.53/173.42 [8241]~P22(f312(f312(f314(x82411),x82415),f312(f168(x82411),x82413)))+E(f312(f312(f173(x82411,x82412),f312(f312(f177(x82411,x82412),x82413),f312(f312(f150(x82411,x82412),x82414),x82413))),x82415),f312(f219(x82412),f312(x82414,x82415)))
% 173.53/173.42 [8279]E(f312(f312(f161(x82791),f312(f312(f150(a852,x82791),x82792),f135(a852,f312(f282(a852,x82793),x82794)))),x82795),f312(x82792,f312(f312(f89(a852),x82793),x82795)))+~P22(f312(f312(f228(a852),x82795),f312(f312(f21(a852),x82794),x82793)))
% 173.53/173.42 [8321]~E(x83213,f189(f860(x83211,a845)))+E(f312(f312(f50(x83211,f860(x83212,a845)),x83213),f312(f312(f8(f860(x83212,a845),f860(x83212,a845),x83211),f312(f124(f860(x83212,a845)),x83214)),x83215)),f189(f860(x83212,a845)))
% 173.53/173.42 [8322]~E(x83223,f189(f860(x83221,a845)))+E(f312(f312(f51(x83221,f860(x83222,a845)),x83223),f312(f312(f8(f860(x83222,a845),f860(x83222,a845),x83221),f312(f21(f860(x83222,a845)),x83224)),x83225)),f235(f860(x83222,a845)))
% 173.53/173.42 [8323]~E(x83233,f189(f860(x83231,a845)))+E(f312(f312(f51(x83231,f860(x83232,a845)),x83233),f312(f312(f8(f860(x83232,a845),f860(x83232,a845),x83231),f312(f115(f860(x83232,a845)),x83234)),x83235)),f235(f860(x83232,a845)))
% 173.53/173.42 [8328]~P135(x83282)+E(f312(f312(f6(x83281,x83282),f312(f312(f8(x83282,x83282,x83281),f312(f90(x83282),x83283)),x83284)),x83285),f312(f312(f90(x83282),x83283),f312(f312(f6(x83281,x83282),x83284),x83285)))
% 173.53/173.42 [8608]E(x86081,f189(f860(x86082,a845)))+E(f312(f312(f50(x86082,f860(x86083,a845)),x86081),f312(f312(f8(f860(x86083,a845),f860(x86083,a845),x86082),f312(f124(f860(x86083,a845)),x86084)),x86085)),f312(f312(f124(f860(x86083,a845)),x86084),f312(f312(f50(x86082,f860(x86083,a845)),x86081),x86085)))
% 173.53/173.42 [8609]E(x86091,f189(f860(x86092,a845)))+E(f312(f312(f51(x86092,f860(x86093,a845)),x86091),f312(f312(f8(f860(x86093,a845),f860(x86093,a845),x86092),f312(f21(f860(x86093,a845)),x86094)),x86095)),f312(f312(f21(f860(x86093,a845)),x86094),f312(f312(f50(x86092,f860(x86093,a845)),x86091),x86095)))
% 173.53/173.42 [8610]E(x86101,f189(f860(x86102,a845)))+E(f312(f312(f51(x86102,f860(x86103,a845)),x86101),f312(f312(f8(f860(x86103,a845),f860(x86103,a845),x86102),f312(f115(f860(x86103,a845)),x86104)),x86105)),f312(f312(f115(f860(x86103,a845)),x86104),f312(f312(f51(x86102,f860(x86103,a845)),x86101),x86105)))
% 173.53/173.42 [8801]~P22(f312(f312(f228(a852),f312(x88014,x88012)),f312(x88014,x88013)))+P22(f312(f312(f314(f859(x88011,x88011)),f312(f312(f239(x88011,x88011),x88012),x88013)),f149(x88011,f312(f312(f147(f860(x88011,a852)),x88014),x88015))))
% 173.53/173.42 [9052]~P49(f860(x90525,a845),f860(x90521,a845),x90522)+P22(f312(f312(f227(f860(x90521,a845)),f312(f312(f124(f860(x90521,a845)),f312(x90522,x90523)),f312(x90522,x90524))),f312(x90522,f312(f312(f124(f860(x90525,a845)),x90523),x90524))))
% 173.53/173.42 [9066]~P19(x90662,x90661,x90663,f312(f312(f124(f860(x90662,a845)),x90664),x90665))+E(f312(f312(f115(f860(x90661,a845)),f312(f290(x90662,x90661,x90663),f312(f312(f21(f860(x90662,a845)),x90664),x90665))),f312(f290(x90662,x90661,x90663),f312(f312(f21(f860(x90662,a845)),x90665),x90664))),f189(f860(x90661,a845)))
% 173.53/173.42 [9347]~P22(f312(f312(f227(f860(x93473,a845)),f312(f264(x93471,x93473,x93474),x93472)),x93475))+P22(f312(f312(f227(f860(x93471,a845)),x93472),f312(f88(f860(x93471,a845)),f312(f264(x93473,x93471,f312(f265(x93471,x93473),x93474)),f312(f88(f860(x93473,a845)),x93475)))))
% 173.53/173.42 [9369]~P19(x93691,x93692,x93693,f312(f312(f289(x93691),x93694),x93695))+~P22(f312(f312(f314(x93692),f312(x93693,x93694)),f312(f290(x93691,x93692,x93693),f312(f312(f21(f860(x93691,a845)),x93695),f312(f312(f289(x93691),x93694),f189(f860(x93691,a845)))))))
% 173.53/173.42 [9422]P22(f312(f312(f227(f860(x94221,a845)),f312(f264(x94222,x94221,x94223),x94224)),x94225))+~P22(f312(f312(f227(f860(x94222,a845)),x94224),f312(f88(f860(x94222,a845)),f312(f264(x94221,x94222,f312(f265(x94222,x94221),x94223)),f312(f88(f860(x94221,a845)),x94225)))))
% 173.53/173.42 [9497]~P83(x94971)+P22(f312(f312(f227(x94971),f312(f84(x94971),f312(f312(f21(x94971),f312(f312(f89(x94971),x94972),x94973)),f312(f312(f89(x94971),x94974),x94975)))),f312(f312(f89(x94971),f312(f84(x94971),f312(f312(f21(x94971),x94972),x94974))),f312(f84(x94971),f312(f312(f21(x94971),x94973),x94975)))))
% 173.53/173.42 [9592]P22(f312(f312(f314(x95921),f414(x95922,x95923,x95924,x95921,x95925)),x95924))+P22(f312(f312(f227(f860(x95925,a845)),f312(f312(f50(x95921,f860(x95925,a845)),x95924),x95923)),x95922))
% 173.53/173.42 [9792]~P22(f312(f312(f227(f860(x97921,a845)),f312(x97924,f414(x97925,x97924,x97923,x97922,x97921))),x97925))+P22(f312(f312(f227(f860(x97921,a845)),f312(f312(f50(x97922,f860(x97921,a845)),x97923),x97924)),x97925))
% 173.53/173.42 [8439]E(f312(f312(f129(x84391),x84392),f312(f312(f155(x84391,x84393),f312(f312(f21(a852),x84394),f312(f190(f853(x84391)),x84392))),x84395)),f312(f312(f155(x84391,f312(f312(f129(x84391),x84392),x84393)),x84394),x84395))+P22(f312(f312(f228(a852),x84394),f312(f190(f853(x84391)),x84392)))
% 173.53/173.42 [8469]~P132(x84691)+E(f312(f312(f89(x84691),f312(f312(f90(x84691),x84692),x84693)),f312(f312(f89(x84691),f312(f312(f90(x84691),x84694),x84693)),x84695)),f312(f312(f89(x84691),f312(f312(f90(x84691),f312(f312(f89(x84691),x84692),x84694)),x84693)),x84695))
% 173.53/173.42 [9023]~P135(x90231)+E(f312(f162(x90231),f312(f312(f150(x90232,x90231),f312(f312(f8(x90231,x90231,x90232),f312(f90(x90231),x90233)),x90234)),x90235)),f312(f312(f90(x90231),x90233),f312(f162(x90231),f312(f312(f150(x90232,x90231),x90234),x90235))))
% 173.53/173.42 [9196]E(f312(f190(f853(x91961)),f312(f312(f169(x91961),f312(f312(f225(a852),f312(f190(f853(x91961)),x91962)),f312(f190(f853(x91963)),x91964))),x91962)),f312(f190(f853(x91963)),f312(f312(f169(x91963),f312(f312(f225(a852),f312(f190(f853(x91961)),x91962)),f312(f190(f853(x91963)),x91964))),x91964)))+P22(f312(x91965,f312(f312(f177(x91961,x91963),x91962),x91964)))
% 173.53/173.42 [9434]~P135(x94342)+E(f312(f312(f6(x94341,x94342),f312(f312(f7(x94341,x94342,x94342),f312(f312(f8(x94342,f860(x94342,x94342),x94341),f90(x94342)),x94343)),x94344)),x94345),f312(f312(f90(x94342),f312(f312(f6(x94341,x94342),x94343),x94345)),x94344))
% 173.53/173.42 [9435]~P65(x94352)+E(f312(f312(f6(x94351,x94352),f312(f312(f7(x94351,x94352,x94352),f312(f312(f8(x94352,f860(x94352,x94352),x94351),f268(x94352)),x94353)),x94354)),x94355),f312(f312(f268(x94352),f312(f312(f6(x94351,x94352),x94353),x94355)),x94354))
% 173.53/173.42 [9441]~P72(x94412)+E(f312(f312(f9(x94411,x94412),f312(f312(f18(x94411,x94412,x94412),f312(f312(f8(x94412,f860(x94412,x94412),x94411),f90(x94412)),x94413)),x94414)),x94415),f312(f312(f90(x94412),f312(f312(f9(x94411,x94412),x94413),x94415)),f312(f312(f9(x94411,x94412),x94414),x94415)))
% 173.53/173.42 [9442]~P26(x94422)+E(f312(f312(f6(x94421,x94422),f312(f312(f18(x94421,x94422,x94422),f312(f312(f8(x94422,f860(x94422,x94422),x94421),f89(x94422)),x94423)),x94424)),x94425),f312(f312(f89(x94422),f312(f312(f6(x94421,x94422),x94423),x94425)),f312(f312(f6(x94421,x94422),x94424),x94425)))
% 173.53/173.42 [9443]~P30(x94432)+E(f312(f312(f6(x94431,x94432),f312(f312(f18(x94431,x94432,x94432),f312(f312(f8(x94432,f860(x94432,x94432),x94431),f21(x94432)),x94433)),x94434)),x94435),f312(f312(f21(x94432),f312(f312(f6(x94431,x94432),x94433),x94435)),f312(f312(f6(x94431,x94432),x94434),x94435)))
% 173.53/173.42 [9480]~E(x94803,f189(f860(x94801,a845)))+E(f312(f312(f50(x94801,f860(x94802,a845)),x94803),f312(f312(f7(x94801,f860(x94802,a845),f860(x94802,a845)),f312(f312(f8(f860(x94802,a845),f860(f860(x94802,a845),f860(x94802,a845)),x94801),f124(f860(x94802,a845))),x94804)),x94805)),f189(f860(x94802,a845)))
% 173.53/173.42 [9481]~E(x94813,f189(f860(x94811,a845)))+E(f312(f312(f51(x94811,f860(x94812,a845)),x94813),f312(f312(f7(x94811,f860(x94812,a845),f860(x94812,a845)),f312(f312(f8(f860(x94812,a845),f860(f860(x94812,a845),f860(x94812,a845)),x94811),f21(f860(x94812,a845))),x94814)),x94815)),f235(f860(x94812,a845)))
% 173.53/173.42 [9482]~E(x94823,f189(f860(x94821,a845)))+E(f312(f312(f51(x94821,f860(x94822,a845)),x94823),f312(f312(f7(x94821,f860(x94822,a845),f860(x94822,a845)),f312(f312(f8(f860(x94822,a845),f860(f860(x94822,a845),f860(x94822,a845)),x94821),f115(f860(x94822,a845))),x94824)),x94825)),f235(f860(x94822,a845)))
% 173.53/173.42 [9505]E(x95051,f189(f860(x95052,a845)))+E(f312(f312(f50(x95052,f860(x95053,a845)),x95051),f312(f312(f7(x95052,f860(x95053,a845),f860(x95053,a845)),f312(f312(f8(f860(x95053,a845),f860(f860(x95053,a845),f860(x95053,a845)),x95052),f124(f860(x95053,a845))),x95054)),x95055)),f312(f312(f124(f860(x95053,a845)),f312(f312(f50(x95052,f860(x95053,a845)),x95051),x95054)),x95055))
% 173.53/173.42 [9506]E(x95061,f189(f860(x95062,a845)))+E(f312(f312(f51(x95062,f860(x95063,a845)),x95061),f312(f312(f7(x95062,f860(x95063,a845),f860(x95063,a845)),f312(f312(f8(f860(x95063,a845),f860(f860(x95063,a845),f860(x95063,a845)),x95062),f21(f860(x95063,a845))),x95064)),x95065)),f312(f312(f21(f860(x95063,a845)),f312(f312(f51(x95062,f860(x95063,a845)),x95061),x95064)),x95065))
% 173.53/173.42 [9507]E(x95071,f189(f860(x95072,a845)))+E(f312(f312(f51(x95072,f860(x95073,a845)),x95071),f312(f312(f7(x95072,f860(x95073,a845),f860(x95073,a845)),f312(f312(f8(f860(x95073,a845),f860(f860(x95073,a845),f860(x95073,a845)),x95072),f115(f860(x95073,a845))),x95074)),x95075)),f312(f312(f115(f860(x95073,a845)),f312(f312(f51(x95072,f860(x95073,a845)),x95071),x95074)),x95075))
% 173.53/173.42 [9073]~P22(f312(f312(f227(a852),x90731),x90734))+E(f312(f312(f21(a852),f312(f312(f89(a852),f312(f312(f90(a852),x90731),x90732)),x90733)),f312(f312(f89(a852),f312(f312(f90(a852),x90734),x90732)),x90735)),f312(f312(f21(a852),x90733),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x90734),x90731)),x90732)),x90735)))
% 173.53/173.42 [9653]~P135(x96531)+E(f312(f162(x96531),f312(f312(f150(x96532,x96531),f312(f312(f7(x96532,x96531,x96531),f312(f312(f8(x96531,f860(x96531,x96531),x96532),f90(x96531)),x96533)),x96534)),x96535)),f312(f312(f90(x96531),f312(f162(x96531),f312(f312(f150(x96532,x96531),x96533),x96535))),x96534))
% 173.53/173.42 [9659]~P26(x96591)+E(f312(f162(x96591),f312(f312(f150(x96592,x96591),f312(f312(f18(x96592,x96591,x96591),f312(f312(f8(x96591,f860(x96591,x96591),x96592),f89(x96591)),x96593)),x96594)),x96595)),f312(f312(f89(x96591),f312(f162(x96591),f312(f312(f150(x96592,x96591),x96593),x96595))),f312(f162(x96591),f312(f312(f150(x96592,x96591),x96594),x96595))))
% 173.53/173.42 [9660]~P30(x96601)+E(f312(f162(x96601),f312(f312(f150(x96602,x96601),f312(f312(f18(x96602,x96601,x96601),f312(f312(f8(x96601,f860(x96601,x96601),x96602),f21(x96601)),x96603)),x96604)),x96605)),f312(f312(f21(x96601),f312(f162(x96601),f312(f312(f150(x96602,x96601),x96603),x96605))),f312(f162(x96601),f312(f312(f150(x96602,x96601),x96604),x96605))))
% 173.53/173.42 [9805]P22(f312(x98051,f312(f312(f177(x98052,x98053),x98054),x98055)))+~P22(f312(x98051,f312(f312(f177(x98052,x98053),f312(f312(f169(x98052),f312(f312(f225(a852),f312(f190(f853(x98052)),x98054)),f312(f190(f853(x98053)),x98055))),x98054)),f312(f312(f169(x98053),f312(f312(f225(a852),f312(f190(f853(x98052)),x98054)),f312(f190(f853(x98053)),x98055))),x98055))))
% 173.53/173.42 [9314]~P22(f312(f312(f227(a852),x93144),x93141))+E(f312(f312(f21(a852),f312(f312(f89(a852),f312(f312(f90(a852),x93141),x93142)),x93143)),f312(f312(f89(a852),f312(f312(f90(a852),x93144),x93142)),x93145)),f312(f312(f21(a852),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x93141),x93144)),x93142)),x93143)),x93145))
% 173.53/173.42 [10066]P18(x100661,x100662,f312(f290(a848,f851(x100661),f312(f312(f18(a848,f860(x100661,f860(a847,a845)),f851(x100661)),f312(f312(f18(a848,a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),f312(f312(f8(f860(x100661,f860(a847,a845)),f860(a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),a848),f100(x100661)),x100663)),a27)),x100664)),x100665))+~P18(x100661,f312(f312(f124(f860(f851(x100661),a845)),x100662),f312(f290(a848,f851(x100661),f312(f312(f18(a848,f860(x100661,f860(a847,a845)),f851(x100661)),f312(f312(f18(a848,a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),f312(f312(f8(f860(x100661,f860(a847,a845)),f860(a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),a848),f100(x100661)),x100663)),a27)),x100664)),x100665)),f312(f290(a848,f851(x100661),f312(f312(f18(a848,f860(x100661,f860(a847,a845)),f851(x100661)),f312(f312(f18(a848,a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),f312(f312(f8(f860(x100661,f860(a847,a845)),f860(a846,f860(f860(x100661,f860(a847,a845)),f851(x100661))),a848),f100(x100661)),x100663)),f312(f312(f8(f856(a846),a846,a848),f223(a846)),a30))),x100664)),x100665))
% 173.53/173.42 [10067]P21(x100671,x100672,f312(f290(a848,f851(x100671),f312(f312(f18(a848,f860(x100671,f860(a847,a845)),f851(x100671)),f312(f312(f18(a848,a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),f312(f312(f8(f860(x100671,f860(a847,a845)),f860(a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),a848),f100(x100671)),x100673)),a27)),x100674)),x100675))+~P21(x100671,f312(f312(f124(f860(f851(x100671),a845)),x100672),f312(f290(a848,f851(x100671),f312(f312(f18(a848,f860(x100671,f860(a847,a845)),f851(x100671)),f312(f312(f18(a848,a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),f312(f312(f8(f860(x100671,f860(a847,a845)),f860(a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),a848),f100(x100671)),x100673)),a27)),x100674)),x100675)),f312(f290(a848,f851(x100671),f312(f312(f18(a848,f860(x100671,f860(a847,a845)),f851(x100671)),f312(f312(f18(a848,a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),f312(f312(f8(f860(x100671,f860(a847,a845)),f860(a846,f860(f860(x100671,f860(a847,a845)),f851(x100671))),a848),f100(x100671)),x100673)),f312(f312(f8(f856(a846),a846,a848),f223(a846)),a30))),x100674)),x100675))
% 173.53/173.42 [5191]E(x51911,x51912)+~E(f33(x51913,x51914,x51911),f33(x51915,x51916,x51912))
% 173.53/173.42 [5192]E(x51921,x51922)+~E(f33(x51923,x51921,x51924),f33(x51925,x51922,x51926))
% 173.53/173.42 [5193]E(x51931,x51932)+~E(f33(x51931,x51933,x51934),f33(x51932,x51935,x51936))
% 173.53/173.42 [5194]E(x51941,x51942)+~E(f32(x51943,x51944,x51941),f32(x51945,x51946,x51942))
% 173.53/173.42 [5195]E(x51951,x51952)+~E(f32(x51953,x51951,x51954),f32(x51955,x51952,x51956))
% 173.53/173.42 [5196]E(x51961,x51962)+~E(f32(x51961,x51963,x51964),f32(x51962,x51965,x51966))
% 173.53/173.42 [5197]E(x51971,x51972)+~E(f31(x51973,x51974,x51971),f31(x51975,x51976,x51972))
% 173.53/173.42 [5198]E(x51981,x51982)+~E(f31(x51983,x51981,x51984),f31(x51985,x51982,x51986))
% 173.53/173.42 [5199]E(x51991,x51992)+~E(f31(x51991,x51993,x51994),f31(x51992,x51995,x51996))
% 173.53/173.42 [7145]E(x71451,x71452)+~E(f209(x71453,x71454,x71455,x71451),f209(x71453,x71454,x71456,x71452))
% 173.53/173.42 [7146]E(x71461,x71462)+~E(f209(x71463,x71464,x71461,x71465),f209(x71463,x71464,x71462,x71466))
% 173.53/173.42 [9320]~P36(x93201,x93202,x93203,x93206)+P36(x93201,x93202,f182(x93201,x93202,x93203,x93204,x93205),f182(x93201,x93202,x93206,x93204,x93205))
% 173.53/173.42 [6609]E(f312(f180(x66091,x66092,x66093,x66094),x66095),f312(f219(x66092),x66096))+~E(f312(x66094,x66095),f312(f219(x66092),x66096))
% 173.53/173.42 [6747]E(f312(f221(f856(x67471),x67472,f192(x67471),x67473),f312(x67474,x67475)),f312(x67473,x67476))+~E(f312(x67474,x67475),f312(f219(x67472),x67476))
% 173.53/173.42 [8263]~P14(x82635,x82631,x82632,x82636)+E(f312(f82(x82631,x82631,x82631,f312(x82632,x82633)),f312(x82632,x82634)),f312(f82(x82631,x82631,x82631,f312(x82632,x82634)),f312(x82632,x82633)))
% 173.53/173.42 [8510]~P56(x85104,x85105,x85102,x85101,x85106)+E(f312(x85101,f312(x85102,x85103)),x85103)
% 173.53/173.42 [8658]P19(x86581,x86582,x86583,x86584)+~P19(x86581,x86585,f312(f82(x86582,x86585,x86581,x86586),x86583),x86584)
% 173.53/173.42 [8739]~P19(x87394,x87392,f312(f82(x87391,x87392,x87394,x87393),x87395),x87396)+P19(x87391,x87392,x87393,f312(f290(x87394,x87391,x87395),x87396))
% 173.53/173.42 [9444]P22(f312(f70(x94441),x94442))+~P22(f312(f75(x94441,x94443,x94444,x94445,x94442),x94446))
% 173.53/173.42 [9451]~P22(f312(f312(f314(x94514),x94513),f278(x94514,x94515,x94511,x94512,x94516)))+P22(f312(f312(x94511,x94512),x94513))
% 173.53/173.42 [9452]~P22(f312(f312(f314(x94524),x94523),f275(x94524,x94521,x94525,x94522,x94526)))+P22(f312(f312(x94521,x94522),x94523))
% 173.53/173.42 [9453]~P22(f312(f312(f314(x94534),x94532),f278(x94534,x94531,x94535,x94536,x94533)))+P22(f312(f312(x94531,x94532),x94533))
% 173.53/173.42 [9454]~P22(f312(f312(f314(x94544),x94542),f275(x94544,x94545,x94541,x94546,x94543)))+P22(f312(f312(x94541,x94542),x94543))
% 173.53/173.42 [5686]E(x56861,x56862)+~E(f312(f312(f239(x56863,x56864),x56865),x56861),f312(f312(f239(x56863,x56864),x56866),x56862))
% 173.53/173.42 [5688]E(x56881,x56882)+~E(f312(f312(f239(x56883,x56884),x56881),x56885),f312(f312(f239(x56883,x56884),x56882),x56886))
% 173.53/173.42 [7195]~P37(x71954,x71951,f312(f312(f147(x71954),x71952),x71955),f312(f312(f147(x71954),x71953),x71956))+P22(f312(f312(x71951,x71952),x71953))
% 173.53/173.42 [7560]P37(x75601,x75602,x75603,x75604)+~P37(x75601,x75602,f312(f312(f147(x75601),x75605),x75603),f312(f312(f147(x75601),x75606),x75604))
% 173.53/173.42 [8373]~P36(x83731,x83732,x83733,x83735)+P36(x83731,x83732,f312(f312(f312(f81(x83731,f856(x83732)),x83733),x83734),f192(x83732)),f312(f312(f312(f81(x83731,f856(x83732)),x83735),x83734),f312(f219(x83732),x83736)))
% 173.53/173.42 [8599]~P56(x85995,x85991,x85992,x85996,x85994)+P22(f312(f312(f314(x85991),f312(x85992,x85993)),x85994))
% 173.53/173.42 [8766]E(f312(f85(x87661,x87662,x87663,x87664,x87665),x87666),f312(x87663,x87666))+P22(f312(f312(f314(x87661),x87666),x87665))
% 173.53/173.42 [8786]~E(x87863,f312(f312(f147(x87861),x87865),x87866))+P22(f312(f312(f314(f859(f853(x87861),f853(x87861))),f312(f312(f239(f853(x87861),f853(x87861)),x87862),f312(f312(f129(x87861),x87862),x87863))),f143(x87861,x87864)))
% 173.53/173.42 [8792]E(f312(f85(x87921,x87922,x87923,x87924,x87925),x87926),f312(x87924,x87926))+~P22(f312(f312(f314(x87921),x87926),x87925))
% 173.53/173.42 [8797]E(f312(f182(x87971,x87972,x87973,x87974,x87975),x87976),f312(x87973,x87976))+P22(f312(f312(f314(x87971),x87976),f312(f168(x87971),x87974)))
% 173.53/173.42 [9027]~P39(x90271,x90272,x90273,x90275,x90276)+P39(x90271,x90272,x90273,f312(f312(f169(x90271),x90274),x90275),f312(f312(f169(x90272),x90274),x90276))
% 173.53/173.42 [9028]~P39(x90281,x90282,x90283,x90285,x90286)+P39(x90281,x90282,x90283,f312(f312(f134(x90281),x90284),x90285),f312(f312(f134(x90282),x90284),x90286))
% 173.53/173.42 [9516]~P17(x95164,x95162,x95165,x95163,x95166,x95161)+E(f312(x95161,f189(f860(x95162,a845))),x95163)
% 173.53/173.42 [9752]~E(f312(x97524,f312(f246(x97521,x97523),x97525)),f312(x97526,f312(f246(x97521,x97523),x97525)))+E(f312(f250(x97521,x97522,x97523,x97523,x97524,f39(x97523)),x97525),f312(f250(x97521,x97522,x97523,x97523,x97526,f39(x97523)),x97525))
% 173.53/173.42 [9753]~E(f312(x97534,f312(f248(x97531,x97532),x97535)),f312(x97536,f312(f248(x97531,x97532),x97535)))+E(f312(f250(x97531,x97531,x97532,x97533,f39(x97531),x97534),x97535),f312(f250(x97531,x97531,x97532,x97533,f39(x97531),x97536),x97535))
% 173.53/173.42 [9802]~E(f312(f250(x98022,x98026,x98023,x98023,x98021,f39(x98023)),x98024),f312(f250(x98022,x98026,x98023,x98023,x98025,f39(x98023)),x98024))+E(f312(x98021,f312(f246(x98022,x98023),x98024)),f312(x98025,f312(f246(x98022,x98023),x98024)))
% 173.53/173.42 [9803]~E(f312(f250(x98032,x98032,x98033,x98036,f39(x98032),x98031),x98034),f312(f250(x98032,x98032,x98033,x98036,f39(x98032),x98035),x98034))+E(f312(x98031,f312(f248(x98032,x98033),x98034)),f312(x98035,f312(f248(x98032,x98033),x98034)))
% 173.53/173.42 [8695]P22(f312(f312(f314(x86951),x86952),x86953))+~P22(f312(f312(f314(f859(x86951,x86954)),f312(f312(f239(x86951,x86954),x86952),x86955)),f312(f312(f247(x86951,x86954),x86953),x86956)))
% 173.53/173.42 [8709]P22(f312(f312(f314(x87091),x87092),f312(x87093,x87094)))+~P22(f312(f312(f314(f859(x87095,x87091)),f312(f312(f239(x87095,x87091),x87094),x87092)),f312(f312(f247(x87095,x87091),x87096),x87093)))
% 173.53/173.42 [8794]~E(f312(f190(f853(x87941)),x87944),f312(f190(f853(x87942)),x87945))+E(f182(x87941,x87942,x87943,x87944,f312(f312(f129(x87942),x87945),x87946)),f182(x87941,x87942,x87943,x87944,x87945))
% 173.53/173.42 [8795]~E(f312(f190(f853(x87951)),x87954),f312(f190(f853(x87952)),x87956))+E(f182(x87951,x87952,x87953,f312(f312(f129(x87951),x87954),x87955),x87956),f182(x87951,x87952,x87953,x87954,x87956))
% 173.53/173.42 [9046]P22(f312(f312(f314(x90461),x90464),f179(x90461,x90462,x90466)))+E(f180(x90461,x90462,f312(f312(f312(f81(x90461,f856(x90462)),x90463),x90464),f312(f219(x90462),x90465)),x90466),f312(f312(f312(f81(x90461,f856(x90462)),f180(x90461,x90462,x90463,x90466)),x90464),f312(f219(x90462),x90465)))
% 173.53/173.42 [9146]P22(f312(f312(f314(f859(x91461,x91461)),f312(f312(f239(x91461,x91461),f312(x91462,x91463)),f312(x91462,x91464))),x91465))+~P22(f312(f312(f314(f859(x91466,x91466)),f312(f312(f239(x91466,x91466),x91463),x91464)),f312(f312(f266(x91461,x91466),x91465),x91462)))
% 173.53/173.42 [9165]~P22(f312(f312(f314(f859(x91654,x91654)),f312(f312(f239(x91654,x91654),f312(x91656,x91652)),f312(x91656,x91653))),x91655))+P22(f312(f312(f314(f859(x91651,x91651)),f312(f312(f239(x91651,x91651),x91652),x91653)),f312(f312(f266(x91654,x91651),x91655),x91656)))
% 173.53/173.42 [9787]P22(f312(f312(f312(f312(a198,x97871),f312(f312(f312(a201,x97872),f40(x97873)),f312(x97874,x97872))),x97875),f453(x97876,x97875,x97872,x97871,x97874,x97873)))+~P22(f312(f312(f312(f312(a198,f32(x97873,x97874,x97871)),x97872),x97875),f312(f312(f312(a201,x97876),f40(x97873)),f312(f312(a202,x97872),x97873))))
% 173.53/173.42 [9806]P22(f312(f312(f312(f312(a198,f312(a27,x98061)),f312(f312(f312(a201,f312(f312(a203,x98062),a204)),f40(a26)),f312(x98063,x98062))),x98064),f528(x98065,x98064,x98062,x98063,x98061,x98066)))+~P22(f312(f312(f312(f312(a198,f31(x98066,x98061,x98063)),x98062),x98064),f312(f312(f312(a201,f312(f312(a203,x98065),f312(a202,x98062))),x98066),f312(f312(a202,x98065),a25))))
% 173.53/173.42 [9882]E(f312(f312(f312(a201,f453(x98821,x98822,x98823,x98824,x98825,x98826)),f40(x98826)),f312(f312(a202,x98823),x98826)),f312(f312(f312(a201,x98821),f40(x98826)),f312(f312(a202,x98823),x98826)))+~P22(f312(f312(f312(f312(a198,f32(x98826,x98825,x98824)),x98823),x98822),f312(f312(f312(a201,x98821),f40(x98826)),f312(f312(a202,x98823),x98826))))
% 173.53/173.42 [10002]E(f312(f312(f312(a201,f312(f312(a203,f528(x100021,x100022,x100023,x100024,x100025,x100026)),f312(a202,x100023))),x100026),f312(f312(a202,f528(x100021,x100022,x100023,x100024,x100025,x100026)),a25)),f312(f312(f312(a201,f312(f312(a203,x100021),f312(a202,x100023))),x100026),f312(f312(a202,x100021),a25)))+~P22(f312(f312(f312(f312(a198,f31(x100026,x100025,x100024)),x100023),x100022),f312(f312(f312(a201,f312(f312(a203,x100021),f312(a202,x100023))),x100026),f312(f312(a202,x100021),a25))))
% 173.53/173.42 [6079]~E(x60796,x60794)+E(f312(f312(f312(f312(f81(x60791,x60792),x60793),x60794),x60795),x60796),x60795)
% 173.53/173.42 [6128]E(x61281,x61282)+E(f312(f312(f312(f312(f81(x61283,x61284),x61285),x61282),x61286),x61281),f312(x61285,x61281))
% 173.53/173.42 [7631]~P31(x76312)+E(f312(f312(f50(x76311,x76312),x76313),f312(f312(f7(x76311,x76314,x76312),x76315),x76316)),f312(f312(f312(f50(x76311,f860(x76314,x76312)),x76313),x76315),x76316))
% 173.53/173.42 [7632]~P31(x76322)+E(f312(f312(f51(x76321,x76322),x76323),f312(f312(f7(x76321,x76324,x76322),x76325),x76326)),f312(f312(f312(f51(x76321,f860(x76324,x76322)),x76323),x76325),x76326))
% 173.53/173.42 [8291]~P36(x82911,x82912,x82913,x82916)+P36(x82911,x82912,f312(f312(f312(f81(x82911,f856(x82912)),x82913),x82914),x82915),f312(f312(f312(f81(x82911,f856(x82912)),x82916),x82914),x82915))
% 173.53/173.42 [8420]E(f312(f312(f50(x84201,f860(x84202,a845)),x84203),f312(f312(f8(f860(x84202,a845),f860(x84202,a845),x84201),f312(f289(x84202),x84204)),x84205)),f312(f312(f289(x84202),x84204),f312(f312(f50(x84201,f860(x84202,a845)),x84203),x84205)))+~P22(f312(f312(f314(x84201),x84206),x84203))
% 173.53/173.42 [8848]~P31(x88482)+E(f312(f312(f50(x88481,x88482),x88483),f312(f312(f8(f860(x88484,x88482),x88482,x88481),f312(f50(x88484,x88482),x88485)),f312(f7(x88484,x88481,x88482),x88486))),f312(f312(f50(x88484,x88482),x88485),f312(f312(f8(f860(x88481,x88482),x88482,x88484),f312(f50(x88481,x88482),x88483)),x88486)))
% 173.53/173.42 [8849]~P31(x88492)+E(f312(f312(f51(x88491,x88492),x88493),f312(f312(f8(f860(x88494,x88492),x88492,x88491),f312(f51(x88494,x88492),x88495)),f312(f7(x88494,x88491,x88492),x88496))),f312(f312(f51(x88494,x88492),x88495),f312(f312(f8(f860(x88491,x88492),x88492,x88494),f312(f51(x88491,x88492),x88493)),x88496)))
% 173.53/173.42 [9056]P22(f312(f312(f314(x90561),x90562),f312(f168(x90561),x90563)))+~P22(f312(f312(f314(f859(x90564,x90561)),f312(f312(f239(x90564,x90561),x90565),x90562)),f312(f168(f859(x90564,x90561)),f312(f312(f177(x90564,x90561),x90566),x90563))))
% 173.53/173.42 [9057]P22(f312(f312(f314(x90571),x90572),f312(f168(x90571),x90573)))+~P22(f312(f312(f314(f859(x90571,x90574)),f312(f312(f239(x90571,x90574),x90572),x90575)),f312(f168(f859(x90571,x90574)),f312(f312(f177(x90571,x90574),x90573),x90576))))
% 173.53/173.42 [9159]P22(f312(f312(f227(f860(x91591,a845)),f312(f264(x91592,x91591,x91593),x91594)),x91595))+~P22(f312(f312(f227(f860(f859(x91592,x91591),a845)),x91593),f312(f312(f247(x91592,x91591),x91596),f312(f16(f860(x91591,a845),x91592),x91595))))
% 173.53/173.42 [9350]P22(f312(f312(f314(f859(f853(x93501),f853(x93501))),f312(f312(f239(f853(x93501),f853(x93501)),f312(f312(f147(x93501),x93502),x93503)),f312(f312(f147(x93501),x93504),x93505))),f143(x93501,x93506)))+~P22(f312(f312(f314(f859(x93501,x93501)),f312(f312(f239(x93501,x93501),x93502),x93504)),x93506))
% 173.53/173.42 [9388]P22(f312(f312(f312(f312(a198,f32(x93881,x93882,x93883)),x93884),x93885),f312(f312(f312(a201,x93886),f40(x93881)),f312(f312(a202,x93884),x93881))))+~P22(f312(f312(f312(f312(a198,x93883),f312(f312(f312(a201,x93884),f40(x93881)),f312(x93882,x93884))),x93885),x93886))
% 173.53/173.42 [9662]P22(f312(f312(f312(f312(a198,f31(x96621,x96622,x96623)),x96624),x96625),f312(f312(f312(a201,f312(f312(a203,x96626),f312(a202,x96624))),x96621),f312(f312(a202,x96626),a25))))+~P22(f312(f312(f312(f312(a198,f312(a27,x96622)),f312(f312(f312(a201,f312(f312(a203,x96624),a204)),f40(a26)),f312(x96623,x96624))),x96625),x96626))
% 173.53/173.42 [9782]P22(f312(f312(f312(f312(a198,x97821),f312(f312(f312(a201,x97822),f40(x97823)),f312(x97824,x97822))),x97825),f485(x97826,x97825,x97822,x97821,x97824,x97823)))+~P22(f312(f312(f312(f312(a198,f32(x97823,x97824,x97821)),x97822),x97825),x97826))
% 173.53/173.42 [9798]P22(f312(f312(f312(f312(a198,f312(a27,x97981)),f312(f312(f312(a201,f312(f312(a203,x97982),a204)),f40(a26)),f312(x97983,x97982))),x97984),f619(x97985,x97984,x97982,x97983,x97981,x97986)))+~P22(f312(f312(f312(f312(a198,f31(x97986,x97981,x97983)),x97982),x97984),x97985))
% 173.53/173.42 [9801]E(f312(f312(f239(x98011,x98012),f713(x98013,x98014,x98015,x98012,x98011,x98016)),f714(x98013,x98014,x98015,x98012,x98011,x98016)),x98016)+P22(f312(f312(f314(x98015),x98014),f312(f312(f249(x98011,x98012,f860(x98015,a845)),x98013),x98016)))
% 173.53/173.42 [9807]E(f312(f312(f239(x98071,x98072),f715(x98073,x98074,x98072,x98071,x98075,x98076)),f716(x98073,x98074,x98072,x98071,x98075,x98076)),x98073)+~P22(f312(f312(f314(x98076),x98075),f312(f312(f249(x98071,x98072,f860(x98076,a845)),x98074),x98073)))
% 173.53/173.42 [9878]E(f312(f312(f312(a201,f485(x98781,x98782,x98783,x98784,x98785,x98786)),f40(x98786)),f312(f312(a202,x98783),x98786)),x98781)+~P22(f312(f312(f312(f312(a198,f32(x98786,x98785,x98784)),x98783),x98782),x98781))
% 173.53/173.42 [9968]P22(f312(f312(f314(x99681),x99682),f312(f312(x99683,f715(x99684,x99683,x99685,x99686,x99682,x99681)),f716(x99684,x99683,x99685,x99686,x99682,x99681))))+~P22(f312(f312(f314(x99681),x99682),f312(f312(f249(x99686,x99685,f860(x99681,a845)),x99683),x99684)))
% 173.53/173.42 [9988]~P22(f312(f312(f314(x99881),x99882),f312(f312(x99885,f713(x99885,x99882,x99881,x99884,x99883,x99886)),f714(x99885,x99882,x99881,x99884,x99883,x99886))))+P22(f312(f312(f314(x99881),x99882),f312(f312(f249(x99883,x99884,f860(x99881,a845)),x99885),x99886)))
% 173.53/173.42 [10000]E(f312(f312(f312(a201,f312(f312(a203,f619(x100001,x100002,x100003,x100004,x100005,x100006)),f312(a202,x100003))),x100006),f312(f312(a202,f619(x100001,x100002,x100003,x100004,x100005,x100006)),a25)),x100001)+~P22(f312(f312(f312(f312(a198,f31(x100006,x100005,x100004)),x100003),x100002),x100001))
% 173.53/173.42 [7754]P22(f312(f312(f314(x77541),x77544),x77546))+E(f183(x77541,x77542,f312(f312(f312(f81(x77541,f856(x77542)),x77543),x77544),x77545),x77546),f183(x77541,x77542,x77543,x77546))
% 173.53/173.42 [7823]P22(f312(f312(f314(x78231),x78234),x78236))+E(f312(f290(x78231,x78232,f312(f312(f312(f81(x78231,x78232),x78233),x78234),x78235)),x78236),f312(f290(x78231,x78232,x78233),x78236))
% 173.53/173.42 [7849]P22(f312(f312(f314(x78491),x78494),f312(f168(x78491),x78496)))+E(f312(f312(f150(x78491,x78492),f312(f312(f312(f81(x78491,x78492),x78493),x78494),x78495)),x78496),f312(f312(f150(x78491,x78492),x78493),x78496))
% 173.53/173.42 [8312]E(x83121,x83122)+E(f312(f312(f155(x83123,f312(f312(f155(x83123,x83124),x83121),x83125)),x83122),x83126),f312(f312(f155(x83123,f312(f312(f155(x83123,x83124),x83122),x83126)),x83121),x83125))
% 173.53/173.42 [8854]~P22(f312(f312(f314(x88543),x88546),x88545))+E(f312(f312(f289(x88541),x88542),f312(f290(x88543,x88541,x88544),f312(f312(f21(f860(x88543,a845)),x88545),f312(f312(f289(x88543),x88546),f189(f860(x88543,a845)))))),f312(f290(x88543,x88541,f312(f312(f312(f81(x88543,x88541),x88544),x88546),x88542)),x88545))
% 173.53/173.42 [9617]E(f182(x96171,x96172,x96173,f312(f312(f129(x96171),x96174),f312(f312(f147(x96171),x96175),f127(x96171))),x96176),f312(f312(f312(f81(x96171,f856(x96172)),f182(x96171,x96172,x96173,x96174,x96176)),x96175),f312(f219(x96172),f312(f312(f161(x96172),x96176),f312(f190(f853(x96171)),x96174)))))+~P22(f312(f312(f228(a852),f312(f190(f853(x96171)),x96174)),f312(f190(f853(x96172)),x96176)))
% 173.53/173.42 [8639]~E(x86393,x86396)+E(f312(f312(f173(x86391,x86392),f312(f312(f147(f859(x86391,x86392)),f312(f312(f239(x86391,x86392),x86393),x86394)),x86395)),x86396),f312(f219(x86392),x86394))
% 173.53/173.42 [8667]E(x86671,x86672)+E(f312(f312(f173(x86673,x86674),f312(f312(f147(f859(x86673,x86674)),f312(f312(f239(x86673,x86674),x86671),x86675)),x86676)),x86672),f312(f312(f173(x86673,x86674),x86676),x86672))
% 173.53/173.42 [8934]~P22(f312(f312(x89344,x89345),x89346))+P22(f312(f312(f312(f312(f124(f860(x89341,f860(x89342,a845))),x89343),x89344),x89345),x89346))
% 173.53/173.42 [8936]~P22(f312(f312(x89363,x89365),x89366))+P22(f312(f312(f312(f312(f124(f860(x89361,f860(x89362,a845))),x89363),x89364),x89365),x89366))
% 173.53/173.42 [9217]P22(f312(f312(x92171,x92172),x92173))+~P22(f312(f312(f312(f312(f115(f860(x92174,f860(x92175,a845))),x92176),x92171),x92172),x92173))
% 173.53/173.42 [9218]P22(f312(f312(x92181,x92182),x92183))+~P22(f312(f312(f312(f312(f115(f860(x92184,f860(x92185,a845))),x92181),x92186),x92182),x92183))
% 173.53/173.42 [9640]~P72(x96402)+E(f312(f312(f9(x96401,x96402),f312(f312(f7(x96401,f860(x96403,a845),x96402),f312(f312(f8(f860(x96403,x96402),f860(f860(x96403,a845),x96402),x96401),f9(x96403,x96402)),x96404)),x96405)),x96406),f312(f312(f9(f859(x96401,x96403),x96402),f312(f249(x96401,x96403,x96402),x96404)),f312(f312(f247(x96401,x96403),x96406),f312(f16(f860(x96403,a845),x96401),x96405))))
% 173.53/173.42 [9641]~P26(x96412)+E(f312(f312(f6(x96411,x96412),f312(f312(f7(x96411,f860(x96413,a845),x96412),f312(f312(f8(f860(x96413,x96412),f860(f860(x96413,a845),x96412),x96411),f6(x96413,x96412)),x96414)),x96415)),x96416),f312(f312(f6(f859(x96411,x96413),x96412),f312(f249(x96411,x96413,x96412),x96414)),f312(f312(f247(x96411,x96413),x96416),f312(f16(f860(x96413,a845),x96411),x96415))))
% 173.53/173.42 [9779]~P26(x97792)+E(f312(f312(f6(x97791,x97792),f312(f312(f7(x97791,f860(x97793,a845),x97792),f312(f312(f8(f860(x97793,x97792),f860(f860(x97793,a845),x97792),x97791),f6(x97793,x97792)),f312(f7(x97793,x97791,x97792),x97794))),x97795)),x97796),f312(f312(f6(x97793,x97792),f312(f312(f7(x97793,f860(x97791,a845),x97792),f312(f312(f8(f860(x97791,x97792),f860(f860(x97791,a845),x97792),x97793),f6(x97791,x97792)),x97794)),x97796)),x97795))
% 173.53/173.42 [9485]~P22(f312(f312(f314(x94851),x94855),x94854))+E(f312(f312(f312(f81(x94851,f856(x94852)),f183(x94851,x94852,x94853,f312(f312(f21(f860(x94851,a845)),x94854),f312(f312(f289(x94851),x94855),f189(f860(x94851,a845)))))),x94855),x94856),f183(x94851,x94852,f312(f312(f312(f81(x94851,f856(x94852)),x94853),x94855),x94856),x94854))
% 173.53/173.42 [10070]~P22(f312(f312(f314(f859(x100701,x100702)),f312(f312(f239(x100701,x100702),x100705),x100706)),f312(f312(f124(f860(f859(x100701,x100702),a845)),x100703),x100704)))+P22(f312(f312(f312(f312(f124(f860(x100701,f860(x100702,a845))),f312(f312(f7(x100701,f860(f859(x100701,x100702),a845),f860(x100702,a845)),f312(f312(f8(f860(x100702,f860(f860(f859(x100701,x100702),a845),a845)),f860(f860(f859(x100701,x100702),a845),f860(x100702,a845)),x100701),f7(x100702,f860(f859(x100701,x100702),a845),a845)),f312(f312(f8(f860(x100702,f859(x100701,x100702)),f860(x100702,f860(f860(f859(x100701,x100702),a845),a845)),x100701),f312(f8(f859(x100701,x100702),f860(f860(f859(x100701,x100702),a845),a845),x100702),f314(f859(x100701,x100702)))),f239(x100701,x100702)))),x100703)),f312(f312(f7(x100701,f860(f859(x100701,x100702),a845),f860(x100702,a845)),f312(f312(f8(f860(x100702,f860(f860(f859(x100701,x100702),a845),a845)),f860(f860(f859(x100701,x100702),a845),f860(x100702,a845)),x100701),f7(x100702,f860(f859(x100701,x100702),a845),a845)),f312(f312(f8(f860(x100702,f859(x100701,x100702)),f860(x100702,f860(f860(f859(x100701,x100702),a845),a845)),x100701),f312(f8(f859(x100701,x100702),f860(f860(f859(x100701,x100702),a845),a845),x100702),f314(f859(x100701,x100702)))),f239(x100701,x100702)))),x100704)),x100705),x100706))
% 173.53/173.42 [10071]~P22(f312(f312(f314(f859(x100711,x100712)),f312(f312(f239(x100711,x100712),x100715),x100716)),f312(f312(f115(f860(f859(x100711,x100712),a845)),x100713),x100714)))+P22(f312(f312(f312(f312(f115(f860(x100711,f860(x100712,a845))),f312(f312(f7(x100711,f860(f859(x100711,x100712),a845),f860(x100712,a845)),f312(f312(f8(f860(x100712,f860(f860(f859(x100711,x100712),a845),a845)),f860(f860(f859(x100711,x100712),a845),f860(x100712,a845)),x100711),f7(x100712,f860(f859(x100711,x100712),a845),a845)),f312(f312(f8(f860(x100712,f859(x100711,x100712)),f860(x100712,f860(f860(f859(x100711,x100712),a845),a845)),x100711),f312(f8(f859(x100711,x100712),f860(f860(f859(x100711,x100712),a845),a845),x100712),f314(f859(x100711,x100712)))),f239(x100711,x100712)))),x100713)),f312(f312(f7(x100711,f860(f859(x100711,x100712),a845),f860(x100712,a845)),f312(f312(f8(f860(x100712,f860(f860(f859(x100711,x100712),a845),a845)),f860(f860(f859(x100711,x100712),a845),f860(x100712,a845)),x100711),f7(x100712,f860(f859(x100711,x100712),a845),a845)),f312(f312(f8(f860(x100712,f859(x100711,x100712)),f860(x100712,f860(f860(f859(x100711,x100712),a845),a845)),x100711),f312(f8(f859(x100711,x100712),f860(f860(f859(x100711,x100712),a845),a845),x100712),f314(f859(x100711,x100712)))),f239(x100711,x100712)))),x100714)),x100715),x100716))
% 173.53/173.42 [10077]P22(f312(f312(f314(f859(x100771,x100772)),f312(f312(f239(x100771,x100772),x100773),x100774)),f312(f312(f124(f860(f859(x100771,x100772),a845)),x100775),x100776)))+~P22(f312(f312(f312(f312(f124(f860(x100771,f860(x100772,a845))),f312(f312(f7(x100771,f860(f859(x100771,x100772),a845),f860(x100772,a845)),f312(f312(f8(f860(x100772,f860(f860(f859(x100771,x100772),a845),a845)),f860(f860(f859(x100771,x100772),a845),f860(x100772,a845)),x100771),f7(x100772,f860(f859(x100771,x100772),a845),a845)),f312(f312(f8(f860(x100772,f859(x100771,x100772)),f860(x100772,f860(f860(f859(x100771,x100772),a845),a845)),x100771),f312(f8(f859(x100771,x100772),f860(f860(f859(x100771,x100772),a845),a845),x100772),f314(f859(x100771,x100772)))),f239(x100771,x100772)))),x100775)),f312(f312(f7(x100771,f860(f859(x100771,x100772),a845),f860(x100772,a845)),f312(f312(f8(f860(x100772,f860(f860(f859(x100771,x100772),a845),a845)),f860(f860(f859(x100771,x100772),a845),f860(x100772,a845)),x100771),f7(x100772,f860(f859(x100771,x100772),a845),a845)),f312(f312(f8(f860(x100772,f859(x100771,x100772)),f860(x100772,f860(f860(f859(x100771,x100772),a845),a845)),x100771),f312(f8(f859(x100771,x100772),f860(f860(f859(x100771,x100772),a845),a845),x100772),f314(f859(x100771,x100772)))),f239(x100771,x100772)))),x100776)),x100773),x100774))
% 173.53/173.42 [10078]P22(f312(f312(f314(f859(x100781,x100782)),f312(f312(f239(x100781,x100782),x100783),x100784)),f312(f312(f115(f860(f859(x100781,x100782),a845)),x100785),x100786)))+~P22(f312(f312(f312(f312(f115(f860(x100781,f860(x100782,a845))),f312(f312(f7(x100781,f860(f859(x100781,x100782),a845),f860(x100782,a845)),f312(f312(f8(f860(x100782,f860(f860(f859(x100781,x100782),a845),a845)),f860(f860(f859(x100781,x100782),a845),f860(x100782,a845)),x100781),f7(x100782,f860(f859(x100781,x100782),a845),a845)),f312(f312(f8(f860(x100782,f859(x100781,x100782)),f860(x100782,f860(f860(f859(x100781,x100782),a845),a845)),x100781),f312(f8(f859(x100781,x100782),f860(f860(f859(x100781,x100782),a845),a845),x100782),f314(f859(x100781,x100782)))),f239(x100781,x100782)))),x100785)),f312(f312(f7(x100781,f860(f859(x100781,x100782),a845),f860(x100782,a845)),f312(f312(f8(f860(x100782,f860(f860(f859(x100781,x100782),a845),a845)),f860(f860(f859(x100781,x100782),a845),f860(x100782,a845)),x100781),f7(x100782,f860(f859(x100781,x100782),a845),a845)),f312(f312(f8(f860(x100782,f859(x100781,x100782)),f860(x100782,f860(f860(f859(x100781,x100782),a845),a845)),x100781),f312(f8(f859(x100781,x100782),f860(f860(f859(x100781,x100782),a845),a845),x100782),f314(f859(x100781,x100782)))),f239(x100781,x100782)))),x100786)),x100783),x100784))
% 173.53/173.42 [10064]~P22(f312(f312(f314(f859(x100642,x100643)),f312(f312(f239(x100642,x100643),x100645),x100646)),f312(f312(f50(x100641,f860(f859(x100642,x100643),a845)),f235(f860(x100641,a845))),x100644)))+P22(f312(f312(f312(f312(f50(x100641,f860(x100642,f860(x100643,a845))),f235(f860(x100641,a845))),f312(f312(f8(f860(f859(x100642,x100643),a845),f860(x100642,f860(x100643,a845)),x100641),f312(f7(x100642,f860(f859(x100642,x100643),a845),f860(x100643,a845)),f312(f312(f8(f860(x100643,f860(f860(f859(x100642,x100643),a845),a845)),f860(f860(f859(x100642,x100643),a845),f860(x100643,a845)),x100642),f7(x100643,f860(f859(x100642,x100643),a845),a845)),f312(f312(f8(f860(x100643,f859(x100642,x100643)),f860(x100643,f860(f860(f859(x100642,x100643),a845),a845)),x100642),f312(f8(f859(x100642,x100643),f860(f860(f859(x100642,x100643),a845),a845),x100643),f314(f859(x100642,x100643)))),f239(x100642,x100643))))),x100644)),x100645),x100646))
% 173.53/173.42 [10065]~P22(f312(f312(f314(f859(x100652,x100653)),f312(f312(f239(x100652,x100653),x100655),x100656)),f312(f312(f51(x100651,f860(f859(x100652,x100653),a845)),f235(f860(x100651,a845))),x100654)))+P22(f312(f312(f312(f312(f51(x100651,f860(x100652,f860(x100653,a845))),f235(f860(x100651,a845))),f312(f312(f8(f860(f859(x100652,x100653),a845),f860(x100652,f860(x100653,a845)),x100651),f312(f7(x100652,f860(f859(x100652,x100653),a845),f860(x100653,a845)),f312(f312(f8(f860(x100653,f860(f860(f859(x100652,x100653),a845),a845)),f860(f860(f859(x100652,x100653),a845),f860(x100653,a845)),x100652),f7(x100653,f860(f859(x100652,x100653),a845),a845)),f312(f312(f8(f860(x100653,f859(x100652,x100653)),f860(x100653,f860(f860(f859(x100652,x100653),a845),a845)),x100652),f312(f8(f859(x100652,x100653),f860(f860(f859(x100652,x100653),a845),a845),x100653),f314(f859(x100652,x100653)))),f239(x100652,x100653))))),x100654)),x100655),x100656))
% 173.53/173.42 [10074]P22(f312(f312(f314(f859(x100741,x100742)),f312(f312(f239(x100741,x100742),x100743),x100744)),f312(f312(f50(x100745,f860(f859(x100741,x100742),a845)),f235(f860(x100745,a845))),x100746)))+~P22(f312(f312(f312(f312(f50(x100745,f860(x100741,f860(x100742,a845))),f235(f860(x100745,a845))),f312(f312(f8(f860(f859(x100741,x100742),a845),f860(x100741,f860(x100742,a845)),x100745),f312(f7(x100741,f860(f859(x100741,x100742),a845),f860(x100742,a845)),f312(f312(f8(f860(x100742,f860(f860(f859(x100741,x100742),a845),a845)),f860(f860(f859(x100741,x100742),a845),f860(x100742,a845)),x100741),f7(x100742,f860(f859(x100741,x100742),a845),a845)),f312(f312(f8(f860(x100742,f859(x100741,x100742)),f860(x100742,f860(f860(f859(x100741,x100742),a845),a845)),x100741),f312(f8(f859(x100741,x100742),f860(f860(f859(x100741,x100742),a845),a845),x100742),f314(f859(x100741,x100742)))),f239(x100741,x100742))))),x100746)),x100743),x100744))
% 173.53/173.42 [10075]P22(f312(f312(f314(f859(x100751,x100752)),f312(f312(f239(x100751,x100752),x100753),x100754)),f312(f312(f51(x100755,f860(f859(x100751,x100752),a845)),f235(f860(x100755,a845))),x100756)))+~P22(f312(f312(f312(f312(f51(x100755,f860(x100751,f860(x100752,a845))),f235(f860(x100755,a845))),f312(f312(f8(f860(f859(x100751,x100752),a845),f860(x100751,f860(x100752,a845)),x100755),f312(f7(x100751,f860(f859(x100751,x100752),a845),f860(x100752,a845)),f312(f312(f8(f860(x100752,f860(f860(f859(x100751,x100752),a845),a845)),f860(f860(f859(x100751,x100752),a845),f860(x100752,a845)),x100751),f7(x100752,f860(f859(x100751,x100752),a845),a845)),f312(f312(f8(f860(x100752,f859(x100751,x100752)),f860(x100752,f860(f860(f859(x100751,x100752),a845),a845)),x100751),f312(f8(f859(x100751,x100752),f860(f860(f859(x100751,x100752),a845),a845),x100752),f314(f859(x100751,x100752)))),f239(x100751,x100752))))),x100756)),x100753),x100754))
% 173.53/173.42 [9126]E(x91261,x91262)+~E(f299(x91263,x91264,x91265,x91266,x91261),f299(x91263,x91264,x91265,x91267,x91262))
% 173.53/173.42 [9127]E(x91271,x91272)+~E(f299(x91273,x91274,x91275,x91271,x91276),f299(x91273,x91274,x91275,x91272,x91277))
% 173.53/173.42 [7310]E(f312(x73101,f312(x73102,x73103)),f312(x73104,x73103))+~E(f312(f82(x73105,x73106,x73107,x73101),x73102),x73104)
% 173.53/173.42 [9864]~P53(x98645,x98646,x98647,x98641,x98644,x98642,x98643)+P22(f312(f312(x98641,x98642),f569(x98643,x98642,x98644,x98641)))
% 173.53/173.42 [9887]~E(f312(f221(f856(x98877),x98871,f192(x98877),x98875),f312(x98874,x98873)),f312(f219(x98877),x98872))+E(f312(f219(x98871),f595(x98872,x98873,x98874,x98875,x98876,x98877,x98871)),f312(x98874,x98873))
% 173.53/173.42 [9888]~E(f312(f221(f856(x98886),x98887,f192(x98886),x98881),f312(x98884,x98883)),f312(f219(x98886),x98882))+E(f312(x98881,f595(x98882,x98883,x98884,x98881,x98885,x98886,x98887)),f312(f219(x98886),x98882))
% 173.53/173.42 [5912]~E(f312(f312(f150(x59121,x59125),x59126),x59122),f312(f312(f150(x59123,x59125),x59127),x59124))+E(f312(f190(f853(x59121)),x59122),f312(f190(f853(x59123)),x59124))
% 173.53/173.42 [7385]E(x73851,x73852)+~E(f312(f312(f312(f81(x73853,f856(x73854)),x73855),x73856),f312(f219(x73854),x73851)),f312(f312(f312(f81(x73853,f856(x73854)),x73857),x73856),f312(f219(x73854),x73852)))
% 173.53/173.42 [8354]E(f312(x83541,f312(x83542,x83543)),f312(x83544,x83543))+~E(f312(f82(x83545,x83546,x83547,x83541),x83542),f312(f82(x83546,x83546,x83547,f39(x83546)),x83544))
% 173.53/173.42 [8685]~P39(x86854,x86855,x86851,f312(f312(f147(x86854),x86852),x86856),f312(f312(f147(x86855),x86853),x86857))+P22(f312(f312(x86851,x86852),x86853))
% 173.53/173.42 [9061]P39(x90611,x90612,x90613,x90614,x90615)+~P39(x90611,x90612,x90613,f312(f312(f147(x90611),x90616),x90614),f312(f312(f147(x90612),x90617),x90615))
% 173.53/173.42 [9869]~P53(x98695,x98696,x98697,x98694,x98691,x98693,x98692)+P22(f312(f312(x98691,f569(x98692,x98693,x98691,x98694)),x98692))
% 173.53/173.42 [5954]E(x59541,x59542)+~E(f312(f312(f312(f100(x59543),x59544),x59545),x59541),f312(f312(f312(f100(x59543),x59546),x59547),x59542))
% 173.53/173.42 [5955]E(x59551,x59552)+~E(f312(f312(f312(f100(x59553),x59554),x59551),x59555),f312(f312(f312(f100(x59553),x59556),x59552),x59557))
% 173.53/173.42 [5956]E(x59561,x59562)+~E(f312(f312(f312(f100(x59563),x59561),x59564),x59565),f312(f312(f312(f100(x59563),x59562),x59566),x59567))
% 173.53/173.42 [8799]~P15(x87996,x87991,x87993,x87997)+E(f312(f82(x87991,x87991,x87992,f312(x87993,x87994)),f312(f82(x87991,x87991,x87992,f312(x87993,x87994)),x87995)),f312(f82(x87991,x87991,x87992,f312(x87993,x87994)),x87995))
% 173.53/173.42 [9169]~P39(x91693,x91692,x91694,f312(f312(f150(x91691,x91693),x91695),x91696),x91697)+P39(x91691,x91692,f312(f312(f8(x91693,f860(x91692,a845),x91691),x91694),x91695),x91696,x91697)
% 173.53/173.42 [9193]P39(x91931,x91932,x91933,f312(f312(f150(x91934,x91931),x91935),x91936),x91937)+~P39(x91934,x91932,f312(f312(f8(x91931,f860(x91932,a845),x91934),x91933),x91935),x91936,x91937)
% 173.53/173.42 [9595]E(f182(x95951,x95952,f312(f312(f312(f81(x95951,f856(x95952)),x95953),x95954),f312(f219(x95952),x95955)),x95956,x95957),f312(f312(f312(f81(x95951,f856(x95952)),f182(x95951,x95952,x95953,x95956,x95957)),x95954),f312(f219(x95952),x95955)))+P22(f312(f312(f314(x95951),x95954),f312(f168(x95951),x95956)))
% 173.53/173.42 [8798]~P22(f312(f312(f314(x87981),x87982),f312(f312(x87985,x87986),x87987)))+P22(f312(f312(f314(x87981),x87982),f312(f312(f249(x87983,x87984,f860(x87981,a845)),x87985),f312(f312(f239(x87983,x87984),x87986),x87987))))
% 173.53/173.42 [9087]P22(f312(f312(f312(x90871,x90872),x90873),x90874))+~P22(f312(f312(f312(f249(x90875,x90876,f860(x90877,a845)),x90871),f312(f312(f239(x90875,x90876),x90872),x90873)),x90874))
% 173.53/173.42 [9231]P22(f312(f312(f314(x92311),f312(f312(x92312,x92313),x92314)),f312(f290(f859(x92315,x92316),x92311,f312(f249(x92315,x92316,x92311),x92312)),x92317)))+~P22(f312(f312(f314(f859(x92315,x92316)),f312(f312(f239(x92315,x92316),x92313),x92314)),x92317))
% 173.53/173.42 [9557]P22(f312(f312(f314(f859(f853(x95571),f853(x95571))),f312(f312(f239(f853(x95571),f853(x95571)),f312(f312(f129(x95571),x95572),f312(f312(f147(x95571),x95573),x95574))),f312(f312(f129(x95571),x95572),f312(f312(f147(x95571),x95575),x95576)))),f143(x95571,x95577)))+~P22(f312(f312(f314(f859(x95571,x95571)),f312(f312(f239(x95571,x95571),x95573),x95575)),x95577))
% 173.53/173.42 [9618]~P39(x96181,x96183,x96184,x96186,f312(f312(f150(x96182,x96183),x96185),x96187))+P39(x96181,x96182,f312(f312(f7(x96181,f860(x96182,x96183),f860(x96182,a845)),f312(f312(f8(f860(x96183,a845),f860(f860(x96182,x96183),f860(x96182,a845)),x96181),f8(x96183,a845,x96182)),x96184)),x96185),x96186,x96187)
% 173.53/173.42 [9698]P39(x96981,x96982,x96983,x96984,f312(f312(f150(x96985,x96982),x96986),x96987))+~P39(x96981,x96985,f312(f312(f7(x96981,f860(x96985,x96982),f860(x96985,a845)),f312(f312(f8(f860(x96982,a845),f860(f860(x96985,x96982),f860(x96985,a845)),x96981),f8(x96982,a845,x96985)),x96983)),x96986),x96984,x96987)
% 173.53/173.42 [9987]P53(x99871,x99872,x99873,f312(f312(f7(x99871,f860(f859(x99871,x99872),a845),f860(x99872,a845)),f312(f312(f8(f860(x99872,f860(f860(f859(x99871,x99872),a845),a845)),f860(f860(f859(x99871,x99872),a845),f860(x99872,a845)),x99871),f7(x99872,f860(f859(x99871,x99872),a845),a845)),f312(f312(f8(f860(x99872,f859(x99871,x99872)),f860(x99872,f860(f860(f859(x99871,x99872),a845),a845)),x99871),f312(f8(f859(x99871,x99872),f860(f860(f859(x99871,x99872),a845),a845),x99872),f314(f859(x99871,x99872)))),f239(x99871,x99872)))),x99874),f312(f312(f7(x99872,f860(f859(x99872,x99873),a845),f860(x99873,a845)),f312(f312(f8(f860(x99873,f860(f860(f859(x99872,x99873),a845),a845)),f860(f860(f859(x99872,x99873),a845),f860(x99873,a845)),x99872),f7(x99873,f860(f859(x99872,x99873),a845),a845)),f312(f312(f8(f860(x99873,f859(x99872,x99873)),f860(x99873,f860(f860(f859(x99872,x99873),a845),a845)),x99872),f312(f8(f859(x99872,x99873),f860(f860(f859(x99872,x99873),a845),a845),x99873),f314(f859(x99872,x99873)))),f239(x99872,x99873)))),x99875),x99876,x99877)+~P22(f312(f312(f314(f859(x99871,x99873)),f312(f312(f239(x99871,x99873),x99876),x99877)),f312(f312(f267(x99871,x99872,x99873),x99874),x99875)))
% 173.53/173.42 [10018]~P53(x100181,x100185,x100182,f312(f312(f7(x100181,f860(f859(x100181,x100185),a845),f860(x100185,a845)),f312(f312(f8(f860(x100185,f860(f860(f859(x100181,x100185),a845),a845)),f860(f860(f859(x100181,x100185),a845),f860(x100185,a845)),x100181),f7(x100185,f860(f859(x100181,x100185),a845),a845)),f312(f312(f8(f860(x100185,f859(x100181,x100185)),f860(x100185,f860(f860(f859(x100181,x100185),a845),a845)),x100181),f312(f8(f859(x100181,x100185),f860(f860(f859(x100181,x100185),a845),a845),x100185),f314(f859(x100181,x100185)))),f239(x100181,x100185)))),x100186),f312(f312(f7(x100185,f860(f859(x100185,x100182),a845),f860(x100182,a845)),f312(f312(f8(f860(x100182,f860(f860(f859(x100185,x100182),a845),a845)),f860(f860(f859(x100185,x100182),a845),f860(x100182,a845)),x100185),f7(x100182,f860(f859(x100185,x100182),a845),a845)),f312(f312(f8(f860(x100182,f859(x100185,x100182)),f860(x100182,f860(f860(f859(x100185,x100182),a845),a845)),x100185),f312(f8(f859(x100185,x100182),f860(f860(f859(x100185,x100182),a845),a845),x100182),f314(f859(x100185,x100182)))),f239(x100185,x100182)))),x100187),x100183,x100184)+P22(f312(f312(f314(f859(x100181,x100182)),f312(f312(f239(x100181,x100182),x100183),x100184)),f312(f312(f267(x100181,x100185,x100182),x100186),x100187)))
% 173.53/173.42 [9079]E(x90791,x90792)+E(f312(f312(f312(f81(x90793,x90794),f312(f312(f312(f81(x90793,x90794),x90795),x90791),x90796)),x90792),x90797),f312(f312(f312(f81(x90793,x90794),f312(f312(f312(f81(x90793,x90794),x90795),x90792),x90797)),x90791),x90796))
% 173.53/173.42 [9324]E(f182(x93241,x93242,f312(f312(f312(f81(x93241,f856(x93242)),x93243),x93244),f312(f219(x93242),x93245)),x93246,x93247),f182(x93241,x93242,x93243,x93246,x93247))+~P22(f312(f312(f314(x93241),x93244),f312(f168(x93241),f312(f312(f169(x93241),f312(f190(f853(x93242)),x93247)),x93246))))
% 173.53/173.42 [9630]E(f182(x96301,x96302,f312(f312(f312(f81(x96301,f856(x96302)),x96303),x96304),f312(f219(x96302),x96305)),x96306,x96307),f312(f312(f312(f81(x96301,f856(x96302)),f182(x96301,x96302,x96303,x96306,x96307)),x96304),f312(f219(x96302),x96305)))+P22(f312(f312(f314(x96301),x96304),f312(f168(x96301),f312(f312(f169(x96301),f312(f190(f853(x96302)),x96307)),x96306))))
% 173.53/173.42 [9999]P22(f312(f312(f314(x99991),f641(x99992,x99993,x99994,x99995,x99996,x99997,x99991)),x99995))+P22(f312(f312(f312(f312(f51(x99991,f860(x99997,f860(x99996,a845))),x99995),x99994),x99993),x99992))
% 173.53/173.42 [10001]P22(f312(f312(f314(x100011),f424(x100012,x100013,x100014,x100015,x100016,x100017,x100011)),x100015))+~P22(f312(f312(f312(f312(f50(x100011,f860(x100017,f860(x100016,a845))),x100015),x100014),x100013),x100012))
% 173.53/173.42 [10027]P22(f312(f312(f312(x100271,f424(x100272,x100273,x100271,x100274,x100275,x100276,x100277)),x100273),x100272))+~P22(f312(f312(f312(f312(f50(x100277,f860(x100276,f860(x100275,a845))),x100274),x100271),x100273),x100272))
% 173.53/173.42 [10044]~P22(f312(f312(f312(x100445,f641(x100447,x100446,x100445,x100444,x100443,x100442,x100441)),x100446),x100447))+P22(f312(f312(f312(f312(f51(x100441,f860(x100442,f860(x100443,a845))),x100444),x100445),x100446),x100447))
% 173.53/173.42 [10011]~P135(x100112)+E(f312(f312(f6(x100111,x100112),f312(f312(f7(x100111,f860(x100113,a845),x100112),f312(f312(f8(f860(x100113,x100112),f860(f860(x100113,a845),x100112),x100111),f6(x100113,x100112)),f312(f312(f7(x100111,f860(x100113,x100112),f860(x100113,x100112)),f312(f312(f8(f860(x100112,x100112),f860(f860(x100113,x100112),f860(x100113,x100112)),x100111),f8(x100112,x100112,x100113)),f312(f312(f8(x100112,f860(x100112,x100112),x100111),f90(x100112)),x100114))),x100115))),x100116)),x100117),f312(f312(f90(x100112),f312(f312(f6(x100111,x100112),x100114),x100117)),f312(f312(f6(x100113,x100112),x100115),x100116)))
% 173.53/173.42 [9121]~P14(x91217,x91211,x91213,x91218)+E(f312(f82(x91211,x91211,x91212,f312(x91213,x91214)),f312(f82(x91211,x91211,x91212,f312(x91213,x91215)),x91216)),f312(f82(x91211,x91211,x91212,f312(x91213,x91215)),f312(f82(x91211,x91211,x91212,f312(x91213,x91214)),x91216)))
% 173.53/173.42 [10059]P18(x100591,x100592,f312(f312(f289(f851(x100591)),f312(f312(f312(f100(x100591),f312(f312(f8(f860(a847,a845),f860(a847,a845),x100591),f312(f18(a847,a845,a845),f312(f312(f8(a845,f860(a845,a845),a847),a310),f312(a309,x100593)))),f312(f312(f7(x100591,f860(a847,a847),f860(a847,a845)),f312(f312(f8(f860(a847,a845),f860(f860(a847,a847),f860(a847,a845)),x100591),f8(a847,a845,a847)),x100594)),f312(f312(f18(a847,a852,a847),f312(f312(f7(a847,a850,f860(a852,a847)),a201),f40(x100595))),x100596)))),f32(x100595,x100596,x100597)),x100598)),f189(f860(f851(x100591),a845))))+~P18(x100591,x100592,f312(f312(f289(f851(x100591)),f312(f312(f312(f100(x100591),x100594),x100597),f312(f312(f7(x100591,f860(a847,a847),f860(a847,a845)),f312(f312(f8(f860(a847,a845),f860(f860(a847,a847),f860(a847,a845)),x100591),f8(a847,a845,a847)),x100598)),f312(f312(f7(a847,a852,a847),f312(f312(f7(a847,a850,f860(a852,a847)),a201),f40(x100595))),f312(f312(a202,x100593),x100595))))),f189(f860(f851(x100591),a845))))
% 173.53/173.42 [10068]E(f312(f312(f239(x100681,x100682),f312(x100683,f534(x100684,x100685,x100683,x100686,x100687,x100688,x100682,x100681))),f312(x100685,f535(x100684,x100685,x100683,x100686,x100687,x100688,x100682,x100681))),x100688)+~P22(f312(f312(f314(f859(x100681,x100682)),x100688),f312(f290(f859(x100687,x100686),f859(x100681,x100682),f250(x100687,x100681,x100686,x100682,x100683,x100685)),x100684)))
% 173.53/173.42 [10083]P18(x100831,x100832,f312(f312(f289(f851(x100831)),f312(f312(f312(f100(x100831),f312(f312(f8(f860(a847,a845),f860(a847,a845),x100831),f312(f18(a847,a845,a845),f312(f312(f8(a845,f860(a845,a845),a847),a310),f312(a309,x100833)))),f312(f312(f7(x100831,f860(a847,a847),f860(a847,a845)),f312(f312(f8(f860(a847,a845),f860(f860(a847,a847),f860(a847,a845)),x100831),f8(a847,a845,a847)),x100834)),f312(f312(f18(a847,a852,a847),f312(f312(f7(a847,a850,f860(a852,a847)),f312(f312(f8(a847,f860(a850,f860(a852,a847)),a847),a201),f312(f312(f7(a847,f860(a849,a852),a847),a203),a204))),f40(a26))),x100835)))),f31(x100836,x100837,x100835)),x100838)),f189(f860(f851(x100831),a845))))+~P18(x100831,x100832,f312(f312(f289(f851(x100831)),f312(f312(f312(f100(x100831),x100834),f312(a27,x100837)),f312(f312(f7(x100831,f860(a847,a847),f860(a847,a845)),f312(f312(f8(f860(a847,a845),f860(f860(a847,a847),f860(a847,a845)),x100831),f8(a847,a845,a847)),x100838)),f312(f312(f18(a847,a852,a847),f312(f312(f7(a847,a850,f860(a852,a847)),f312(f312(f8(a847,f860(a850,f860(a852,a847)),a847),a201),f312(f312(f7(a847,f860(a849,a852),a847),a203),f312(a202,x100833)))),x100836)),f312(f312(f7(a847,a849,a852),a202),a25))))),f189(f860(f851(x100831),a845))))
% 173.53/173.42 [10084]~P22(f312(f312(f314(f859(x100848,x100847)),x100846),f312(f290(f859(x100841,x100842),f859(x100848,x100847),f250(x100841,x100848,x100842,x100847,x100845,x100844)),x100843)))+P22(f312(f312(f314(f859(x100841,x100842)),f312(f312(f239(x100841,x100842),f534(x100843,x100844,x100845,x100842,x100841,x100846,x100847,x100848)),f535(x100843,x100844,x100845,x100842,x100841,x100846,x100847,x100848))),x100843))
% 173.53/173.42 [9547]P22(f312(f312(f314(f859(f859(x95471,x95472),f859(x95471,x95472))),f312(f312(f239(f859(x95471,x95472),f859(x95471,x95472)),f312(f312(f239(x95471,x95472),x95473),x95474)),f312(f312(f239(x95471,x95472),x95475),x95476))),f304(x95471,x95472,x95477,x95478)))+~P22(f312(f312(f314(f859(x95471,x95471)),f312(f312(f239(x95471,x95471),x95473),x95475)),x95477))
% 173.53/173.42 [10057]E(f312(f138(x100571,x100572,f312(f7(x100572,x100571,x100571),x100573),f312(x100574,x100575)),x100576),f312(x100574,f312(f138(x100577,x100572,f312(f7(x100572,x100577,x100577),x100578),x100575),x100576)))+P22(f312(f312(f314(x100572),f708(x100575,x100578,x100574,x100573,x100577,x100571,x100576,x100572)),f312(f168(x100572),x100576)))
% 173.53/173.42 [10076]~E(f312(f82(x100761,x100761,x100767,f312(x100763,f708(x100765,x100768,x100764,x100763,x100767,x100761,x100766,x100762))),x100764),f312(f82(x100767,x100761,x100767,x100764),f312(x100768,f708(x100765,x100768,x100764,x100763,x100767,x100761,x100766,x100762))))+E(f312(f138(x100761,x100762,f312(f7(x100762,x100761,x100761),x100763),f312(x100764,x100765)),x100766),f312(x100764,f312(f138(x100767,x100762,f312(f7(x100762,x100767,x100767),x100768),x100765),x100766)))
% 173.53/173.42 [8360]E(f312(x83601,f312(x83602,x83603)),f312(x83604,f312(x83605,x83603)))+~E(f312(f82(x83606,x83607,x83608,x83601),x83602),f312(f82(x83609,x83607,x83608,x83604),x83605))
% 173.53/173.42 [9938]P22(f312(f312(f314(f859(x99381,x99382)),f312(f312(f239(x99381,x99382),f312(x99383,x99384)),f312(x99385,x99386))),f312(f290(f859(x99387,x99388),f859(x99381,x99382),f250(x99387,x99381,x99388,x99382,x99383,x99385)),x99389)))+~P22(f312(f312(f314(f859(x99387,x99388)),f312(f312(f239(x99387,x99388),x99384),x99386)),x99389))
% 173.53/173.42 [8632]~E(f312(x86324,f312(x86325,x86326)),f312(x86329,f312(x863210,x863211)))+E(f312(f312(f82(x86321,x86322,x86323,x86324),x86325),x86326),f312(f312(f82(x86327,x86322,x86328,x86329),x863210),x863211))
% 173.53/173.42 [4520]~P99(x45201)+~P103(x45201)+E(f115(x45201),f225(x45201))
% 173.53/173.42 [4521]~P98(x45211)+~P103(x45211)+E(f124(x45211),f226(x45211))
% 173.53/173.42 [4768]~P112(x47681)+~P90(x47681)+E(f312(f84(x47681),f312(f117(x47681),a111)),f87(x47681))
% 173.53/173.42 [5041]E(x50411,f2(a1))+E(f91(a1,x50411),f312(f88(a1),f87(a1)))+P22(f312(f312(f228(a1),f2(a1)),x50411))
% 173.53/173.42 [5252]E(x52521,f2(a1))+E(f91(a1,x52521),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x52521))
% 173.53/173.42 [7201]~P43(x72011)+P22(f312(f70(a1),x72011))+~P22(f312(f70(a852),f312(f290(a1,a852,a118),x72011)))
% 173.53/173.42 [8466]~P4(a5000)+~P22(f312(f312(f314(f859(a848,a846)),x84661),f312(f168(f859(a848,a846)),a29)))+P22(f312(f312(f249(a848,a846,a845),f312(f16(f860(a846,a845),a848),a24)),x84661))
% 173.53/173.42 [9515]E(x95151,f189(f860(f859(a852,a852),a845)))+~P22(f312(f70(f859(a852,a852)),x95151))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f189(f860(f859(a852,a852),a845))),x95151)),a46))
% 173.53/173.42 [9676]E(x96761,f2(a852))+E(x96761,f312(a126,f2(a852)))+~P22(f312(f312(f228(a852),x96761),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.42 [9967]E(x99671,f2(a113))+E(f312(f312(f89(a1),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(a20,f312(f47(a113,x99671),f312(f117(a113),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))),f87(a1)),f312(a20,x99671))+E(f54(a113,x99671,f312(f117(a113),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f2(a113))
% 173.53/173.42 [9811]E(x98111,f2(a113))+~E(f54(a113,x98111,f312(f117(a113),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f2(a113))+E(f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(a20,f312(f47(a113,x98111),f312(f117(a113),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f312(a20,x98111))
% 173.53/173.42 [4595]~P57(x45951,x45952)+P46(x45951,x45952)+~P47(a845)
% 173.53/173.42 [4532]~P23(x45321)+P35(x45321,x45322)+~E(x45322,f2(x45321))
% 173.53/173.42 [4533]~P103(x45331)+P33(x45331,x45332)+~E(x45332,f127(x45331))
% 173.53/173.42 [4542]~P112(x45421)+~E(x45422,f2(x45421))+E(f91(x45421,x45422),f2(x45421))
% 173.53/173.42 [4543]~P85(x45431)+~E(x45432,f2(x45431))+E(f91(x45431,x45432),f2(x45431))
% 173.53/173.42 [4551]~P23(x45512)+~P35(x45512,x45511)+E(x45511,f2(x45512))
% 173.53/173.42 [4585]~P112(x45852)+~E(f91(x45852,x45851),f2(x45852))+E(x45851,f2(x45852))
% 173.53/173.42 [4603]~P32(x46032)+~P32(x46031)+P32(f196(x46031,x46032))
% 173.53/173.42 [4604]~P138(x46042)+~P138(x46041)+P138(f859(x46041,x46042))
% 173.53/173.42 [4605]~P62(x46052)+~P62(x46051)+P62(f860(x46051,x46052))
% 173.53/173.42 [4606]~P62(x46062)+~P62(x46061)+P62(f858(x46061,x46062))
% 173.53/173.42 [4607]~P62(x46072)+~P62(x46071)+P62(f859(x46071,x46072))
% 173.53/173.42 [4608]~P63(x46082)+~P63(x46081)+P63(f860(x46081,x46082))
% 173.53/173.42 [4609]~P63(x46092)+~P63(x46091)+P63(f858(x46091,x46092))
% 173.53/173.42 [4610]~P63(x46102)+~P63(x46101)+P63(f859(x46101,x46102))
% 173.53/173.42 [4611]~P63(x46111)+~P92(x46112)+P92(f860(x46111,x46112))
% 173.53/173.42 [4739]~P103(x47391)+~P33(x47391,x47392)+P33(x47391,f148(x47391,x47392))
% 173.53/173.42 [4971]~P32(x49712)+~P32(x49711)+P32(f54(a1,x49711,x49712))
% 173.53/173.42 [4553]~P70(x45531)+~E(x45532,f2(x45531))+E(f312(f88(x45531),x45532),x45532)
% 173.53/173.42 [4557]~P89(x45571)+~E(x45572,f2(a1))+E(f312(f116(x45571),x45572),f2(x45571))
% 173.53/173.42 [4558]~P111(x45581)+~E(x45582,f2(a1))+E(f312(f116(x45581),x45582),f2(x45581))
% 173.53/173.42 [4582]~P71(x45821)+~E(f2(x45821),x45822)+E(f312(f88(x45821),x45822),f2(x45821))
% 173.53/173.42 [4583]~P71(x45831)+~E(x45832,f2(x45831))+E(f312(f88(x45831),x45832),f2(x45831))
% 173.53/173.42 [4584]~P83(x45841)+~E(x45842,f2(x45841))+E(f312(f84(x45841),x45842),f2(x45841))
% 173.53/173.42 [4614]~P70(x46142)+E(x46141,f2(x46142))+~E(f312(f88(x46142),x46141),x46141)
% 173.53/173.42 [4622]E(x46221,f312(a118,x46222))+~E(x46221,f2(a852))+~E(x46222,f312(f114(a1),x46221))
% 173.53/173.42 [4623]E(f312(a118,x46231),x46232)+~E(x46232,f2(a852))+~E(x46231,f312(f114(a1),x46232))
% 173.53/173.42 [4627]~P89(x46272)+E(x46271,f2(a1))+~E(f312(f116(x46272),x46271),f2(x46272))
% 173.53/173.42 [4632]~P71(x46322)+E(x46321,f2(x46322))+~E(f312(f88(x46322),x46321),f2(x46322))
% 173.53/173.42 [4633]~P83(x46332)+E(x46331,f2(x46332))+~E(f312(f84(x46332),x46331),f2(x46332))
% 173.53/173.42 [4634]~P71(x46341)+E(f2(x46341),x46342)+~E(f312(f88(x46341),x46342),f2(x46341))
% 173.53/173.42 [4654]~P60(x46542)+E(x46541,f2(x46542))+E(f312(f47(x46542,x46541),x46541),f87(x46542))
% 173.53/173.42 [4773]~P4(a5000)+~E(f312(a30,x47732),f312(f219(a846),x47731))+P22(f312(a24,x47731))
% 173.53/173.42 [4814]~P103(x48141)+~P33(x48141,x48142)+P33(x48141,f312(f167(x48141),x48142))
% 173.53/173.42 [4840]~P22(x48402)+~P22(x48401)+P22(f312(f312(a310,x48401),x48402))
% 173.53/173.42 [4841]~P32(x48412)+~P32(x48411)+P32(f312(f47(a1,x48411),x48412))
% 173.53/173.42 [4873]~E(f87(a852),f2(a852))+E(f312(f53(x48731),x48732),f2(a852))+~P22(f312(f70(x48731),x48732))
% 173.53/173.42 [4908]~P109(x49081)+~P135(x49081)+E(f312(f312(f240(x49081),f2(x49081)),f312(a126,x49082)),f2(x49081))
% 173.53/173.42 [4940]~P103(x49401)+P33(x49401,f135(x49401,x49402))+~P22(f312(f70(x49401),x49402))
% 173.53/173.42 [4941]~P103(x49411)+P33(x49411,f687(x49412,x49411))+~P22(f312(f70(x49411),x49412))
% 173.53/173.42 [4961]~P103(x49611)+E(f312(f168(x49611),f135(x49611,x49612)),x49612)+~P22(f312(f70(x49611),x49612))
% 173.53/173.42 [4962]~P103(x49621)+E(f312(f168(x49621),f687(x49622,x49621)),x49622)+~P22(f312(f70(x49621),x49622))
% 173.53/173.42 [4991]P22(x49911)+P22(x49912)+~P22(f312(f312(a311,x49912),x49911))
% 173.53/173.42 [5003]E(x50031,f189(f860(x50032,a845)))+~E(f312(f53(x50032),x50031),f2(a852))+~P22(f312(f70(x50032),x50031))
% 173.53/173.42 [5008]P22(x50081)+~P22(x50082)+~P22(f312(f312(a315,x50082),x50081))
% 173.53/173.42 [5059]~P69(x50591)+E(f312(f84(x50591),x50592),x50592)+P22(f312(f312(f228(x50591),x50592),f2(x50591)))
% 173.53/173.42 [5060]~P31(x50602)+~P49(x50602,x50602,x50601)+E(f312(x50601,f110(x50602,x50601)),f110(x50602,x50601))
% 173.53/173.42 [5061]~P31(x50612)+~P49(x50612,x50612,x50611)+E(f312(x50611,f109(x50612,x50611)),f109(x50612,x50611))
% 173.53/173.42 [5132]~P63(x51322)+~P22(f312(f66(x51322),x51321))+P22(f312(x51321,f650(x51321,x51322)))
% 173.53/173.42 [5133]~P63(x51332)+~P22(f312(f66(x51332),x51331))+P22(f312(x51331,f668(x51331,x51332)))
% 173.53/173.42 [5160]~P22(f312(a24,x51602))+~P22(f312(a24,x51601))+P22(f312(a24,f36(x51601,x51602)))
% 173.53/173.42 [5168]E(x51681,f127(x51682))+P22(f312(f133(x51682),f128(x51682,x51681)))+~P22(f312(f133(x51682),x51681))
% 173.53/173.42 [5173]~P103(x51731)+~P22(f312(f70(x51731),x51732))+P22(f312(f133(x51731),f135(x51731,x51732)))
% 173.53/173.42 [5174]~P103(x51741)+~P22(f312(f70(x51741),x51742))+P22(f312(f133(x51741),f687(x51742,x51741)))
% 173.53/173.42 [5180]~P111(x51801)+E(f312(f114(x51801),f312(a118,x51802)),f312(f116(x51801),x51802))+P22(f312(f312(f228(a1),x51802),f2(a1)))
% 173.53/173.42 [5207]P2(x52072,x52071)+E(f312(x52071,f366(x52071)),f312(x52071,f385(x52071)))+P22(f312(f312(x52071,f366(x52071)),f385(x52071)))
% 173.53/173.42 [5220]E(f312(f114(a1),f327(x52201,x52202)),x52201)+P22(f312(x52202,f312(a118,x52201)))+~P22(f312(x52202,f2(a852)))
% 173.53/173.42 [5231]~P63(x52311)+~P22(f312(x52312,f651(x52312,x52311)))+P22(f312(f67(x52311),x52312))
% 173.53/173.42 [5232]~P63(x52321)+~P22(f312(x52322,f669(x52322,x52321)))+P22(f312(f67(x52321),x52322))
% 173.53/173.42 [5261]~P112(x52611)+~E(f91(x52611,x52612),f312(f88(x52611),f87(x52611)))+P22(f312(f312(f228(x52611),x52612),f2(x52611)))
% 173.53/173.42 [5333]~E(x53332,f2(a1))+E(f210(x53331,x53332),f312(f312(f239(a1,a1),f2(a1)),f87(a1)))+P22(f312(f312(f228(a1),x53332),f2(a1)))
% 173.53/173.42 [5334]~E(x53341,f2(a1))+E(f210(x53341,x53342),f312(f312(f239(a1,a1),f2(a1)),f87(a1)))+P22(f312(f312(f228(a1),x53342),f2(a1)))
% 173.53/173.42 [5387]E(f312(f114(a1),f327(x53871,x53872)),x53871)+P22(f312(x53872,f312(a118,x53871)))+P22(f312(f312(f228(a1),x53871),f2(a1)))
% 173.53/173.42 [5449]~P112(x54491)+E(f91(x54491,x54492),f312(f88(x54491),f87(x54491)))+~P22(f312(f312(f228(x54491),x54492),f2(x54491)))
% 173.53/173.42 [5450]~P83(x54501)+E(f312(f84(x54501),x54502),f312(f88(x54501),x54502))+~P22(f312(f312(f228(x54501),x54502),f2(x54501)))
% 173.53/173.42 [5451]~P83(x54511)+E(f312(f84(x54511),x54512),f312(f88(x54511),x54512))+~P22(f312(f312(f227(x54511),x54512),f2(x54511)))
% 173.53/173.42 [5452]~P69(x54521)+E(f312(f84(x54521),x54522),f312(f88(x54521),x54522))+~P22(f312(f312(f228(x54521),x54522),f2(x54521)))
% 173.53/173.42 [5554]~P22(f312(x55541,f327(x55542,x55541)))+P22(f312(x55541,f312(a118,x55542)))+~P22(f312(x55541,f2(a852)))
% 173.53/173.42 [5561]E(x55611,f2(a852))+E(f312(a126,f816(x55612,x55611)),x55611)+~P22(f312(f312(f228(a852),x55611),f312(a126,x55612)))
% 173.53/173.42 [5566]P2(x55661,x55662)+~E(f312(x55662,f366(x55662)),f312(x55662,f385(x55662)))+~P22(f312(f312(x55662,f366(x55662)),f385(x55662)))
% 173.53/173.42 [5585]~P103(x55851)+P33(x55851,x55852)+P22(f312(f312(f227(a852),f652(x55852,x55851)),f653(x55852,x55851)))
% 173.53/173.42 [5586]~P103(x55861)+P33(x55861,x55862)+P22(f312(f312(f227(a852),f655(x55862,x55861)),f665(x55862,x55861)))
% 173.53/173.42 [5669]~P83(x56691)+~E(x56692,f2(x56691))+P22(f312(f312(f227(x56691),f312(f84(x56691),x56692)),f2(x56691)))
% 173.53/173.42 [5738]~P63(x57382)+~P63(x57381)+E(f68(x57381,x57382,f64(x57381),f64(x57382)),f64(f859(x57381,x57382)))
% 173.53/173.42 [5743]~P22(f312(x57431,f327(x57432,x57431)))+P22(f312(x57431,f312(a118,x57432)))+P22(f312(f312(f228(a1),x57432),f2(a1)))
% 173.53/173.42 [5765]~P22(f312(x57651,f312(a118,x57652)))+P22(f312(x57651,f2(a852)))+~P22(f312(f312(f228(a1),x57652),f2(a1)))
% 173.53/173.42 [6100]~P112(x61001)+~P22(f312(f312(f228(x61001),x61002),f2(x61001)))+P22(f312(f312(f228(x61001),f91(x61001,x61002)),f2(x61001)))
% 173.53/173.42 [6216]~P112(x62161)+P22(f312(f312(f228(x62161),f312(f116(x62161),x62162)),f2(x62161)))+~P22(f312(f312(f228(a1),x62162),f2(a1)))
% 173.53/173.42 [6217]~P112(x62171)+P22(f312(f312(f227(x62171),f312(f116(x62171),x62172)),f2(x62171)))+~P22(f312(f312(f227(a1),x62172),f2(a1)))
% 173.53/173.42 [6221]~P83(x62212)+E(x62211,f2(x62212))+~P22(f312(f312(f227(x62212),f312(f84(x62212),x62211)),f2(x62212)))
% 173.53/173.42 [6299]~P111(x62991)+~P22(f312(f312(f314(x62991),x62992),f123(x62991)))+P22(f312(f312(f314(x62991),f312(f88(x62991),x62992)),f123(x62991)))
% 173.53/173.42 [6330]~P112(x63301)+~P22(f312(f312(f228(x63301),f91(x63301,x63302)),f2(x63301)))+P22(f312(f312(f228(x63301),x63302),f2(x63301)))
% 173.53/173.42 [6494]~P112(x64942)+~P22(f312(f312(f228(x64942),f312(f116(x64942),x64941)),f2(x64942)))+P22(f312(f312(f228(a1),x64941),f2(a1)))
% 173.53/173.42 [6495]~P112(x64952)+~P22(f312(f312(f227(x64952),f312(f116(x64952),x64951)),f2(x64952)))+P22(f312(f312(f227(a1),x64951),f2(a1)))
% 173.53/173.42 [6580]~P31(x65801)+~P49(x65801,x65801,x65802)+P22(f312(f312(f227(x65801),f312(x65802,f110(x65801,x65802))),f110(x65801,x65802)))
% 173.53/173.42 [6581]~P31(x65811)+~P49(x65811,x65811,x65812)+P22(f312(f312(f227(x65811),f312(x65812,f109(x65811,x65812))),f109(x65811,x65812)))
% 173.53/173.42 [6999]~P70(x69991)+~P22(f312(f312(f228(x69991),x69992),f2(x69991)))+P22(f312(f312(f228(x69991),f312(f312(f89(x69991),x69992),x69992)),f2(x69991)))
% 173.53/173.42 [7000]~P112(x70001)+~P22(f312(f312(f228(x70001),x70002),f2(x70001)))+P22(f312(f312(f228(x70001),f312(f312(f89(x70001),x70002),x70002)),f2(x70001)))
% 173.53/173.42 [7001]~P70(x70011)+~P22(f312(f312(f227(x70011),x70012),f2(x70011)))+P22(f312(f312(f227(x70011),f312(f312(f89(x70011),x70012),x70012)),f2(x70011)))
% 173.53/173.42 [7554]~P70(x75541)+~P22(f312(f312(f228(x75541),f312(f312(f89(x75541),x75542),x75542)),f2(x75541)))+P22(f312(f312(f228(x75541),x75542),f2(x75541)))
% 173.53/173.42 [7555]~P112(x75551)+~P22(f312(f312(f228(x75551),f312(f312(f89(x75551),x75552),x75552)),f2(x75551)))+P22(f312(f312(f228(x75551),x75552),f2(x75551)))
% 173.53/173.42 [7556]~P70(x75561)+~P22(f312(f312(f227(x75561),f312(f312(f89(x75561),x75562),x75562)),f2(x75561)))+P22(f312(f312(f227(x75561),x75562),f2(x75561)))
% 173.53/173.42 [4674]~E(x46742,f2(a852))+~E(x46741,f2(a852))+E(f312(f312(f89(a852),x46741),x46742),f2(a852))
% 173.53/173.42 [4675]~E(x46752,f87(a852))+~E(x46751,f87(a852))+E(f312(f312(f90(a852),x46751),x46752),f87(a852))
% 173.53/173.42 [4676]~E(x46762,f87(a1))+~E(x46761,f87(a1))+E(f312(f312(f90(a1),x46761),x46762),f87(a1))
% 173.53/173.42 [4727]~P114(x47272)+E(x47271,f2(x47272))+E(f312(f312(f268(x47272),x47271),x47271),f87(x47272))
% 173.53/173.42 [4728]~P115(x47282)+E(x47281,f2(x47282))+E(f312(f312(f268(x47282),x47281),x47281),f87(x47282))
% 173.53/173.42 [4744]~P70(x47441)+~E(x47442,f2(x47441))+E(f312(f312(f89(x47441),x47442),x47442),f2(x47441))
% 173.53/173.42 [4747]~P134(x47471)+~E(x47472,f87(x47471))+E(f312(f312(f90(x47471),x47472),x47472),f87(x47471))
% 173.53/173.42 [4748]~P115(x47481)+~E(x47482,f2(x47481))+E(f312(f312(f268(x47481),x47482),x47482),f2(x47481))
% 173.53/173.42 [4793]~E(x47932,f2(a852))+~E(x47931,f2(a852))+E(f312(f88(a1),f312(f114(a1),x47931)),f312(f114(a1),x47932))
% 173.53/173.42 [4811]E(x48111,f87(a852))+E(x48112,f2(a852))+~E(f312(f312(f90(a852),x48112),x48111),x48112)
% 173.53/173.42 [4821]E(x48211,f2(a852))+E(x48212,f2(a852))+~E(f312(f312(f90(a852),x48212),x48211),f2(a852))
% 173.53/173.42 [4850]~E(x48502,f2(a852))+~E(x48501,f312(a126,f2(a852)))+E(f312(f312(f89(a852),x48501),x48502),f312(a126,f2(a852)))
% 173.53/173.42 [4851]~E(x48511,f2(a852))+~E(x48512,f312(a126,f2(a852)))+E(f312(f312(f89(a852),x48511),x48512),f312(a126,f2(a852)))
% 173.53/173.42 [4856]E(x48561,f87(a1))+E(x48562,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48561),x48562),f87(a1))
% 173.53/173.42 [4857]E(x48571,f87(a1))+E(x48572,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48572),x48571),f87(a1))
% 173.53/173.42 [4858]E(x48581,f87(a1))+E(x48581,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48582),x48581),f87(a1))
% 173.53/173.42 [4860]E(x48601,f87(a1))+E(x48601,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48601),x48602),f87(a1))
% 173.53/173.42 [4878]~P70(x48782)+E(x48781,f2(x48782))+~E(f312(f312(f89(x48782),x48781),x48781),f2(x48782))
% 173.53/173.42 [4884]~E(x48841,f312(f117(a1),a111))+~E(x48842,f312(f117(a1),a111))+E(f312(f312(f90(a1),x48841),x48842),f87(a1))
% 173.53/173.42 [4897]E(x48971,f2(a852))+E(x48972,f2(a852))+~E(f312(f312(f89(a852),x48972),x48971),f312(a126,f2(a852)))
% 173.53/173.42 [4907]~P90(x49071)+~P64(x49071)+E(f312(f312(f268(x49071),x49072),f312(f117(x49071),a92)),f2(x49071))
% 173.53/173.42 [4913]~P134(x49131)+~E(x49132,f312(f88(x49131),f87(x49131)))+E(f312(f312(f90(x49131),x49132),x49132),f87(x49131))
% 173.53/173.42 [4916]~P32(x49162)+~P32(x49161)+P32(f312(f312(f89(a1),x49161),x49162))
% 173.53/173.42 [4917]~P32(x49172)+~P32(x49171)+P32(f312(f312(f90(a1),x49171),x49172))
% 173.53/173.42 [4938]~E(x49382,f312(a126,f2(a852)))+~E(x49381,f312(a126,f2(a852)))+E(f312(f312(f90(a852),x49381),x49382),f312(a126,f2(a852)))
% 173.53/173.42 [4952]E(x49521,f2(a852))+E(x49522,f312(a126,f2(a852)))+~E(f312(f312(f240(a852),x49522),x49521),f312(a126,f2(a852)))
% 173.53/173.42 [4953]E(x49531,f2(a852))+E(x49531,f312(a126,f2(a852)))+~E(f312(f312(f89(a852),x49532),x49531),f312(a126,f2(a852)))
% 173.53/173.42 [4954]E(x49541,f2(a852))+E(x49541,f312(a126,f2(a852)))+~E(f312(f312(f89(a852),x49541),x49542),f312(a126,f2(a852)))
% 173.53/173.42 [4963]~P90(x49631)+~P64(x49631)+E(f312(f312(f268(x49631),x49632),f312(f117(x49631),a111)),f312(f88(x49631),x49632))
% 173.53/173.42 [4983]E(x49831,f312(a118,x49832))+~E(x49831,f2(a852))+P22(f312(f312(f227(a1),f2(a1)),x49832))
% 173.53/173.42 [4984]E(f312(a118,x49841),x49842)+~E(x49842,f2(a852))+P22(f312(f312(f227(a1),f2(a1)),x49841))
% 173.53/173.42 [4999]E(x49991,f312(a126,f2(a852)))+E(x49992,f312(a126,f2(a852)))+~E(f312(f312(f89(a852),x49991),x49992),f312(a126,f2(a852)))
% 173.53/173.42 [5009]~E(x50091,f312(a118,x50092))+E(x50091,f2(a852))+P22(f312(f312(f227(a1),f2(a1)),x50092))
% 173.53/173.42 [5010]~E(f312(a118,x50102),x50101)+E(x50101,f2(a852))+P22(f312(f312(f227(a1),f2(a1)),x50102))
% 173.53/173.42 [5035]~P87(x50351)+E(f312(f72(x50351,f115(x50351)),x50352),f11(x50351,x50352))+~P22(f312(f70(x50351),x50352))
% 173.53/173.42 [5036]~P87(x50361)+E(f312(f72(x50361,f124(x50361)),x50362),f10(x50361,x50362))+~P22(f312(f70(x50361),x50362))
% 173.53/173.42 [5037]~P103(x50371)+E(f312(f72(x50371,f226(x50371)),x50372),f14(x50371,x50372))+~P22(f312(f70(x50371),x50372))
% 173.53/173.42 [5038]~P103(x50381)+E(f312(f72(x50381,f225(x50381)),x50382),f15(x50381,x50382))+~P22(f312(f70(x50381),x50382))
% 173.53/173.42 [5040]~P63(x50401)+~P22(f312(x50402,f192(x50401)))+P22(f312(f66(f856(x50401)),x50402))
% 173.53/173.42 [5125]~P63(x51252)+P22(f312(x51251,f192(x51252)))+~P22(f312(f67(f856(x51252)),x51251))
% 173.53/173.42 [5126]E(x51261,x51262)+~E(f312(f312(f21(a852),x51262),x51261),f2(a852))+~E(f312(f312(f21(a852),x51261),x51262),f2(a852))
% 173.53/173.42 [5140]P32(x51401)+~P43(x51402)+~P22(f312(f312(f314(a1),x51401),x51402))
% 173.53/173.42 [5169]~P112(x51691)+~E(f91(x51691,x51692),f87(x51691))+P22(f312(f312(f228(x51691),f2(x51691)),x51692))
% 173.53/173.42 [5181]~P90(x51811)+E(f312(f114(x51811),f312(f117(a852),x51812)),f312(f117(x51811),x51812))+P22(f312(a194,f312(f117(a1),x51812)))
% 173.53/173.42 [5186]~P46(x51861,x51862)+P47(a845)+P22(f312(f70(f859(x51861,x51861)),x51862))
% 173.53/173.42 [5253]~P103(x52531)+E(f312(f72(x52531,f226(x52531)),x52532),f12(x52531,f226(x52531),x52532))+~P22(f312(f70(x52531),x52532))
% 173.53/173.42 [5254]~P103(x52541)+E(f312(f72(x52541,f225(x52541)),x52542),f13(x52541,f225(x52541),x52542))+~P22(f312(f70(x52541),x52542))
% 173.53/173.42 [5268]E(x52681,x52682)+P22(f312(f312(f228(a852),x52682),x52681))+P22(f312(f312(f228(a852),x52681),x52682))
% 173.53/173.42 [5269]E(x52691,x52692)+P22(f312(f312(f228(a1),x52692),x52691))+P22(f312(f312(f228(a1),x52691),x52692))
% 173.53/173.42 [5320]~P90(x53201)+E(f312(f114(x53201),f312(f117(a852),x53202)),f2(x53201))+~P22(f312(a194,f312(f117(a1),x53202)))
% 173.53/173.42 [5323]~E(x53232,f312(a118,x53231))+E(x53231,f312(f114(a1),x53232))+~P22(f312(f312(f227(a1),f2(a1)),x53231))
% 173.53/173.42 [5324]~E(f312(a118,x53241),x53242)+E(x53241,f312(f114(a1),x53242))+~P22(f312(f312(f227(a1),f2(a1)),x53241))
% 173.53/173.42 [5325]~E(x53251,f312(a118,x53252))+E(f312(f114(a1),x53251),x53252)+~P22(f312(f312(f227(a1),f2(a1)),x53252))
% 173.53/173.42 [5335]E(x53351,f312(a118,x53352))+~E(x53352,f312(f114(a1),x53351))+~P22(f312(f312(f227(a1),f2(a1)),x53352))
% 173.53/173.42 [5336]E(f312(a118,x53361),x53362)+~E(x53361,f312(f114(a1),x53362))+~P22(f312(f312(f227(a1),f2(a1)),x53361))
% 173.53/173.42 [5376]~P83(x53762)+E(x53761,f2(x53762))+P22(f312(f312(f228(x53762),f2(x53762)),f312(f84(x53762),x53761)))
% 173.53/173.42 [5442]~P112(x54421)+E(f91(x54421,x54422),f87(x54421))+~P22(f312(f312(f228(x54421),f2(x54421)),x54422))
% 173.53/173.42 [5446]~P90(x54461)+E(f312(f114(x54461),f312(f117(a852),x54462)),f2(x54461))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x54462)))
% 173.53/173.42 [5453]~P83(x54531)+E(f312(f84(x54531),x54532),x54532)+~P22(f312(f312(f228(x54531),f2(x54531)),x54532))
% 173.53/173.42 [5454]~P83(x54541)+E(f312(f84(x54541),x54542),x54542)+~P22(f312(f312(f227(x54541),f2(x54541)),x54542))
% 173.53/173.42 [5461]E(x54611,f2(a852))+~E(f135(a852,f312(f282(a852,x54612),x54611)),f127(a852))+P22(f312(f312(f227(a852),x54611),x54612))
% 173.53/173.42 [5471]~P26(x54711)+E(f312(f312(f6(x54711,x54711),f5(x54711)),f312(f168(x54711),x54712)),f312(f162(x54711),x54712))+~P22(f312(f133(x54711),x54712))
% 173.53/173.42 [5476]~P111(x54761)+E(f312(f114(x54761),f312(a118,x54762)),f312(f116(x54761),x54762))+~P22(f312(f312(f227(a1),f2(a1)),x54762))
% 173.53/173.42 [5503]E(x55031,x55032)+P22(f312(f312(f228(a852),x55031),x55032))+~P22(f312(f312(f227(a852),x55031),x55032))
% 173.53/173.42 [5504]E(x55041,x55042)+P22(f312(f312(f228(a1),x55041),x55042))+~P22(f312(f312(f227(a1),x55041),x55042))
% 173.53/173.42 [5507]E(x55071,f87(a1))+~E(f312(f312(f90(a1),x55072),x55071),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x55072))
% 173.53/173.42 [5508]E(x55081,f87(a1))+~E(f312(f312(f90(a1),x55081),x55082),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x55081))
% 173.53/173.42 [5510]E(x55101,f2(a1))+~E(f54(a1,x55102,x55101),f2(a1))+E(f312(f47(a1,x55102),f312(f88(a1),x55101)),f312(f88(a1),f312(f47(a1,x55102),x55101)))
% 173.53/173.42 [5551]~P43(x55512)+P22(f312(f312(f227(a1),f2(a1)),x55511))+~P22(f312(f312(f314(a1),x55511),x55512))
% 173.53/173.42 [5572]~P57(x55721,x55722)+P41(x55721,x55722)+~P22(f312(f70(f859(x55721,x55721)),x55722))
% 173.53/173.42 [5574]~P57(x55741,x55742)+P46(x55741,x55742)+~P22(f312(f70(f859(x55741,x55741)),x55742))
% 173.53/173.42 [5611]E(x56111,f189(f860(x56112,a845)))+~P22(f312(f70(x56112),x56111))+P22(f312(f312(f228(a852),f2(a852)),f312(f53(x56112),x56111)))
% 173.53/173.42 [5638]~P22(f312(x56381,x56382))+P22(f312(x56381,f2(a852)))+P22(f312(f312(f228(a852),f838(x56382,x56381)),x56382))
% 173.53/173.42 [5663]E(x56631,f2(a852))+~E(f312(f162(a852),x56632),f2(a852))+~P22(f312(f312(f314(a852),x56631),f312(f168(a852),x56632)))
% 173.53/173.42 [5723]E(x57231,x57232)+~P22(f312(f312(f227(a852),x57232),x57231))+~P22(f312(f312(f227(a852),x57231),x57232))
% 173.53/173.42 [5724]E(x57241,x57242)+~P22(f312(f312(f227(a1),x57242),x57241))+~P22(f312(f312(f227(a1),x57241),x57242))
% 173.53/173.42 [5725]E(f312(f53(x57251),x57252),f2(a852))+~P22(f312(f70(x57251),x57252))+P22(f312(f312(f314(x57251),f724(x57252,x57251)),x57252))
% 173.53/173.42 [5754]~P22(f312(x57541,f321(x57541)))+P22(f312(x57541,f312(a118,x57542)))+~P22(f312(f312(f227(a1),f2(a1)),x57542))
% 173.53/173.42 [5756]P22(f312(f312(f228(a852),x57561),f372(x57562)))+~P22(f312(f70(a852),x57562))+~P22(f312(f312(f314(a852),x57561),x57562))
% 173.53/173.42 [5757]P22(f312(f312(f227(a852),x57571),f368(x57572)))+~P22(f312(f70(a852),x57572))+~P22(f312(f312(f314(a852),x57571),x57572))
% 173.53/173.42 [5788]E(x57881,x57882)+~P22(f312(f312(f228(a852),x57881),f312(a126,x57882)))+P22(f312(f312(f228(a852),x57881),x57882))
% 173.53/173.42 [5821]E(x58211,f312(a126,x58212))+~P22(f312(f312(f227(a852),x58211),f312(a126,x58212)))+P22(f312(f312(f227(a852),x58211),x58212))
% 173.53/173.42 [5832]P22(f312(x58321,f328(x58321)))+~P22(f312(x58321,f312(a118,x58322)))+~P22(f312(f312(f227(a1),f2(a1)),x58322))
% 173.53/173.42 [5845]~P22(f312(x58451,x58452))+~P22(f312(f312(f227(a1),f2(a1)),x58452))+P22(f312(x58451,f312(f114(a1),f831(x58451))))
% 173.53/173.42 [5860]~P83(x58602)+~E(x58601,f2(x58602))+~P22(f312(f312(f228(x58602),f2(x58602)),f312(f84(x58602),x58601)))
% 173.53/173.42 [5887]~P57(x58871,x58872)+P41(x58871,f312(f265(x58871,x58871),x58872))+~P22(f312(f70(f859(x58871,x58871)),x58872))
% 173.53/173.42 [5891]E(f312(f47(a1,x58911),x58912),f2(a1))+~P22(f312(f312(f227(a1),x58911),f2(a1)))+~P22(f312(f312(f228(a1),x58912),x58911))
% 173.53/173.42 [5900]~P90(x59001)+E(f312(f114(x59001),f312(f117(a852),x59002)),f312(f117(x59001),x59002))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x59002)))
% 173.53/173.42 [5904]E(f312(a126,x59041),x59042)+~P22(f312(f312(f228(a852),x59041),x59042))+P22(f312(f312(f228(a852),f312(a126,x59041)),x59042))
% 173.53/173.42 [5920]E(f312(f47(a1,x59201),x59202),f2(a1))+~P22(f312(f312(f227(a1),f2(a1)),x59201))+~P22(f312(f312(f228(a1),x59201),x59202))
% 173.53/173.42 [5931]E(f54(a1,x59311,x59312),x59311)+~P22(f312(f312(f227(a1),x59311),f2(a1)))+~P22(f312(f312(f228(a1),x59312),x59311))
% 173.53/173.42 [5960]E(f54(a852,f312(f117(a852),x59601),f312(f117(a852),x59602)),f312(f117(a852),x59601))+P22(f312(a194,f312(f117(a1),x59601)))+~P22(f312(a194,f312(f117(a1),x59602)))
% 173.53/173.42 [5962]E(f54(a1,x59621,x59622),x59621)+~P22(f312(f312(f227(a1),f2(a1)),x59621))+~P22(f312(f312(f228(a1),x59621),x59622))
% 173.53/173.42 [5963]E(x59631,x59632)+~P22(f312(f312(f228(a852),x59631),f312(a126,x59632)))+~P22(f312(f312(f227(a852),x59632),x59631))
% 173.53/173.42 [5979]~P112(x59791)+~P22(f312(f312(f228(x59791),x59792),f2(x59791)))+P22(f312(f312(f228(x59791),x59792),f312(f88(x59791),x59792)))
% 173.53/173.42 [5980]~P70(x59801)+~P22(f312(f312(f227(x59801),x59802),f2(x59801)))+P22(f312(f312(f227(x59801),x59802),f312(f88(x59801),x59802)))
% 173.53/173.42 [5990]~P31(x59901)+E(f312(f312(f73(x59901,x59901,f124(x59901)),f189(x59901)),x59902),f48(x59901,x59902))+~P22(f312(f70(x59901),x59902))
% 173.53/173.42 [6003]~P117(x60031)+~P22(f312(f312(f228(a852),f2(a852)),x60032))+P22(f312(f312(f228(x60031),f2(x60031)),f312(f114(x60031),x60032)))
% 173.53/173.42 [6004]~P112(x60041)+~P22(f312(f312(f228(a1),f2(a1)),x60042))+P22(f312(f312(f228(x60041),f2(x60041)),f312(f116(x60041),x60042)))
% 173.53/173.42 [6005]~P112(x60051)+~P22(f312(f312(f227(a1),f2(a1)),x60052))+P22(f312(f312(f227(x60051),f2(x60051)),f312(f116(x60051),x60052)))
% 173.53/173.42 [6008]~P32(x60082)+~P32(x60081)+E(f312(f290(a852,a1,f114(a1)),f283(a852,f312(a118,x60081),f312(a118,x60082))),f283(a1,x60081,x60082))
% 173.53/173.42 [6012]P22(f312(x60121,x60122))+~P22(f312(f312(f227(a1),f2(a1)),x60122))+~P22(f312(x60121,f312(f114(a1),f835(x60121))))
% 173.53/173.42 [6036]E(f312(f312(f89(a852),f312(f117(a852),x60361)),f312(f117(a852),x60362)),f312(f117(a852),x60361))+P22(f312(f312(f228(a1),x60361),a92))+~P22(f312(f312(f228(a1),x60362),a92))
% 173.53/173.42 [6038]~P112(x60381)+P22(f312(f312(f228(x60381),f2(x60381)),f91(x60381,x60382)))+~P22(f312(f312(f228(x60381),f2(x60381)),x60382))
% 173.53/173.42 [6052]~P76(x60521)+~P22(f312(f312(f228(x60521),x60522),f2(x60521)))+P22(f312(f312(f228(x60521),f2(x60521)),f312(f88(x60521),x60522)))
% 173.53/173.42 [6053]~P76(x60531)+~P22(f312(f312(f227(x60531),x60532),f2(x60531)))+P22(f312(f312(f227(x60531),f2(x60531)),f312(f88(x60531),x60532)))
% 173.53/173.42 [6056]E(x60561,f235(f860(x60562,a845)))+~E(f312(f53(x60562),x60561),f312(f53(x60562),f235(f860(x60562,a845))))+~P22(f312(f70(x60562),f235(f860(x60562,a845))))
% 173.53/173.42 [6092]~P112(x60921)+P22(f312(f312(f228(x60921),x60922),f2(x60921)))+~P22(f312(f312(f228(x60921),x60922),f312(f88(x60921),x60922)))
% 173.53/173.42 [6093]~P70(x60931)+P22(f312(f312(f227(x60931),x60932),f2(x60931)))+~P22(f312(f312(f227(x60931),x60932),f312(f88(x60931),x60932)))
% 173.53/173.42 [6102]~P90(x61021)+P22(f312(f312(f314(x61021),f312(f117(x61021),x61022)),f187(x61021)))+~P22(f312(f312(f227(a1),a92),x61022))
% 173.53/173.42 [6136]~E(x61362,f2(a1))+E(x61361,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x61361),x61362)),f54(a1,x61361,x61362)),f312(f312(f239(a1,a1),f2(a1)),x61361))
% 173.53/173.42 [6137]E(x61371,f2(a852))+~P22(f312(f312(f228(a852),x61371),f312(a126,x61372)))+P22(f312(f312(f228(a852),f816(x61372,x61371)),x61372))
% 173.53/173.42 [6140]E(f312(f246(a1,a1),f58(x61401,x61402)),f312(f47(a1,x61401),x61402))+~P22(f312(f312(f228(a1),x61401),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x61402))
% 173.53/173.42 [6157]~P112(x61571)+~P22(f312(f312(f228(x61571),f2(x61571)),f91(x61571,x61572)))+P22(f312(f312(f228(x61571),f2(x61571)),x61572))
% 173.53/173.42 [6159]~E(f312(f117(a852),x61592),f312(f117(a852),x61591))+P22(f312(f312(f227(a1),f312(f117(a1),x61591)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x61592)))
% 173.53/173.42 [6194]E(f312(f246(a1,a1),f55(x61941,x61942)),f312(f47(a1,x61941),x61942))+~P22(f312(f312(f228(a1),f2(a1)),x61941))+~P22(f312(f312(f227(a1),f2(a1)),x61942))
% 173.53/173.42 [6219]E(f312(f248(a1,a1),f58(x62191,x62192)),f54(a1,x62191,x62192))+~P22(f312(f312(f228(a1),x62191),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x62192))
% 173.53/173.42 [6222]~P117(x62222)+~P22(f312(f312(f228(x62222),f2(x62222)),f312(f114(x62222),x62221)))+P22(f312(f312(f228(a852),f2(a852)),x62221))
% 173.53/173.42 [6223]~P112(x62232)+~P22(f312(f312(f228(x62232),f2(x62232)),f312(f116(x62232),x62231)))+P22(f312(f312(f228(a1),f2(a1)),x62231))
% 173.53/173.42 [6224]~P112(x62242)+~P22(f312(f312(f227(x62242),f2(x62242)),f312(f116(x62242),x62241)))+P22(f312(f312(f227(a1),f2(a1)),x62241))
% 173.53/173.42 [6242]E(f312(f248(a1,a1),f55(x62421,x62422)),f54(a1,x62421,x62422))+~P22(f312(f312(f228(a1),f2(a1)),x62421))+~P22(f312(f312(f227(a1),f2(a1)),x62422))
% 173.53/173.42 [6259]~P76(x62591)+P22(f312(f312(f228(x62591),x62592),f2(x62591)))+~P22(f312(f312(f228(x62591),f2(x62591)),f312(f88(x62591),x62592)))
% 173.53/173.42 [6260]~P76(x62601)+P22(f312(f312(f227(x62601),x62602),f2(x62601)))+~P22(f312(f312(f227(x62601),f2(x62601)),f312(f88(x62601),x62602)))
% 173.53/173.42 [6281]~P31(x62811)+~P49(x62811,x62811,x62812)+P22(f312(f312(f227(x62811),f110(x62811,x62812)),f312(x62812,f110(x62811,x62812))))
% 173.53/173.42 [6282]~P31(x62821)+~P49(x62821,x62821,x62822)+P22(f312(f312(f227(x62821),f109(x62821,x62822)),f312(x62822,f109(x62821,x62822))))
% 173.53/173.42 [6286]P22(f312(f57(x62861,x62862),f58(x62861,x62862)))+~P22(f312(f312(f228(a1),x62861),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x62862))
% 173.53/173.42 [6306]P22(f312(f57(x63061,x63062),f55(x63061,x63062)))+~P22(f312(f312(f228(a1),f2(a1)),x63062))+~P22(f312(f312(f227(a1),f2(a1)),x63061))
% 173.53/173.42 [6351]~P76(x63511)+P22(f312(f312(f228(x63511),f312(f88(x63511),x63512)),f2(x63511)))+~P22(f312(f312(f228(x63511),f2(x63511)),x63512))
% 173.53/173.42 [6352]~P76(x63521)+P22(f312(f312(f227(x63521),f312(f88(x63521),x63522)),f2(x63521)))+~P22(f312(f312(f227(x63521),f2(x63521)),x63522))
% 173.53/173.42 [6369]E(f312(f312(f21(a852),f312(a118,x63691)),f312(a118,x63692)),f312(a118,f196(x63691,x63692)))+~P22(f312(f312(f227(a1),f2(a1)),x63692))+~P22(f312(f312(f227(a1),f2(a1)),x63691))
% 173.53/173.42 [6386]P22(f312(f312(f227(a1),f2(a1)),f196(x63861,x63862)))+~P22(f312(f312(f227(a1),f2(a1)),x63862))+~P22(f312(f312(f227(a1),f2(a1)),x63861))
% 173.53/173.42 [6423]~P22(f312(x64231,x64232))+P22(f312(x64231,f2(a852)))+P22(f312(x64231,f312(f312(f89(a852),f838(x64232,x64231)),f87(a852))))
% 173.53/173.42 [6471]E(x64711,f2(a1))+E(f54(a1,x64712,x64711),f2(a1))+E(f312(f312(f21(a1),f312(f88(a1),f312(f47(a1,x64712),x64711))),f87(a1)),f312(f47(a1,x64712),f312(f88(a1),x64711)))
% 173.53/173.42 [6501]E(f312(f117(a852),x65011),f312(f117(a852),x65012))+~P22(f312(f312(f227(a1),f312(f117(a1),x65012)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x65011)))
% 173.53/173.42 [6511]~E(x65111,f2(a852))+~E(f614(x65112,x65111),f2(a852))+E(f312(f138(a852,a852,f89(a852),x65111),x65112),f2(a852))
% 173.53/173.42 [6536]~P22(f312(f70(x65361),f674(x65362,x65361)))+~P22(f312(f70(f860(x65361,a845)),x65362))+P22(f312(f70(x65361),f48(f860(x65361,a845),x65362)))
% 173.53/173.42 [6542]E(x65421,x65422)+P22(f312(f312(f228(a1),x65421),x65422))+~P22(f312(f312(f228(a1),x65421),f312(f312(f89(a1),x65422),f87(a1))))
% 173.53/173.42 [6544]P22(f312(f312(f228(a852),f312(a118,x65441)),f312(a118,x65442)))+~P22(f312(f312(f228(a1),f2(a1)),x65442))+~P22(f312(f312(f228(a1),x65441),x65442))
% 173.53/173.42 [6545]P22(f312(f312(f228(a852),f312(a118,x65451)),f312(a118,x65452)))+~P22(f312(f312(f227(a1),f2(a1)),x65451))+~P22(f312(f312(f228(a1),x65451),x65452))
% 173.53/173.42 [6546]P22(f312(f312(f227(a852),f312(a118,x65461)),f312(a118,x65462)))+~P22(f312(f312(f228(a1),f2(a1)),x65461))+~P22(f312(f312(f227(a1),x65461),x65462))
% 173.53/173.42 [6547]P22(f312(f312(f227(a852),f312(a118,x65471)),f312(a118,x65472)))+~P22(f312(f312(f227(a1),f2(a1)),x65472))+~P22(f312(f312(f227(a1),x65471),x65472))
% 173.53/173.42 [6559]E(f54(a852,f312(a118,x65591),f312(a118,x65592)),f312(a118,f54(a1,x65591,x65592)))+~P22(f312(f312(f227(a1),f2(a1)),x65592))+~P22(f312(f312(f227(a1),f2(a1)),x65591))
% 173.53/173.42 [6583]~P76(x65831)+~P22(f312(f312(f228(x65831),f312(f88(x65831),x65832)),f2(x65831)))+P22(f312(f312(f228(x65831),f2(x65831)),x65832))
% 173.53/173.42 [6584]~P76(x65841)+~P22(f312(f312(f227(x65841),f312(f88(x65841),x65842)),f2(x65841)))+P22(f312(f312(f227(x65841),f2(x65841)),x65842))
% 173.53/173.42 [6589]~P22(f312(f312(f228(a1),f2(a1)),x65892))+P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x65891),x65892)))+~P22(f312(f312(f227(a1),x65892),x65891))
% 173.53/173.42 [6590]~P22(f312(f312(f228(a1),x65902),f2(a1)))+~P22(f312(f312(f227(a1),x65901),f2(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x65901),x65902)))
% 173.53/173.42 [6601]~P22(f312(f312(f228(a1),a92),x66012))+~P22(f312(f312(f228(a1),x66011),x66012))+P22(f312(f312(f228(a852),f312(f117(a852),x66011)),f312(f117(a852),x66012)))
% 173.53/173.42 [6623]~P22(f312(f312(f228(a1),f2(a1)),x66232))+~P22(f312(f312(f227(a1),f2(a1)),x66231))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x66231),x66232)))
% 173.53/173.42 [6624]~P22(f312(f312(f227(a1),f2(a1)),x66242))+~P22(f312(f312(f227(a1),f2(a1)),x66241))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x66241),x66242)))
% 173.53/173.42 [6688]~P22(f312(f312(f227(a1),f2(a1)),x66881))+P22(f312(f312(f228(a852),f312(a118,x66881)),x66882))+~P22(f312(f312(f228(a1),x66881),f312(f114(a1),x66882)))
% 173.53/173.42 [6710]E(f312(f312(f239(a1,a1),f312(f47(a1,x67101),x67102)),f54(a1,x67101,x67102)),f58(x67101,x67102))+P22(f312(f312(f227(a1),f2(a1)),x67101))+~P22(f312(f312(f228(a1),f2(a1)),x67102))
% 173.53/173.42 [6717]~P22(f312(f312(f227(a1),f2(a1)),x67171))+~P22(f312(f312(f228(a852),f312(a118,x67171)),x67172))+P22(f312(f312(f228(a1),x67171),f312(f114(a1),x67172)))
% 173.53/173.42 [6751]~P22(f312(f312(f227(a852),f312(a118,x67511)),f312(a118,x67512)))+~P22(f312(f312(f228(a1),f2(a1)),x67511))+P22(f312(f312(f227(a1),x67511),x67512))
% 173.53/173.42 [6752]~P22(f312(f312(f227(a852),f312(a118,x67521)),f312(a118,x67522)))+~P22(f312(f312(f227(a1),f2(a1)),x67522))+P22(f312(f312(f227(a1),x67521),x67522))
% 173.53/173.42 [6777]P22(f312(f312(f227(a1),x67771),x67772))+~P22(f312(f312(f227(a852),f312(f117(a852),x67771)),f312(f117(a852),x67772)))+P22(f312(f312(f227(a1),x67771),a92))
% 173.53/173.42 [6801]P22(f312(f312(f227(a1),f2(a1)),f54(a1,x68011,x68012)))+~P22(f312(f312(f227(a1),f2(a1)),x68012))+~P22(f312(f312(f227(a1),f2(a1)),x68011))
% 173.53/173.42 [6808]P22(f312(f312(f227(a1),x68081),f2(a1)))+~P22(f312(f312(f228(a1),x68082),f2(a1)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x68081),x68082)))
% 173.53/173.42 [6822]~P22(f312(f312(f228(a1),f2(a1)),x68221))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68222),x68221)))+P22(f312(f312(f227(a1),x68221),x68222))
% 173.53/173.42 [6823]~P22(f312(f312(f227(a1),f2(a1)),x68232))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68232),x68231)))+P22(f312(f312(f227(a1),x68231),x68232))
% 173.53/173.42 [6852]E(f312(f312(f239(a1,a1),f312(f47(a1,x68521),x68522)),f54(a1,x68521,x68522)),f58(x68521,x68522))+~P22(f312(f312(f228(a1),x68521),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x68522))
% 173.53/173.42 [6853]P22(f312(f312(f228(a1),f2(a1)),x68531))+~P22(f312(f312(f227(a1),f2(a1)),x68532))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68532),x68531)))
% 173.53/173.42 [6854]P22(f312(f312(f227(a1),f2(a1)),x68541))+~P22(f312(f312(f228(a1),f2(a1)),x68542))+~P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x68541),x68542)))
% 173.53/173.42 [6878]E(f312(f312(f239(a1,a1),f312(f47(a1,x68781),x68782)),f54(a1,x68781,x68782)),f55(x68781,x68782))+~P22(f312(f312(f227(a1),f2(a1)),x68782))+~P22(f312(f312(f227(a1),f2(a1)),x68781))
% 173.53/173.42 [6908]P22(f312(f312(f228(a1),a92),x69081))+~P22(f312(f312(f228(a1),x69082),x69081))+~P22(f312(f312(f228(a852),f312(f117(a852),x69082)),f312(f117(a852),x69081)))
% 173.53/173.42 [6976]~P22(f312(f312(f228(a1),x69762),f2(a1)))+P22(f312(f312(f228(a1),f312(f47(a1,x69761),x69762)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69761))
% 173.53/173.42 [6978]~P22(f312(f312(f228(a1),x69781),f2(a1)))+P22(f312(f312(f228(a1),f312(f47(a1,x69781),x69782)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69782))
% 173.53/173.42 [6979]~P22(f312(f312(f228(a1),x69792),f2(a1)))+P22(f312(f312(f227(a1),f312(f47(a1,x69791),x69792)),f2(a1)))+~P22(f312(f312(f227(a1),f2(a1)),x69791))
% 173.53/173.42 [6980]~P22(f312(f312(f227(a1),x69801),f2(a1)))+P22(f312(f312(f227(a1),f312(f47(a1,x69801),x69802)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69802))
% 173.53/173.42 [7030]~P93(x70302)+E(x70301,f127(x70302))+E(f312(f138(x70302,x70302,f90(x70302),f312(f137(x70302),x70301)),f312(f167(x70302),x70301)),f312(f72(x70302,f90(x70302)),f312(f168(x70302),x70301)))
% 173.53/173.42 [7142]~E(x71421,f2(a852))+E(f312(f138(a852,a852,f89(a852),x71421),x71422),f2(a852))+P22(f312(f312(f314(a852),f614(x71422,x71421)),f312(f168(a852),x71422)))
% 173.53/173.42 [7189]P22(f312(f312(f314(f860(x71891,a845)),f674(x71892,x71891)),x71892))+~P22(f312(f70(f860(x71891,a845)),x71892))+P22(f312(f70(x71891),f48(f860(x71891,a845),x71892)))
% 173.53/173.42 [7289]P19(x72891,x72891,x72892,f235(f860(x72891,a845)))+~E(f312(f290(x72891,x72891,x72892),f235(f860(x72891,a845))),f235(f860(x72891,a845)))+~P22(f312(f70(x72891),f235(f860(x72891,a845))))
% 173.53/173.42 [7359]~P22(f312(f312(f228(a1),x73592),f2(a1)))+~P22(f312(f312(f228(a1),f312(f47(a1,x73591),x73592)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x73591))
% 173.53/173.42 [7362]P22(f312(f312(f228(a1),x73621),f2(a1)))+~P22(f312(f312(f228(a1),f312(f47(a1,x73621),x73622)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x73622))
% 173.53/173.42 [7412]~P19(x74121,x74121,x74122,f235(f860(x74121,a845)))+E(f312(f290(x74121,x74121,x74122),f235(f860(x74121,a845))),f235(f860(x74121,a845)))+~P22(f312(f70(x74121),f235(f860(x74121,a845))))
% 173.53/173.42 [7525]E(f312(f47(a1,x75251),x75252),f312(f117(a1),a111))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x75251),x75252)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x75251))
% 173.53/173.42 [7611]E(f312(f312(f89(a1),x76111),x76112),f54(a1,x76111,x76112))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x76111),x76112)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x76111))
% 173.53/173.42 [7999]~P63(x79991)+~P22(f312(f67(f856(x79991)),x79992))+P22(f312(f67(x79991),f312(f312(f8(f856(x79991),a845,x79991),x79992),f219(x79991))))
% 173.53/173.42 [8317]~P103(x83171)+P33(x83171,x83172)+~P22(f312(f312(f227(x83171),f312(f312(f161(x83171),x83172),f652(x83172,x83171))),f312(f312(f161(x83171),x83172),f653(x83172,x83171))))
% 173.53/173.42 [8318]~P103(x83181)+P33(x83181,x83182)+~P22(f312(f312(f227(x83181),f312(f312(f161(x83181),x83182),f655(x83182,x83181))),f312(f312(f161(x83181),x83182),f665(x83182,x83181))))
% 173.53/173.42 [8482]~P63(x84821)+P22(f312(f66(f856(x84821)),x84822))+~P22(f312(f66(x84821),f312(f312(f8(f856(x84821),a845,x84821),x84822),f219(x84821))))
% 173.53/173.42 [9627]~P63(x96271)+~P63(x96272)+E(f312(f312(f150(f853(x96271),f860(x96272,x96271)),f312(f312(f8(f860(x96272,f856(x96271)),f860(x96272,x96271),f853(x96271)),f82(f856(x96271),x96271,x96272,f223(x96271))),f312(f312(f8(f853(f859(x96272,x96271)),f860(x96272,f856(x96271)),f853(x96271)),f173(x96272,x96271)),f312(f177(x96272,x96271),f64(x96272))))),f63(x96271,f312(f190(f853(x96272)),f64(x96272)),f64(x96271))),f64(f860(x96272,x96271)))
% 173.53/173.42 [5623]~P43(x56232)+~P43(x56231)+P43(f312(f312(f124(f860(a1,a845)),x56231),x56232))
% 173.53/173.42 [5624]~P43(x56242)+~P43(x56241)+P43(f312(f312(f115(f860(a1,a845)),x56241),x56242))
% 173.53/173.42 [5631]E(x56311,f2(a1))+~E(f54(a1,x56312,x56311),f2(a1))+E(f312(f47(a1,f312(f88(a1),x56312)),x56311),f312(f88(a1),f312(f47(a1,x56312),x56311)))
% 173.53/173.42 [5641]~P90(x56411)+~P64(x56411)+E(f312(f88(x56411),f312(f312(f268(x56411),f87(x56411)),x56412)),f312(f312(f268(x56411),f312(f117(x56411),a111)),x56412))
% 173.53/173.42 [5881]~P103(x58811)+P33(x58811,x58812)+P22(f312(f312(f228(a852),f653(x58812,x58811)),f312(f190(f853(x58811)),x58812)))
% 173.53/173.42 [5882]~P103(x58821)+P33(x58821,x58822)+P22(f312(f312(f228(a852),f665(x58822,x58821)),f312(f190(f853(x58821)),x58822)))
% 173.53/173.42 [6033]~P90(x60331)+~E(f312(f117(x60331),x60332),f2(x60331))+P35(x60331,f312(f117(x60331),f312(f312(f89(a1),x60332),f312(f88(a1),a92))))
% 173.53/173.42 [6034]~P90(x60341)+~E(f312(f117(x60341),x60342),f2(x60341))+P35(x60341,f312(f117(x60341),f312(f312(f89(a1),a92),f312(f88(a1),x60342))))
% 173.53/173.42 [6165]~E(x61652,f2(a852))+~E(x61651,f2(a852))+P22(f312(f312(f227(a1),f312(f114(a1),x61651)),f312(f88(a1),f312(f114(a1),x61652))))
% 173.53/173.42 [6184]E(f312(f312(f89(a113),f87(a113)),f258(x61841,f312(f47(a113,x61842),x61841))),f258(x61841,x61842))+P22(f312(f312(f227(a113),x61841),f87(a113)))+P22(f312(f312(f228(a113),x61842),x61841))
% 173.53/173.42 [6193]E(f312(f312(f89(a852),f312(f117(a852),x61931)),f312(f117(a852),x61932)),f312(f117(a852),f312(f312(f89(a1),x61931),x61932)))+P22(f312(f312(f228(a1),x61931),a92))+P22(f312(f312(f228(a1),x61932),a92))
% 173.53/173.42 [6317]~P70(x63171)+~P22(f312(f312(f228(x63171),f2(x63171)),x63172))+P22(f312(f312(f228(x63171),f312(f88(x63171),x63172)),x63172))
% 173.53/173.42 [6318]~P70(x63181)+~P22(f312(f312(f227(x63181),f2(x63181)),x63182))+P22(f312(f312(f227(x63181),f312(f88(x63181),x63182)),x63182))
% 173.53/173.42 [6487]E(f312(f312(f21(a852),f312(a118,x64871)),f312(a118,x64872)),f312(a118,f312(f312(f21(a1),x64871),x64872)))+~P22(f312(f312(f227(a1),f2(a1)),x64872))+~P22(f312(f312(f227(a1),x64872),x64871))
% 173.53/173.42 [6520]E(f312(a118,f54(a1,f312(f117(a1),x65201),f312(f117(a1),x65202))),f54(a852,f312(f117(a852),x65201),f312(f117(a852),x65202)))+P22(f312(a194,f312(f117(a1),x65201)))+P22(f312(a194,f312(f117(a1),x65202)))
% 173.53/173.42 [6537]~P70(x65371)+P22(f312(f312(f228(x65371),f2(x65371)),x65372))+~P22(f312(f312(f228(x65371),f312(f88(x65371),x65372)),x65372))
% 173.53/173.42 [6538]~P70(x65381)+P22(f312(f312(f227(x65381),f2(x65381)),x65382))+~P22(f312(f312(f227(x65381),f312(f88(x65381),x65382)),x65382))
% 173.53/173.42 [6550]~P70(x65501)+~P22(f312(f312(f228(x65501),f2(x65501)),x65502))+P22(f312(f312(f228(x65501),f2(x65501)),f312(f312(f89(x65501),x65502),x65502)))
% 173.53/173.42 [6552]~P70(x65521)+~P22(f312(f312(f227(x65521),f2(x65521)),x65522))+P22(f312(f312(f227(x65521),f2(x65521)),f312(f312(f89(x65521),x65522),x65522)))
% 173.53/173.42 [6563]E(f312(f312(f89(a852),f312(a118,x65631)),f312(a118,x65632)),f312(a118,f312(f312(f89(a1),x65631),x65632)))+~P22(f312(f312(f227(a1),f2(a1)),x65632))+~P22(f312(f312(f227(a1),f2(a1)),x65631))
% 173.53/173.42 [6575]E(x65751,f2(a1))+E(f54(a1,x65752,x65751),f2(a1))+E(f312(f312(f21(a1),f312(f88(a1),f312(f47(a1,x65752),x65751))),f87(a1)),f312(f47(a1,f312(f88(a1),x65752)),x65751))
% 173.53/173.42 [6577]E(x65771,f2(a852))+P22(f312(f312(f228(a852),f2(a852)),x65772))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f240(a852),x65772),x65771)))
% 173.53/173.42 [6605]~P90(x66051)+E(f312(f117(x66051),x66052),f2(x66051))+~P35(x66051,f312(f117(x66051),f312(f312(f89(a1),a92),f312(f88(a1),x66052))))
% 173.53/173.42 [6606]~P90(x66061)+E(f312(f117(x66061),x66062),f2(x66061))+~P35(x66061,f312(f117(x66061),f312(f312(f89(a1),x66062),f312(f88(a1),a92))))
% 173.53/173.42 [6666]~P22(f312(f70(x66661),x66662))+~P22(f312(f70(x66661),f235(f860(x66661,a845))))+P22(f312(f70(x66661),f312(f88(f860(x66661,a845)),x66662)))
% 173.53/173.42 [6724]~P22(f312(f312(f228(a852),f2(a852)),x67242))+~P22(f312(f312(f228(a852),f2(a852)),x67241))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f90(a852),x67241),x67242)))
% 173.53/173.42 [6725]~P22(f312(f312(f227(a1),f2(a1)),x67252))+~P22(f312(f312(f227(a1),f2(a1)),x67251))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x67251),x67252)))
% 173.53/173.42 [6726]~P22(f312(f312(f227(a1),f2(a1)),x67262))+~P22(f312(f312(f227(a1),f2(a1)),x67261))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f90(a1),x67261),x67262)))
% 173.53/173.42 [6845]P22(f312(f312(f228(a852),f2(a852)),x68451))+P22(f312(f312(f228(a852),f2(a852)),x68452))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f89(a852),x68452),x68451)))
% 173.53/173.42 [6847]~P70(x68471)+P22(f312(f312(f228(x68471),f2(x68471)),x68472))+~P22(f312(f312(f228(x68471),f2(x68471)),f312(f312(f89(x68471),x68472),x68472)))
% 173.53/173.42 [6848]~P70(x68481)+P22(f312(f312(f227(x68481),f2(x68481)),x68482))+~P22(f312(f312(f227(x68481),f2(x68481)),f312(f312(f89(x68481),x68482),x68482)))
% 173.53/173.42 [6909]~P22(f312(f70(x69091),x69092))+P22(f312(f70(x69091),f235(f860(x69091,a845))))+~P22(f312(f70(x69091),f312(f88(f860(x69091,a845)),x69092)))
% 173.53/173.42 [6966]E(f312(f312(f239(a1,a1),f312(f47(a1,x69661),x69662)),f54(a1,x69661,x69662)),f312(a59,f55(f312(f88(a1),x69661),f312(f88(a1),x69662))))+P22(f312(f312(f228(a1),f2(a1)),x69662))+P22(f312(f312(f227(a1),f2(a1)),x69661))
% 173.53/173.42 [6993]~P22(f312(f312(f228(a852),f2(a852)),x69931))+~P22(f312(f312(f228(a852),f87(a852)),x69932))+P22(f312(f312(f228(a852),f312(f47(a852,x69931),x69932)),x69931))
% 173.53/173.42 [6994]~P22(f312(f312(f228(a1),f2(a1)),x69941))+~P22(f312(f312(f228(a1),f87(a1)),x69942))+P22(f312(f312(f228(a1),f312(f47(a1,x69941),x69942)),x69941))
% 173.53/173.42 [7442]~P22(f312(f70(x74422),f235(f860(x74422,a845))))+~P22(f312(f70(x74421),f235(f860(x74421,a845))))+P22(f312(f70(f858(x74421,x74422)),f235(f860(f858(x74421,x74422),a845))))
% 173.53/173.42 [7443]~P22(f312(f70(x74432),f235(f860(x74432,a845))))+~P22(f312(f70(x74431),f235(f860(x74431,a845))))+P22(f312(f70(f859(x74431,x74432)),f235(f860(f859(x74431,x74432),a845))))
% 173.53/173.42 [7513]~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x75131))+~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x75132))+P22(f312(f312(f228(a852),x75131),f312(f312(f90(a852),x75132),x75131)))
% 173.53/173.42 [7514]~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x75141))+~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x75142))+P22(f312(f312(f228(a852),x75141),f312(f312(f90(a852),x75141),x75142)))
% 173.53/173.42 [7547]E(f312(f53(x75471),f235(f860(x75471,a845))),f312(a126,f2(a852)))+P22(f312(f70(x75472),f235(f860(x75472,a845))))+~P22(f312(f70(f860(x75472,x75471)),f235(f860(f860(x75472,x75471),a845))))
% 173.53/173.42 [7676]~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x76762))+~P22(f312(f312(f228(a852),f312(a126,f2(a852))),x76761))+P22(f312(f312(f228(a852),f312(a126,f2(a852))),f312(f312(f90(a852),x76761),x76762)))
% 173.53/173.42 [7677]~P22(f312(f312(f227(a852),f312(a126,f2(a852))),x76771))+~P22(f312(f312(f227(a852),f312(a126,f2(a852))),x76772))+P22(f312(f312(f227(a852),f312(a126,f2(a852))),f312(f312(f90(a852),x76771),x76772)))
% 173.53/173.42 [8016]~P105(x80161)+P49(a852,x80161,x80162)+~P22(f312(f312(f227(x80161),f312(x80162,f832(x80162,x80161))),f312(x80162,f312(a126,f832(x80162,x80161)))))
% 173.53/173.42 [8370]E(x83701,f127(x83702))+~P22(f312(f133(x83702),x83701))+E(f172(x83702,f312(f312(f8(a845,a845,x83702),a307),f312(f312(f7(x83702,x83702,a845),a309),f140(x83702,x83701))),x83701),f128(x83702,x83701))
% 173.53/173.42 [8471]~P43(x84712)+~P43(x84711)+E(f312(f290(a852,a1,f114(a1)),f312(f312(f124(f860(a852,a845)),f312(f290(a1,a852,a118),x84711)),f312(f290(a1,a852,a118),x84712))),f312(f312(f124(f860(a1,a845)),x84711),x84712))
% 173.53/173.42 [8472]~P43(x84722)+~P43(x84721)+E(f312(f290(a852,a1,f114(a1)),f312(f312(f115(f860(a852,a845)),f312(f290(a1,a852,a118),x84721)),f312(f290(a1,a852,a118),x84722))),f312(f312(f115(f860(a1,a845)),x84721),x84722))
% 173.53/173.42 [9114]~P90(x91141)+~E(f312(f117(x91141),x91142),f87(x91141))+P35(x91141,f312(f117(x91141),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x91142))))
% 173.53/173.42 [9348]~P90(x93481)+E(f312(f117(x93481),x93482),f87(x93481))+~P35(x93481,f312(f117(x93481),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x93482))))
% 173.53/173.42 [10081]E(x100811,f2(a1))+E(x100812,f2(a1))+E(f312(f250(a1,a1,a1,a1,f39(a1),f312(f90(a1),f91(a1,x100812))),f312(f312(f312(f108(f859(a1,a1)),f312(f312(a309,f91(a1,x100811)),f91(a1,x100812))),f61(x100811,x100812)),f312(f312(f249(a1,a1,f859(a1,a1)),f312(f312(f18(a1,f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f860(f859(a1,a1),f859(a1,a1))),f860(f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),a1),f18(a1,f859(a1,a1),f859(a1,a1))),f312(f312(f8(f859(a1,a1),f860(a1,f860(f859(a1,a1),f859(a1,a1))),a1),f312(f7(a1,f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),f312(f312(f8(a845,f860(f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),a1),f108(f859(a1,a1))),f312(f312(f7(a1,a1,a845),a309),f2(a1))))),f312(f312(f7(a1,a1,f859(a1,a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f88(a1))),f2(a1))))),f312(f312(f7(a1,f860(a1,a1),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f859(a1,a1)),f860(f860(a1,a1),f860(a1,f859(a1,a1))),a1),f8(a1,f859(a1,a1),a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f860(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f312(f21(a1),f312(f84(a1),x100812))))),f61(x100811,x100812)))),f312(f312(f239(a1,a1),f312(f47(a1,x100811),x100812)),f54(a1,x100811,x100812)))
% 173.53/173.42 [10082]E(x100821,f2(a1))+E(x100822,f2(a1))+E(f312(f250(a1,a1,a1,a1,f39(a1),f312(f90(a1),f91(a1,x100822))),f312(f312(f312(f108(f859(a1,a1)),f312(f312(a311,f312(f312(a310,f312(f312(f228(a1),f2(a1)),x100822)),f312(f312(f227(a1),f2(a1)),x100821))),f312(f312(a310,f312(f312(f228(a1),x100822),f2(a1))),f312(f312(f228(a1),x100821),f2(a1))))),f61(x100821,x100822)),f312(f312(f249(a1,a1,f859(a1,a1)),f312(f312(f18(a1,f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f860(f859(a1,a1),f859(a1,a1))),f860(f860(a1,f859(a1,a1)),f860(a1,f859(a1,a1))),a1),f18(a1,f859(a1,a1),f859(a1,a1))),f312(f312(f8(f859(a1,a1),f860(a1,f860(f859(a1,a1),f859(a1,a1))),a1),f312(f7(a1,f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),f312(f312(f8(a845,f860(f859(a1,a1),f860(f859(a1,a1),f859(a1,a1))),a1),f108(f859(a1,a1))),f312(f312(f7(a1,a1,a845),a309),f2(a1))))),f312(f312(f7(a1,a1,f859(a1,a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f88(a1))),f2(a1))))),f312(f312(f7(a1,f860(a1,a1),f860(a1,f859(a1,a1))),f312(f312(f8(f860(a1,f859(a1,a1)),f860(f860(a1,a1),f860(a1,f859(a1,a1))),a1),f8(a1,f859(a1,a1),a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f860(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f312(f21(a1),f312(f84(a1),x100822))))),f61(x100821,x100822)))),f312(f312(f239(a1,a1),f312(f47(a1,x100821),x100822)),f54(a1,x100821,x100822)))
% 173.53/173.42 [5632]~P112(x56321)+~P90(x56321)+E(f312(f84(x56321),f312(f312(f240(x56321),f312(f117(x56321),a111)),x56322)),f87(x56321))
% 173.53/173.42 [6103]~P111(x61031)+~P22(f312(f312(f228(a1),x61032),f2(a1)))+E(f312(f88(x61031),f312(f114(x61031),f312(a118,f312(f88(a1),x61032)))),f312(f116(x61031),x61032))
% 173.53/173.42 [6891]~P89(x68911)+~P22(f312(f312(f314(x68911),x68912),f123(x68911)))+~E(f312(f312(f89(x68911),f312(f312(f89(x68911),f87(x68911)),x68912)),x68912),f2(x68911))
% 173.53/173.42 [6995]~P22(f312(f312(f228(a1),x69951),f2(a1)))+~P22(f312(f312(f227(a1),x69952),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f55(f312(f88(a1),x69951),f312(f88(a1),x69952)))),f312(f47(a1,x69951),x69952))
% 173.53/173.42 [7009]~P22(f312(f312(f228(a1),x70092),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f58(f312(f88(a1),x70091),f312(f88(a1),x70092)))),f312(f47(a1,x70091),x70092))+~P22(f312(f312(f228(a1),f2(a1)),x70091))
% 173.53/173.42 [7026]~P22(f312(f312(f228(a1),x70261),f2(a1)))+~P22(f312(f312(f227(a1),x70262),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f55(f312(f88(a1),x70261),f312(f88(a1),x70262)))),f54(a1,x70261,x70262))
% 173.53/173.42 [7051]~P22(f312(f312(f228(a1),x70512),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f58(f312(f88(a1),x70511),f312(f88(a1),x70512)))),f54(a1,x70511,x70512))+~P22(f312(f312(f228(a1),f2(a1)),x70511))
% 173.53/173.42 [7060]E(f312(f47(a1,f312(f312(f240(a1),x70601),x70602)),x70601),f312(f312(f240(a1),x70601),f312(f312(f21(a852),x70602),f312(a126,f2(a852)))))+~P22(f312(f312(f228(a852),f2(a852)),x70602))+~P22(f312(f312(f228(a1),f2(a1)),x70601))
% 173.53/173.42 [7188]~P22(f312(f312(f228(a852),f2(a852)),x71881))+~P22(f312(f312(f228(a852),f2(a852)),x71882))+P22(f312(f312(f228(a852),f312(f312(f21(a852),x71881),x71882)),x71881))
% 173.53/173.42 [7336]E(x73361,f2(a852))+~E(x73362,f2(a1))+~P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x73362)),x73361)))
% 173.53/173.42 [7707]~P22(f312(x77071,x77072))+P22(f312(x77071,f2(a852)))+E(f312(a126,f231(a852,f312(f312(f8(a852,a845,a852),x77071),a126))),f231(a852,x77071))
% 173.53/173.42 [7756]~E(x77562,f127(f853(x77561)))+E(f312(f190(f853(f853(x77561))),f175(x77561,x77562)),f2(a852))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x77561),a852),f190(f853(x77561))),x77562)))
% 173.53/173.42 [7998]P22(f312(x79981,x79982))+~P22(f312(x79981,f312(a121,f550(x79981,x79982))))+~P22(f312(f312(f314(f860(f859(a852,a852),a845)),x79982),a112))
% 173.53/173.42 [8020]E(x80201,f127(f853(x80202)))+E(f312(f190(f853(x80202)),f312(f312(f161(f853(x80202)),x80201),f2(a852))),f312(f190(f853(f853(x80202))),f175(x80202,x80201)))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x80202),a852),f190(f853(x80202))),x80201)))
% 173.53/173.42 [8728]~P22(f312(f70(x87281),f312(f233(x87281),x87282)))+~P22(f312(f70(x87281),f235(f860(x87281,a845))))+P22(f312(f70(x87281),f312(f233(x87281),f312(f312(f8(a845,a845,x87281),a307),x87282))))
% 173.53/173.42 [8752]E(f312(f312(f239(a852,a852),f312(a126,f312(f47(a852,f312(f312(f21(a852),x87521),x87522)),x87522))),f54(a852,f312(f312(f21(a852),x87521),x87522),x87522)),f94(f859(a852,a852),f56(x87521,x87522)))+~P22(f312(f312(f228(a852),f2(a852)),x87522))+~P22(f312(f312(f227(a852),x87522),x87521))
% 173.53/173.42 [9077]~P22(f312(f70(x90771),f312(f233(x90771),x90772)))+P22(f312(f70(x90771),f235(f860(x90771,a845))))+~P22(f312(f70(x90771),f312(f233(x90771),f312(f312(f8(a845,a845,x90771),a307),x90772))))
% 173.53/173.42 [9794]P20(x97941,x97942)+~P41(x97941,f312(f246(f860(f859(x97941,x97941),a845),f860(f859(x97941,x97941),a845)),x97942))+~P22(f312(f312(f227(f860(f859(x97941,x97941),a845)),f312(f312(f267(x97941,x97941,x97941),f312(f246(f860(f859(x97941,x97941),a845),f860(f859(x97941,x97941),a845)),x97942)),f312(f248(f860(f859(x97941,x97941),a845),f860(f859(x97941,x97941),a845)),x97942))),f312(f246(f860(f859(x97941,x97941),a845),f860(f859(x97941,x97941),a845)),x97942)))
% 173.53/173.42 [7050]~P22(f312(f312(f228(a852),f2(a852)),x70502))+P22(f312(f312(f228(a852),x70501),x70502))+E(f312(a126,f312(f47(a852,f312(f312(f21(a852),x70501),x70502)),x70502)),f312(f47(a852,x70501),x70502))
% 173.53/173.42 [7203]~P22(f312(f312(f228(a852),f2(a852)),x72032))+~P22(f312(f312(f227(a852),x72032),x72031))+E(f312(a126,f312(f47(a852,f312(f312(f21(a852),x72031),x72032)),x72032)),f312(f47(a852,x72031),x72032))
% 173.53/173.42 [8233]~P90(x82331)+~P89(x82331)+~P35(x82331,f312(f117(x82331),f312(f312(f21(a1),f312(f312(f89(a1),x82332),x82332)),a111)))
% 173.53/173.42 [8986]E(x89861,f2(a852))+E(f312(f312(f249(a852,a852,f859(a852,a852)),f312(f312(f8(a852,f860(a852,f859(a852,a852)),a852),f239(a852,a852)),a126)),f94(f859(a852,a852),f56(f312(f312(f21(a852),x89862),x89861),x89861))),f94(f859(a852,a852),f56(x89862,x89861)))+P22(f312(f312(f228(a852),x89862),x89861))
% 173.53/173.42 [7471]~P90(x74711)+~P65(x74711)+E(f312(f312(f268(x74711),x74712),f312(f117(x74711),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x74712)
% 173.53/173.42 [9113]~P90(x91131)+~E(f312(f117(x91131),x91132),f87(x91131))+P35(x91131,f312(f117(x91131),f312(f312(f89(a1),x91132),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.42 [9289]~P134(x92891)+~E(x92892,f2(x92891))+E(f312(f312(f240(x92891),x92892),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f2(x92891))
% 173.53/173.42 [9290]~P134(x92901)+~E(x92902,f87(x92901))+E(f312(f312(f240(x92901),x92902),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(x92901))
% 173.53/173.42 [9303]~P134(x93031)+~E(x93032,f312(f88(x93031),f87(x93031)))+E(f312(f312(f240(x93031),x93032),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(x93031))
% 173.53/173.42 [9349]~P90(x93491)+E(f312(f117(x93491),x93492),f87(x93491))+~P35(x93491,f312(f117(x93491),f312(f312(f89(a1),x93492),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.42 [9724]~P112(x97242)+E(x97241,f2(x97242))+P22(f312(f312(f228(x97242),f2(x97242)),f312(f312(f240(x97242),x97241),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.42 [9793]~P112(x97932)+~E(x97931,f2(x97932))+~P22(f312(f312(f228(x97932),f2(x97932)),f312(f312(f240(x97932),x97931),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.42 [9820]P22(f312(f312(f227(a1),x98201),f2(a1)))+P22(f312(f312(f228(a1),x98202),x98201))+E(f312(f52(x98201),f55(x98202,f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98201))),f55(x98202,x98201))
% 173.53/173.42 [9821]~P22(f312(f312(f228(a1),f2(a1)),x98211))+P22(f312(f312(f228(a1),x98212),x98211))+E(f312(f52(x98211),f55(x98212,f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98211))),f55(x98212,x98211))
% 173.53/173.42 [9822]P22(f312(f312(f227(a1),x98221),f2(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x98222),x98221)))+E(f312(f52(x98221),f58(x98222,f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98221))),f58(x98222,x98221))
% 173.53/173.42 [9823]~P22(f312(f312(f228(a1),f2(a1)),x98231))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x98232),x98231)))+E(f312(f52(x98231),f58(x98232,f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98231))),f58(x98232,x98231))
% 173.53/173.42 [9824]~P23(x98241)+~P22(f312(f312(f227(a1),f2(a1)),x98242))+E(f312(f114(x98241),f312(a118,f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x98242))),f312(f312(f89(x98241),f312(f114(x98241),f312(a118,x98242))),f312(f114(x98241),f312(a118,x98242))))
% 173.53/173.42 [4972]~P139(x49721,x49723,x49722)+~E(x49723,f2(a1))+P22(f312(x49721,x49722))
% 173.53/173.42 [5098]~P103(x50981)+~P33(x50981,x50983)+P33(x50981,f166(x50981,x50982,x50983))
% 173.53/173.42 [5099]~P103(x50991)+~P33(x50991,x50993)+P33(x50991,f172(x50991,x50992,x50993))
% 173.53/173.42 [4685]~P71(x46852)+~E(x46853,f312(f88(x46852),x46851))+E(x46851,f312(f88(x46852),x46853))
% 173.53/173.42 [4687]~P71(x46871)+~E(f312(f88(x46871),x46873),x46872)+E(f312(f88(x46871),x46872),x46873)
% 173.53/173.42 [4758]~P71(x47583)+E(x47581,x47582)+~E(f312(f88(x47583),x47581),f312(f88(x47583),x47582))
% 173.53/173.42 [4759]~P88(x47593)+E(x47591,x47592)+~E(f312(f88(x47593),x47591),f312(f88(x47593),x47592))
% 173.53/173.42 [4760]~P100(x47603)+E(x47601,x47602)+~E(f312(f114(x47603),x47601),f312(f114(x47603),x47602))
% 173.53/173.42 [4761]~P89(x47613)+E(x47611,x47612)+~E(f312(f116(x47613),x47611),f312(f116(x47613),x47612))
% 173.53/173.42 [4762]~P103(x47623)+E(x47621,x47622)+~E(f312(f281(x47623),x47621),f312(f281(x47623),x47622))
% 173.53/173.42 [4763]~P103(x47633)+E(x47631,x47632)+~E(f312(f280(x47633),x47631),f312(f280(x47633),x47632))
% 173.53/173.42 [4764]~P103(x47643)+E(x47641,x47642)+~E(f312(f234(x47643),x47641),f312(f234(x47643),x47642))
% 173.53/173.42 [4765]~P103(x47653)+E(x47651,x47652)+~E(f312(f279(x47653),x47651),f312(f279(x47653),x47652))
% 173.53/173.42 [4864]~P63(x48641)+~P22(f312(x48642,x48643))+P22(f312(f66(x48641),x48642))
% 173.53/173.42 [4899]~P63(x48993)+P22(f312(x48991,x48992))+~P22(f312(f67(x48993),x48991))
% 173.53/173.42 [4990]~P140(x49901,x49902,x49903)+~E(x49902,f2(a1))+P22(f312(x49901,f2(a1)))
% 173.53/173.42 [5024]~P101(x50242)+~P22(f312(x50241,x50243))+P22(f312(x50241,f231(x50242,x50241)))
% 173.53/173.42 [5030]~E(x50301,f2(a852))+E(f365(x50301,x50302,x50303),f189(f860(x50303,a845)))+~E(f312(f53(x50303),x50302),f312(a126,x50301))
% 173.53/173.42 [5185]~E(x51852,f2(a852))+E(f312(f246(a852,a852),x51851),f2(a852))+~P22(f312(f56(x51853,x51852),x51851))
% 173.53/173.42 [5229]P22(f312(x52291,x52292))+~E(x52293,f312(f114(a1),x52292))+~P22(f312(x52291,f312(a118,x52293)))
% 173.53/173.42 [5691]~E(x56913,f2(a852))+~P22(f312(x56911,x56912))+P22(f312(x56911,f54(a852,x56912,x56913)))
% 173.53/173.42 [5739]~P101(x57391)+~P22(f312(x57392,x57393))+~P22(f312(f312(f228(x57391),x57393),f231(x57391,x57392)))
% 173.53/173.42 [5816]~P22(f312(a24,x58163))+~P22(f312(a24,x58162))+P22(f312(a24,f33(x58161,x58162,x58163)))
% 173.53/173.42 [5846]~P63(x58463)+~P7(x58463,x58461,x58462)+P22(f312(x58461,f666(x58462,x58461,x58463)))
% 173.53/173.42 [6086]~E(x60863,f2(a852))+P22(f312(x60861,x60862))+~P22(f312(x60861,f54(a852,x60862,x60863)))
% 173.53/173.42 [6097]~P31(x60971)+~P22(f312(f312(f227(x60971),x60972),f312(x60973,x60972)))+P22(f312(f312(f227(x60971),x60972),f110(x60971,x60973)))
% 173.53/173.42 [6233]~P63(x62331)+P8(x62331,x62332,x62333)+~P22(f312(x62332,f667(x62333,x62332,x62331)))
% 173.53/173.42 [6748]E(x67481,f2(a852))+~P22(f312(x67482,f332(x67481,x67483,x67482)))+P22(f312(x67482,f54(a852,x67483,x67481)))
% 173.53/173.42 [6855]~P31(x68551)+~P22(f312(f312(f227(x68551),x68552),f678(x68553,x68552,x68551)))+P22(f312(f312(f227(x68551),x68552),f49(x68551,x68553)))
% 173.53/173.42 [6857]~P22(f312(x68571,x68572))+~P22(f312(x68571,f332(x68573,x68572,x68571)))+P22(f312(x68571,f54(a852,x68572,x68573)))
% 173.53/173.42 [6963]E(x69631,f127(x69632))+E(f312(f312(f147(x69632),f629(x69633,x69631,x69632)),f632(x69633,x69631,x69632)),x69631)+~P22(f312(f312(f314(f853(x69632)),x69631),f157(x69632,x69633)))
% 173.53/173.42 [6998]~P111(x69981)+~P22(f312(f312(f314(x69981),x69982),f123(x69981)))+P22(f312(f312(f314(x69981),f312(f312(f240(x69981),x69982),x69983)),f123(x69981)))
% 173.53/173.42 [7574]E(x75741,f127(x75742))+~P22(f312(f312(f314(f853(x75742)),x75741),f157(x75742,x75743)))+P22(f312(f312(f314(f853(x75742)),f632(x75743,x75741,x75742)),f157(x75742,x75743)))
% 173.53/173.42 [7627]E(x76271,f2(a852))+E(f312(f312(f89(a852),f312(f312(f90(a852),x76271),f333(x76271,x76272,x76273))),f332(x76271,x76272,x76273)),x76272)+P22(f312(x76273,f54(a852,x76272,x76271)))
% 173.53/173.42 [7665]P22(f312(f312(f228(a1),x76651),f334(x76652,x76653,x76651)))+P22(f312(f312(x76653,f312(f47(a1,x76652),x76651)),f54(a1,x76652,x76651)))+~P22(f312(f312(f228(a1),x76651),f2(a1)))
% 173.53/173.42 [7671]~P22(f312(x76713,x76712))+E(f312(f312(f89(a852),f312(f312(f90(a852),x76711),f333(x76711,x76712,x76713))),f332(x76711,x76712,x76713)),x76712)+P22(f312(x76713,f54(a852,x76712,x76711)))
% 173.53/173.42 [7997]P22(f312(f312(x79972,f312(f47(a1,x79971),x79973)),f54(a1,x79971,x79973)))+~P22(f312(f312(f228(a1),x79973),f2(a1)))+P22(f312(f312(f227(a1),f334(x79971,x79972,x79973)),f2(a1)))
% 173.53/173.42 [8223]E(f312(f312(f89(a1),f312(f312(f90(a1),x82231),f335(x82232,x82233,x82231))),f334(x82232,x82233,x82231)),x82232)+P22(f312(f312(x82233,f312(f47(a1,x82232),x82231)),f54(a1,x82232,x82231)))+~P22(f312(f312(f228(a1),x82231),f2(a1)))
% 173.53/173.42 [8480]~P22(f312(f312(x84801,f335(x84802,x84801,x84803)),f334(x84802,x84801,x84803)))+P22(f312(f312(x84801,f312(f47(a1,x84802),x84803)),f54(a1,x84802,x84803)))+~P22(f312(f312(f228(a1),x84803),f2(a1)))
% 173.53/173.42 [8737]~P103(x87371)+~P33(x87371,x87373)+P33(x87371,f146(x87371,x87371,f5(x87371),x87372,x87373))
% 173.53/173.42 [9239]~P118(x92392)+E(x92391,f2(x92392))+~P22(f312(f312(f227(x92392),f312(f312(f89(x92392),f312(f312(f90(x92392),x92393),x92393)),f312(f312(f90(x92392),x92391),x92391))),f2(x92392)))
% 173.53/173.42 [9240]~P118(x92402)+E(x92401,f2(x92402))+~P22(f312(f312(f227(x92402),f312(f312(f89(x92402),f312(f312(f90(x92402),x92401),x92401)),f312(f312(f90(x92402),x92403),x92403))),f2(x92402)))
% 173.53/173.42 [10016]~P112(x100161)+~P22(f312(f312(f228(x100161),x100162),f2(x100161)))+P22(f312(f312(f228(x100161),f312(f312(f240(x100161),x100162),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x100163)))),f2(x100161)))
% 173.53/173.42 [10025]~P112(x100252)+E(x100251,f2(x100252))+~P22(f312(f312(f227(x100252),f312(f312(f89(x100252),f312(f312(f240(x100252),x100253),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x100252),x100251),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f2(x100252)))
% 173.53/173.42 [10026]~P112(x100262)+E(x100261,f2(x100262))+~P22(f312(f312(f227(x100262),f312(f312(f89(x100262),f312(f312(f240(x100262),x100261),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x100262),x100263),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f2(x100262)))
% 173.53/173.42 [4717]~E(x47172,x47173)+~P30(x47171)+E(f312(f312(f21(x47171),x47172),x47173),f2(x47171))
% 173.53/173.42 [4718]~E(x47182,x47183)+~P71(x47181)+E(f312(f312(f21(x47181),x47182),x47183),f2(x47181))
% 173.53/173.42 [4729]~P136(x47291)+~E(x47293,f2(x47291))+E(f312(f312(f89(x47291),x47292),x47293),x47292)
% 173.53/173.42 [4745]~P133(x47451)+~E(x47453,f2(x47451))+E(f312(f312(f90(x47451),x47452),x47453),f2(x47451))
% 173.53/173.42 [4746]~P133(x47461)+~E(x47462,f2(x47461))+E(f312(f312(f90(x47461),x47462),x47463),f2(x47461))
% 173.53/173.42 [4767]~E(x47673,f127(x47671))+~E(x47672,f127(x47671))+E(f312(f312(f129(x47671),x47672),x47673),f127(x47671))
% 173.53/173.42 [4854]~P136(x48542)+E(x48541,f2(x48542))+~E(f312(f312(f89(x48542),x48543),x48541),x48543)
% 173.53/173.42 [4855]~P71(x48551)+~E(x48552,f312(f88(x48551),x48553))+E(f312(f312(f89(x48551),x48552),x48553),f2(x48551))
% 173.53/173.42 [4862]E(x48621,f127(x48622))+E(x48623,f2(a852))+~E(f312(f312(f169(x48622),x48623),x48621),f127(x48622))
% 173.53/173.42 [4868]~P30(x48683)+E(x48681,x48682)+~E(f312(f312(f21(x48683),x48681),x48682),f2(x48683))
% 173.53/173.42 [4869]~P71(x48693)+E(x48691,x48692)+~E(f312(f312(f21(x48693),x48691),x48692),f2(x48693))
% 173.53/173.42 [4879]~P134(x48792)+E(x48791,f2(x48792))+~E(f312(f312(f240(x48792),x48791),x48793),f2(x48792))
% 173.53/173.42 [4880]~P94(x48802)+E(x48801,f189(x48802))+~E(f312(f312(f124(x48802),x48803),x48801),f189(x48802))
% 173.53/173.42 [4881]~P94(x48812)+E(x48811,f189(x48812))+~E(f312(f312(f124(x48812),x48811),x48813),f189(x48812))
% 173.53/173.42 [4882]~P97(x48822)+E(x48821,f235(x48822))+~E(f312(f312(f115(x48822),x48823),x48821),f235(x48822))
% 173.53/173.42 [4883]~P97(x48832)+E(x48831,f235(x48832))+~E(f312(f312(f115(x48832),x48831),x48833),f235(x48832))
% 173.53/173.42 [4944]~P71(x49442)+E(x49441,f312(f88(x49442),x49443))+~E(f312(f312(f89(x49442),x49441),x49443),f2(x49442))
% 173.53/173.42 [4945]~P71(x49451)+E(f312(f88(x49451),x49452),x49453)+~E(f312(f312(f89(x49451),x49452),x49453),f2(x49451))
% 173.53/173.42 [4947]~E(x49472,x49473)+~P102(x49471)+P22(f312(f312(f227(x49471),x49472),x49473))
% 173.53/173.42 [4949]~E(x49492,x49493)+~P105(x49491)+P22(f312(f312(f227(x49491),x49492),x49493))
% 173.53/173.42 [5046]~P113(x50461)+~E(x50462,f312(f88(x50461),x50463))+E(f312(f312(f90(x50461),x50462),x50462),f312(f312(f90(x50461),x50463),x50463))
% 173.53/173.42 [5054]~P103(x50541)+~P33(x50541,x50543)+P33(x50541,f312(f312(f169(x50541),x50542),x50543))
% 173.53/173.42 [5055]~P103(x50551)+~P33(x50551,x50553)+P33(x50551,f312(f312(f134(x50551),x50552),x50553))
% 173.53/173.42 [5096]E(x50961,x50962)+E(x50963,f2(a852))+~E(f312(f312(f90(a852),x50963),x50961),f312(f312(f90(a852),x50963),x50962))
% 173.53/173.42 [5097]E(x50971,x50972)+E(x50973,f2(a852))+~E(f312(f312(f90(a852),x50971),x50973),f312(f312(f90(a852),x50972),x50973))
% 173.53/173.42 [5177]~E(x51772,x51773)+~P105(x51771)+E(f283(x51771,x51772,x51773),f312(f312(f289(x51771),x51772),f189(f860(x51771,a845))))
% 173.53/173.42 [5227]~E(x52271,x52272)+~P103(x52273)+~P22(f312(f312(f228(x52273),x52271),x52272))
% 173.53/173.42 [5228]~E(x52281,x52282)+~P105(x52283)+~P22(f312(f312(f228(x52283),x52281),x52282))
% 173.53/173.42 [5237]~P105(x52371)+E(f312(f282(x52371,x52372),x52373),f189(f860(x52371,a845)))+P22(f312(f312(f228(x52371),x52372),x52373))
% 173.53/173.42 [5282]~P105(x52821)+E(f284(x52821,x52822,x52823),f189(f860(x52821,a845)))+P22(f312(f312(f228(x52821),x52822),x52823))
% 173.53/173.42 [5283]~P105(x52831)+E(f283(x52831,x52832,x52833),f189(f860(x52831,a845)))+P22(f312(f312(f227(x52831),x52832),x52833))
% 173.53/173.42 [5284]~P105(x52841)+E(f189(f860(x52841,a845)),f284(x52841,x52842,x52843))+P22(f312(f312(f228(x52841),x52842),x52843))
% 173.53/173.42 [5285]~P105(x52851)+E(f189(f860(x52851,a845)),f283(x52851,x52852,x52853))+P22(f312(f312(f227(x52851),x52852),x52853))
% 173.53/173.42 [5291]~P98(x52911)+~E(f312(f312(f124(x52911),x52912),x52913),x52913)+P22(f312(f312(f227(x52911),x52912),x52913))
% 173.53/173.42 [5292]~P99(x52921)+~E(f312(f312(f115(x52921),x52922),x52923),x52922)+P22(f312(f312(f227(x52921),x52922),x52923))
% 173.53/173.42 [5293]~P103(x52931)+~E(f312(f312(f225(x52931),x52932),x52933),x52932)+P22(f312(f312(f227(x52931),x52932),x52933))
% 173.53/173.42 [5294]~P103(x52941)+~E(f312(f312(f226(x52941),x52942),x52943),x52943)+P22(f312(f312(f227(x52941),x52942),x52943))
% 173.53/173.42 [5312]~P103(x53121)+P33(x53121,x53122)+~P33(x53121,f312(f312(f147(x53121),x53123),x53122))
% 173.53/173.42 [5313]~P103(x53131)+P33(x53131,x53132)+~P33(x53131,f312(f312(f129(x53131),x53133),x53132))
% 173.53/173.42 [5314]~P103(x53141)+P33(x53141,x53142)+~P33(x53141,f312(f312(f129(x53141),x53142),x53143))
% 173.53/173.42 [5383]~P103(x53831)+P22(f312(f312(f227(x53831),x53833),x53832))+P22(f312(f312(f228(x53831),x53832),x53833))
% 173.53/173.42 [5385]~P103(x53851)+P22(f312(f312(f227(x53851),x53853),x53852))+P22(f312(f312(f227(x53851),x53852),x53853))
% 173.53/173.42 [5422]~P98(x54221)+E(f312(f312(f124(x54221),x54222),x54223),x54222)+~P22(f312(f312(f227(x54221),x54223),x54222))
% 173.53/173.42 [5424]~P98(x54241)+E(f312(f312(f124(x54241),x54242),x54243),x54243)+~P22(f312(f312(f227(x54241),x54242),x54243))
% 173.53/173.42 [5425]~P99(x54251)+E(f312(f312(f115(x54251),x54252),x54253),x54253)+~P22(f312(f312(f227(x54251),x54253),x54252))
% 173.53/173.42 [5427]~P99(x54271)+E(f312(f312(f115(x54271),x54272),x54273),x54272)+~P22(f312(f312(f227(x54271),x54272),x54273))
% 173.53/173.42 [5428]~P103(x54281)+E(f312(f312(f225(x54281),x54282),x54283),x54283)+~P22(f312(f312(f227(x54281),x54283),x54282))
% 173.53/173.42 [5430]~P103(x54301)+E(f312(f312(f225(x54301),x54302),x54303),x54302)+~P22(f312(f312(f227(x54301),x54302),x54303))
% 173.53/173.42 [5431]~P103(x54311)+E(f312(f312(f226(x54311),x54312),x54313),x54312)+~P22(f312(f312(f227(x54311),x54313),x54312))
% 173.53/173.42 [5433]~P103(x54331)+E(f312(f312(f226(x54331),x54332),x54333),x54333)+~P22(f312(f312(f227(x54331),x54332),x54333))
% 173.53/173.42 [5440]~P114(x54402)+E(x54401,f2(x54402))+E(f312(f312(f268(x54402),f312(f88(x54402),x54403)),f312(f88(x54402),x54401)),f312(f312(f268(x54402),x54403),x54401))
% 173.53/173.42 [5475]~E(x54753,f2(a852))+~P22(f312(x54751,f2(a852)))+P22(f312(x54751,f312(f47(a852,x54752),x54753)))
% 173.53/173.42 [5487]~P105(x54871)+E(f312(f282(x54871,x54872),x54873),f189(f860(x54871,a845)))+~P22(f312(f312(f227(x54871),x54873),x54872))
% 173.53/173.42 [5520]~P105(x55201)+E(f285(x55201,x55202,x55203),f189(f860(x55201,a845)))+~P22(f312(f312(f227(x55201),x55203),x55202))
% 173.53/173.42 [5521]~P105(x55211)+E(f284(x55211,x55212,x55213),f189(f860(x55211,a845)))+~P22(f312(f312(f227(x55211),x55213),x55212))
% 173.53/173.42 [5522]~P105(x55221)+E(f283(x55221,x55222,x55223),f189(f860(x55221,a845)))+~P22(f312(f312(f228(x55221),x55223),x55222))
% 173.53/173.42 [5568]~P101(x55681)+~P22(f312(x55682,x55683))+P22(f312(f312(f227(x55681),f231(x55681,x55682)),x55683))
% 173.53/173.42 [5579]~E(f312(f312(f21(a852),x55791),x55793),x55792)+E(x55791,f312(f312(f89(a852),x55792),x55793))+~P22(f312(f312(f227(a852),x55793),x55791))
% 173.53/173.42 [5580]~E(x55801,f312(f312(f89(a852),x55803),x55802))+E(f312(f312(f21(a852),x55801),x55802),x55803)+~P22(f312(f312(f227(a852),x55802),x55801))
% 173.53/173.42 [5619]~P22(f312(x56191,x56193))+P22(f312(x56191,f430(x56191,x56192)))+~P22(f312(f312(f227(a852),x56193),x56192))
% 173.53/173.42 [5620]~P22(f312(x56201,x56203))+P22(f312(x56201,f462(x56201,x56202)))+~P22(f312(f312(f228(a852),x56203),x56202))
% 173.53/173.42 [5629]~P105(x56291)+~E(f312(f282(x56291,x56292),x56293),f189(f860(x56291,a845)))+~P22(f312(f312(f228(x56291),x56292),x56293))
% 173.53/173.42 [5634]~P102(x56341)+~P22(f312(f312(f228(x56341),x56342),x56343))+P22(f312(f312(f227(x56341),x56342),x56343))
% 173.53/173.42 [5636]~P105(x56361)+~P22(f312(f312(f228(x56361),x56362),x56363))+P22(f312(f312(f227(x56361),x56362),x56363))
% 173.53/173.42 [5733]~P105(x57331)+~E(f284(x57331,x57332,x57333),f189(f860(x57331,a845)))+~P22(f312(f312(f228(x57331),x57332),x57333))
% 173.53/173.42 [5734]~P105(x57341)+~E(f283(x57341,x57342,x57343),f189(f860(x57341,a845)))+~P22(f312(f312(f227(x57341),x57342),x57343))
% 173.53/173.42 [5735]~P105(x57351)+~E(f189(f860(x57351,a845)),f284(x57351,x57352,x57353))+~P22(f312(f312(f228(x57351),x57352),x57353))
% 173.53/173.42 [5736]~P105(x57361)+~E(f189(f860(x57361,a845)),f283(x57361,x57362,x57363))+~P22(f312(f312(f227(x57361),x57362),x57363))
% 173.53/173.42 [5745]P22(f312(x57451,x57452))+~P22(f312(x57451,f454(x57451,x57453)))+~P22(f312(f312(f227(a852),x57452),x57453))
% 173.53/173.42 [5746]P22(f312(x57461,x57462))+~P22(f312(x57461,f463(x57461,x57463)))+~P22(f312(f312(f228(a852),x57462),x57463))
% 173.53/173.42 [5753]~E(x57531,f312(a126,x57533))+P22(f312(f312(f228(a852),x57531),f312(a126,x57532)))+~P22(f312(f312(f228(a852),x57533),x57532))
% 173.53/173.42 [5769]E(x57691,x57692)+~E(f312(f312(f90(a852),x57693),x57691),f312(f312(f90(a852),x57693),x57692))+~P22(f312(f312(f228(a852),f2(a852)),x57693))
% 173.53/173.42 [5772]~E(x57722,f2(a852))+P22(f312(x57721,f2(a852)))+~P22(f312(x57721,f312(f47(a852,x57723),x57722)))
% 173.53/173.42 [5827]E(f312(x58271,f495(x58271,x58272,x58273)),f87(a852))+~E(f312(f312(f6(x58273,a852),x58271),x58272),f87(a852))+~P22(f312(f70(x58273),x58272))
% 173.53/173.42 [5837]~P31(x58371)+P22(f312(f312(f227(x58371),x58372),f48(x58371,x58373)))+~P22(f312(f312(f314(x58371),x58372),x58373))
% 173.53/173.42 [5867]~P102(x58671)+~P22(f312(f312(f228(x58671),x58673),x58672))+~P22(f312(f312(f228(x58671),x58672),x58673))
% 173.53/173.42 [5868]~P102(x58681)+~P22(f312(f312(f227(x58681),x58683),x58682))+~P22(f312(f312(f228(x58681),x58682),x58683))
% 173.53/173.42 [5869]~P103(x58691)+~P22(f312(f312(f228(x58691),x58693),x58692))+~P22(f312(f312(f228(x58691),x58692),x58693))
% 173.53/173.42 [5872]~P103(x58721)+~P22(f312(f312(f227(x58721),x58723),x58722))+~P22(f312(f312(f228(x58721),x58722),x58723))
% 173.53/173.42 [5873]~P105(x58731)+~P22(f312(f312(f228(x58731),x58733),x58732))+~P22(f312(f312(f228(x58731),x58732),x58733))
% 173.53/173.42 [5907]~E(f312(x59072,f395(x59072,x59073,x59071)),f87(a852))+E(f312(f312(f9(x59071,a852),x59072),x59073),f87(a852))+~P22(f312(f70(x59071),x59073))
% 173.53/173.42 [5908]~E(f312(x59082,f483(x59082,x59083,x59081)),f2(a852))+E(f312(f312(f6(x59081,a852),x59082),x59083),f2(a852))+~P22(f312(f70(x59081),x59083))
% 173.53/173.42 [5925]~P104(x59251)+~P22(f312(f312(f228(x59251),x59253),x59252))+P22(f312(f312(f314(x59251),x59252),f312(f280(x59251),x59253)))
% 173.53/173.42 [5926]~P104(x59261)+~P22(f312(f312(f227(x59261),x59263),x59262))+P22(f312(f312(f314(x59261),x59262),f312(f234(x59261),x59263)))
% 173.53/173.42 [5927]~P104(x59271)+~P22(f312(f312(f227(x59271),x59272),x59273))+P22(f312(f312(f314(x59271),x59272),f312(f281(x59271),x59273)))
% 173.53/173.42 [5928]~P104(x59281)+~P22(f312(f312(f228(x59281),x59282),x59283))+P22(f312(f312(f314(x59281),x59282),f312(f279(x59281),x59283)))
% 173.53/173.42 [5939]E(f312(x59391,f492(x59391,x59392,x59393)),f312(a126,f2(a852)))+~E(f312(f312(f6(x59393,a852),x59391),x59392),f312(a126,f2(a852)))+~P22(f312(f70(x59393),x59392))
% 173.53/173.42 [6013]~P31(x60131)+~P22(f312(f312(f314(x60131),x60133),x60132))+P22(f312(f312(f227(x60131),f49(x60131,x60132)),x60133))
% 173.53/173.42 [6030]~P22(f312(f312(f227(a852),x60301),x60303))+P22(f312(f312(f227(a852),x60301),x60302))+~P22(f312(f312(f227(a852),x60303),x60302))
% 173.53/173.42 [6031]~P22(f312(f312(f227(a1),x60311),x60313))+P22(f312(f312(f227(a1),x60311),x60312))+~P22(f312(f312(f227(a1),x60313),x60312))
% 173.53/173.42 [6048]~P104(x60481)+~P22(f312(f312(f314(x60481),x60483),f312(f280(x60481),x60482)))+P22(f312(f312(f228(x60481),x60482),x60483))
% 173.53/173.42 [6049]~P104(x60491)+~P22(f312(f312(f314(x60491),x60492),f312(f279(x60491),x60493)))+P22(f312(f312(f228(x60491),x60492),x60493))
% 173.53/173.42 [6050]~P104(x60501)+~P22(f312(f312(f314(x60501),x60503),f312(f234(x60501),x60502)))+P22(f312(f312(f227(x60501),x60502),x60503))
% 173.53/173.43 [6051]~P104(x60511)+~P22(f312(f312(f314(x60511),x60512),f312(f281(x60511),x60513)))+P22(f312(f312(f227(x60511),x60512),x60513))
% 173.53/173.43 [6171]P22(f312(x61711,x61712))+~P22(f312(x61711,f823(x61711)))+~P22(f312(f312(f314(x61713),x61712),f235(f860(x61713,a845))))
% 173.53/173.43 [6232]~P105(x62321)+~P49(a852,x62321,x62322)+P22(f312(f312(f227(x62321),f312(x62322,x62323)),f312(x62322,f312(a126,x62323))))
% 173.53/173.43 [6269]~P66(x62691)+P22(f312(f312(f228(x62691),f2(x62691)),f505(x62693,x62692,x62691)))+P22(f312(f312(f227(x62691),x62692),x62693))
% 173.53/173.43 [6335]~P76(x63351)+~P22(f312(f312(f228(x63351),x63353),f312(f88(x63351),x63352)))+P22(f312(f312(f228(x63351),x63352),f312(f88(x63351),x63353)))
% 173.53/173.43 [6337]~P76(x63371)+~P22(f312(f312(f227(x63371),x63373),f312(f88(x63371),x63372)))+P22(f312(f312(f227(x63371),x63372),f312(f88(x63371),x63373)))
% 173.53/173.43 [6348]~P22(f312(f312(f228(a852),x63481),x63483))+~P22(f312(f312(f228(a852),x63483),x63482))+P22(f312(f312(f228(a852),f312(a126,x63481)),x63482))
% 173.53/173.43 [6375]~P112(x63751)+P22(f312(f312(f228(x63751),f312(f116(x63751),x63752)),f312(f116(x63751),x63753)))+~P22(f312(f312(f228(a1),x63752),x63753))
% 173.53/173.43 [6376]~P117(x63761)+P22(f312(f312(f228(x63761),f312(f114(x63761),x63762)),f312(f114(x63761),x63763)))+~P22(f312(f312(f228(a852),x63762),x63763))
% 173.53/173.43 [6377]~P117(x63771)+P22(f312(f312(f227(x63771),f312(f114(x63771),x63772)),f312(f114(x63771),x63773)))+~P22(f312(f312(f227(a852),x63772),x63773))
% 173.53/173.43 [6378]~P112(x63781)+P22(f312(f312(f227(x63781),f312(f116(x63781),x63782)),f312(f116(x63781),x63783)))+~P22(f312(f312(f227(a1),x63782),x63783))
% 173.53/173.43 [6384]~P103(x63841)+E(f312(f312(f124(f860(x63841,a845)),f312(f279(x63841),x63842)),f312(f282(x63841,x63842),x63843)),f312(f279(x63841),x63843))+~P22(f312(f312(f227(x63841),x63842),x63843))
% 173.53/173.43 [6412]~P76(x64121)+~P22(f312(f312(f228(x64121),x64123),x64122))+P22(f312(f312(f228(x64121),f312(f88(x64121),x64122)),f312(f88(x64121),x64123)))
% 173.53/173.43 [6414]~P76(x64141)+~P22(f312(f312(f227(x64141),x64143),x64142))+P22(f312(f312(f227(x64141),f312(f88(x64141),x64142)),f312(f88(x64141),x64143)))
% 173.53/173.43 [6416]~P88(x64161)+~P22(f312(f312(f227(x64161),x64163),x64162))+P22(f312(f312(f227(x64161),f312(f88(x64161),x64162)),f312(f88(x64161),x64163)))
% 173.53/173.43 [6442]E(x64421,f2(a852))+P22(f312(x64422,f330(x64421,x64423,x64422)))+~P22(f312(x64422,f312(f47(a852,x64423),x64421)))
% 173.53/173.43 [6446]~P103(x64461)+E(f312(f312(f124(f860(x64461,a845)),f312(f281(x64461),x64462)),f285(x64461,x64462,x64463)),f312(f279(x64461),x64463))+~P22(f312(f312(f228(x64461),x64462),x64463))
% 173.53/173.43 [6447]~P103(x64471)+E(f312(f312(f124(f860(x64471,a845)),f312(f281(x64471),x64472)),f284(x64471,x64472,x64473)),f312(f281(x64471),x64473))+~P22(f312(f312(f227(x64471),x64472),x64473))
% 173.53/173.43 [6448]~P103(x64481)+E(f312(f312(f124(f860(x64481,a845)),f312(f279(x64481),x64482)),f283(x64481,x64482,x64483)),f312(f281(x64481),x64483))+~P22(f312(f312(f227(x64481),x64482),x64483))
% 173.53/173.43 [6482]~P103(x64821)+E(f312(f312(f124(f860(x64821,a845)),f312(f282(x64821,x64822),x64823)),f312(f234(x64821),x64823)),f312(f234(x64821),x64822))+~P22(f312(f312(f227(x64821),x64822),x64823))
% 173.53/173.43 [6549]~P31(x65491)+~P22(f312(f312(f227(x65491),f312(x65492,x65493)),x65493))+P22(f312(f312(f227(x65491),f109(x65491,x65492)),x65493))
% 173.53/173.43 [6568]P22(f312(x65681,f330(x65682,x65683,x65681)))+P22(f312(x65681,f2(a852)))+~P22(f312(x65681,f312(f47(a852,x65683),x65682)))
% 173.53/173.43 [6576]E(x65761,f2(a852))+~P22(f312(x65762,f331(x65761,x65763,x65762)))+P22(f312(x65762,f312(f47(a852,x65763),x65761)))
% 173.53/173.43 [6638]~P103(x66381)+E(f312(f312(f124(f860(x66381,a845)),f285(x66381,x66382,x66383)),f312(f234(x66381),x66383)),f312(f280(x66381),x66382))+~P22(f312(f312(f228(x66381),x66382),x66383))
% 173.53/173.43 [6639]~P103(x66391)+E(f312(f312(f124(f860(x66391,a845)),f284(x66391,x66392,x66393)),f312(f280(x66391),x66393)),f312(f280(x66391),x66392))+~P22(f312(f312(f227(x66391),x66392),x66393))
% 173.53/173.43 [6640]~P103(x66401)+E(f312(f312(f124(f860(x66401,a845)),f283(x66401,x66402,x66403)),f312(f280(x66401),x66403)),f312(f234(x66401),x66402))+~P22(f312(f312(f227(x66401),x66402),x66403))
% 173.53/173.43 [6648]~E(x66483,f312(f47(a852,x66481),x66482))+~P22(f312(f312(f228(a852),f2(a852)),x66482))+P22(f312(f312(f228(a852),x66481),f312(f312(f90(a852),x66482),f312(a126,x66483))))
% 173.53/173.43 [6658]P22(f312(x66581,x66582))+~P22(f312(f312(f227(a852),x66582),x66583))+P22(f312(f312(f314(a852),f454(x66581,x66583)),f283(a852,f2(a852),x66583)))
% 173.53/173.43 [6689]E(x66891,x66892)+~E(f312(f312(f161(x66893),x66891),f586(x66893,x66892,x66891)),f312(f312(f161(x66893),x66892),f586(x66893,x66892,x66891)))+~E(f312(f190(f853(x66893)),x66891),f312(f190(f853(x66893)),x66892))
% 173.53/173.43 [6708]~P22(f312(x67081,x67083))+~P22(f312(f312(f227(a852),x67083),x67082))+P22(f312(f312(f314(a852),f430(x67081,x67082)),f283(a852,f2(a852),x67082)))
% 173.53/173.43 [6709]~P22(f312(x67091,f331(x67093,x67092,x67091)))+~P22(f312(x67091,f2(a852)))+P22(f312(x67091,f312(f47(a852,x67092),x67093)))
% 173.53/173.43 [6745]~P22(f312(x67451,x67453))+P22(f312(x67451,f455(x67451,x67452)))+~P22(f312(f312(f314(a852),x67453),f283(a852,f2(a852),x67452)))
% 173.53/173.43 [6765]~P117(x67653)+~P22(f312(f312(f228(x67653),f312(f114(x67653),x67651)),f312(f114(x67653),x67652)))+P22(f312(f312(f228(a852),x67651),x67652))
% 173.53/173.43 [6766]~P112(x67663)+~P22(f312(f312(f228(x67663),f312(f116(x67663),x67661)),f312(f116(x67663),x67662)))+P22(f312(f312(f228(a1),x67661),x67662))
% 173.53/173.43 [6767]~P117(x67673)+~P22(f312(f312(f227(x67673),f312(f114(x67673),x67671)),f312(f114(x67673),x67672)))+P22(f312(f312(f227(a852),x67671),x67672))
% 173.53/173.43 [6768]~P112(x67683)+~P22(f312(f312(f227(x67683),f312(f116(x67683),x67681)),f312(f116(x67683),x67682)))+P22(f312(f312(f227(a1),x67681),x67682))
% 173.53/173.43 [6781]~P117(x67811)+~P22(f312(f312(f228(x67811),f87(x67811)),x67812))+P22(f312(f312(f228(x67811),f87(x67811)),f312(f312(f240(x67811),x67812),f312(a126,x67813))))
% 173.53/173.43 [6784]~P76(x67841)+~P22(f312(f312(f228(x67841),f312(f88(x67841),x67843)),f312(f88(x67841),x67842)))+P22(f312(f312(f228(x67841),x67842),x67843))
% 173.53/173.43 [6785]~P76(x67851)+~P22(f312(f312(f227(x67851),f312(f88(x67851),x67853)),f312(f88(x67851),x67852)))+P22(f312(f312(f227(x67851),x67852),x67853))
% 173.53/173.43 [6786]~P88(x67861)+~P22(f312(f312(f227(x67861),f312(f88(x67861),x67863)),f312(f88(x67861),x67862)))+P22(f312(f312(f227(x67861),x67862),x67863))
% 173.53/173.43 [6811]P22(f312(x68111,x68112))+~P22(f312(x68111,f456(x68111,x68113)))+~P22(f312(f312(f314(a852),x68112),f283(a852,f2(a852),x68113)))
% 173.53/173.43 [6832]~P66(x68321)+P22(f312(f312(f228(x68321),f505(x68323,x68322,x68321)),f87(x68321)))+P22(f312(f312(f227(x68321),x68322),x68323))
% 173.53/173.43 [6850]~E(f54(a852,x68503,x68502),f54(a852,x68501,x68502))+E(f312(f312(f89(a852),x68501),f312(f312(f90(a852),x68502),f718(x68501,x68502,x68503))),x68503)+~P22(f312(f312(f227(a852),x68501),x68503))
% 173.53/173.43 [6871]E(f312(x68711,f689(x68711,x68712,x68713)),f192(x68712))+~P22(f312(f70(x68713),f179(x68713,x68712,x68711)))+P22(f312(f70(x68713),f235(f860(x68713,a845))))
% 173.53/173.43 [6916]E(f312(f312(f9(x69161,a852),x69162),x69163),f87(a852))+~P22(f312(f70(x69161),x69163))+P22(f312(f312(f314(x69161),f395(x69162,x69163,x69161)),x69163))
% 173.53/173.43 [6917]E(f312(f312(f6(x69171,a852),x69172),x69173),f2(a852))+~P22(f312(f70(x69171),x69173))+P22(f312(f312(f314(x69171),f483(x69172,x69173,x69171)),x69173))
% 173.53/173.43 [6939]~P103(x69391)+~P22(f312(f312(f228(x69391),x69392),x69393))+P22(f312(f312(f228(f860(x69391,a845)),f312(f279(x69391),x69392)),f312(f279(x69391),x69393)))
% 173.53/173.43 [6940]~P105(x69401)+~P22(f312(f312(f227(x69401),x69402),x69403))+P22(f312(f312(f227(f860(x69401,a845)),f312(f281(x69401),x69402)),f312(f281(x69401),x69403)))
% 173.53/173.43 [6941]~P103(x69411)+~P22(f312(f312(f227(x69411),x69413),x69412))+P22(f312(f312(f227(f860(x69411,a845)),f312(f280(x69411),x69412)),f312(f280(x69411),x69413)))
% 173.53/173.43 [6942]~P105(x69421)+~P22(f312(f312(f227(x69421),x69423),x69422))+P22(f312(f312(f227(f860(x69421,a845)),f312(f234(x69421),x69422)),f312(f234(x69421),x69423)))
% 173.53/173.43 [6943]~P103(x69431)+~P22(f312(f312(f227(x69431),x69432),x69433))+P22(f312(f312(f227(f860(x69431,a845)),f312(f279(x69431),x69432)),f312(f279(x69431),x69433)))
% 173.53/173.43 [6950]E(x69501,f2(a852))+P22(f312(x69502,f312(f47(a852,x69503),x69501)))+P22(f312(f312(f228(a852),f338(x69501,x69503,x69502)),x69501))
% 173.53/173.43 [6951]~P31(x69511)+P22(f312(f312(f227(x69511),x69512),f49(x69511,x69513)))+P22(f312(f312(f314(x69511),f678(x69513,x69512,x69511)),x69513))
% 173.53/173.43 [6956]~P76(x69561)+P22(f312(f312(f228(x69561),f312(f312(f21(x69561),x69562),x69563)),f2(x69561)))+~P22(f312(f312(f228(x69561),x69562),x69563))
% 173.53/173.43 [6957]~P76(x69571)+P22(f312(f312(f227(x69571),f312(f312(f21(x69571),x69572),x69573)),f2(x69571)))+~P22(f312(f312(f227(x69571),x69572),x69573))
% 173.53/173.43 [7002]P22(f312(x70021,x70022))+P22(f312(f312(f227(a852),f456(x70021,x70023)),x70023))+~P22(f312(f312(f314(a852),x70022),f283(a852,f2(a852),x70023)))
% 173.53/173.43 [7038]~E(f312(f312(f6(x70381,a852),x70382),x70383),f87(a852))+~P22(f312(f70(x70381),x70383))+P22(f312(f312(f314(x70381),f495(x70382,x70383,x70381)),x70383))
% 173.53/173.43 [7039]~P22(f312(x70391,x70393))+P22(f312(f312(f227(a852),f455(x70391,x70392)),x70392))+~P22(f312(f312(f314(a852),x70393),f283(a852,f2(a852),x70392)))
% 173.53/173.43 [7082]~P31(x70821)+P22(f312(f312(f314(x70821),f676(x70823,x70822,x70821)),x70822))+P22(f312(f312(f227(x70821),f48(x70821,x70822)),x70823))
% 173.53/173.43 [7083]~P22(f312(x70831,f2(a852)))+P22(f312(x70831,f312(f47(a852,x70832),x70833)))+P22(f312(f312(f228(a852),f338(x70833,x70832,x70831)),x70833))
% 173.53/173.43 [7113]~E(f312(f312(f6(x71131,a852),x71132),x71133),f312(a126,f2(a852)))+~P22(f312(f70(x71131),x71133))+P22(f312(f312(f314(x71131),f492(x71132,x71133,x71131)),x71133))
% 173.53/173.43 [7124]E(x71241,f2(a852))+P22(f312(x71242,f54(a852,x71243,x71241)))+P22(f312(f312(f228(a852),f332(x71241,x71243,x71242)),x71241))
% 173.53/173.43 [7219]~P22(f312(x72191,x72192))+P22(f312(x72191,f54(a852,x72192,x72193)))+P22(f312(f312(f228(a852),f332(x72193,x72192,x72191)),x72193))
% 173.53/173.43 [7274]~P22(f312(f312(f228(a1),x72742),f2(a1)))+~P22(f312(f312(f227(a1),x72743),x72741))+P22(f312(f312(f227(a1),f312(f47(a1,x72741),x72742)),f312(f47(a1,x72743),x72742)))
% 173.53/173.43 [7282]~P22(f312(f312(f228(a852),f2(a852)),x72823))+~P22(f312(f312(f227(a852),x72823),x72822))+P22(f312(f312(f227(a852),f312(f47(a852,x72821),x72822)),f312(f47(a852,x72821),x72823)))
% 173.53/173.43 [7283]~P22(f312(f312(f228(a1),f2(a1)),x72832))+~P22(f312(f312(f227(a1),x72831),x72833))+P22(f312(f312(f227(a1),f312(f47(a1,x72831),x72832)),f312(f47(a1,x72833),x72832)))
% 173.53/173.43 [7340]E(x73401,f127(x73402))+~P22(f312(f312(f314(f853(x73402)),x73401),f157(x73402,x73403)))+P22(f312(f312(f314(x73402),f629(x73403,x73401,x73402)),x73403))
% 173.53/173.43 [7363]~P103(x73631)+E(f312(f312(f124(f860(x73631,a845)),f312(f312(f289(x73631),x73632),f189(f860(x73631,a845)))),f285(x73631,x73632,x73633)),f312(f282(x73631,x73632),x73633))+~P22(f312(f312(f228(x73631),x73632),x73633))
% 173.53/173.43 [7387]~P103(x73871)+E(f312(f312(f124(f860(x73871,a845)),f312(f312(f289(x73871),x73872),f189(f860(x73871,a845)))),f284(x73871,x73872,x73873)),f283(x73871,x73872,x73873))+~P22(f312(f312(f227(x73871),x73872),x73873))
% 173.53/173.43 [7493]~P103(x74931)+P22(f312(f312(f228(x74931),x74932),x74933))+~P22(f312(f312(f228(f860(x74931,a845)),f312(f279(x74931),x74932)),f312(f279(x74931),x74933)))
% 173.53/173.43 [7494]~P103(x74941)+P22(f312(f312(f227(x74941),x74942),x74943))+~P22(f312(f312(f227(f860(x74941,a845)),f312(f280(x74941),x74943)),f312(f280(x74941),x74942)))
% 173.53/173.43 [7495]~P105(x74951)+P22(f312(f312(f227(x74951),x74952),x74953))+~P22(f312(f312(f227(f860(x74951,a845)),f312(f234(x74951),x74953)),f312(f234(x74951),x74952)))
% 173.53/173.43 [7496]~P103(x74961)+P22(f312(f312(f227(x74961),x74962),x74963))+~P22(f312(f312(f227(f860(x74961,a845)),f312(f279(x74961),x74962)),f312(f279(x74961),x74963)))
% 173.53/173.43 [7497]~P105(x74971)+P22(f312(f312(f227(x74971),x74972),x74973))+~P22(f312(f312(f227(f860(x74971,a845)),f312(f281(x74971),x74972)),f312(f281(x74971),x74973)))
% 173.53/173.43 [7516]E(x75161,f2(a852))+E(f312(f312(f89(a852),f312(f312(f90(a852),x75161),f331(x75161,x75162,x75163))),f338(x75161,x75162,x75163)),x75162)+P22(f312(x75163,f312(f47(a852,x75162),x75161)))
% 173.53/173.43 [7520]~P76(x75201)+~P22(f312(f312(f228(x75201),f312(f312(f21(x75201),x75202),x75203)),f2(x75201)))+P22(f312(f312(f228(x75201),x75202),x75203))
% 173.53/173.43 [7521]~P76(x75211)+~P22(f312(f312(f227(x75211),f312(f312(f21(x75211),x75212),x75213)),f2(x75211)))+P22(f312(f312(f227(x75211),x75212),x75213))
% 173.53/173.43 [7614]E(f312(f312(f89(a852),f312(f312(f90(a852),x76141),f331(x76141,x76142,x76143))),f338(x76141,x76142,x76143)),x76142)+~P22(f312(x76143,f2(a852)))+P22(f312(x76143,f312(f47(a852,x76142),x76141)))
% 173.53/173.43 [7678]E(x76781,f2(a852))+~E(f312(f138(a852,a852,f89(a852),x76782),x76783),f2(a852))+~P22(f312(f312(f314(a852),x76781),f312(f168(a852),x76783)))
% 173.53/173.43 [7682]~P31(x76821)+~P22(f312(f312(f227(x76821),f676(x76823,x76822,x76821)),x76823))+P22(f312(f312(f227(x76821),f48(x76821,x76822)),x76823))
% 173.53/173.43 [7708]P22(f312(f312(f227(a1),f2(a1)),f336(x77081,x77082,x77083)))+P22(f312(f312(x77082,f312(f47(a1,x77081),x77083)),f54(a1,x77081,x77083)))+~P22(f312(f312(f228(a1),f2(a1)),x77083))
% 173.53/173.43 [7921]E(x79211,x79212)+~E(f312(f190(f853(x79213)),x79211),f312(f190(f853(x79213)),x79212))+~P22(f312(f312(f249(x79213,x79213,a845),a309),f587(x79213,x79211,x79212)))
% 173.53/173.43 [7988]~P41(x79882,x79883)+E(x79881,f189(f860(x79882,a845)))+~P22(f312(f312(f227(f860(x79882,a845)),x79881),f312(f264(x79882,x79882,x79883),x79881)))
% 173.53/173.43 [8008]P22(f312(f312(x80082,f312(f47(a1,x80081),x80083)),f54(a1,x80081,x80083)))+~P22(f312(f312(f228(a1),f2(a1)),x80083))+P22(f312(f312(f228(a1),f336(x80081,x80082,x80083)),x80083))
% 173.53/173.43 [8063]P50(x80631,x80632,x80633)+P22(f312(f312(f314(x80631),f419(x80633,x80632,x80631)),x80632))+P22(f312(f312(f314(f859(x80631,x80631)),f420(x80633,x80632,x80631)),x80633))
% 173.53/173.43 [8109]E(f312(f290(a852,a852,f312(f312(f7(a852,a852,a852),f21(a852)),x81091)),f312(f282(a852,x81092),x81093)),f189(f860(a852,a845)))+P22(f312(f312(f228(a852),x81091),x81093))+P22(f312(f312(f228(a852),x81092),x81093))
% 173.53/173.43 [8216]E(f312(f290(a852,a852,f312(f312(f7(a852,a852,a852),f21(a852)),x82161)),f312(f282(a852,x82162),x82163)),f312(f312(f289(a852),f2(a852)),f189(f860(a852,a845))))+P22(f312(f312(f228(a852),x82161),x82163))+~P22(f312(f312(f228(a852),x82162),x82163))
% 173.53/173.43 [8235]~P103(x82351)+E(f146(x82351,x82351,f5(x82351),x82352,x82353),x82353)+~P22(f312(f312(f314(x82351),x82352),f312(f168(x82351),x82353)))
% 173.53/173.43 [8236]E(f312(f312(f89(a1),f312(f312(f90(a1),x82361),f337(x82362,x82363,x82361))),f336(x82362,x82363,x82361)),x82362)+P22(f312(f312(x82363,f312(f47(a1,x82362),x82361)),f54(a1,x82362,x82361)))+~P22(f312(f312(f228(a1),f2(a1)),x82361))
% 173.53/173.43 [8252]P19(x82521,x82521,x82522,x82523)+~P22(f312(f70(x82521),x82523))+~P22(f312(f312(f227(f860(x82521,a845)),x82523),f312(f290(x82521,x82521,x82522),x82523)))
% 173.53/173.43 [8481]~P22(f312(f312(x84811,f337(x84812,x84811,x84813)),f336(x84812,x84811,x84813)))+P22(f312(f312(x84811,f312(f47(a1,x84812),x84813)),f54(a1,x84812,x84813)))+~P22(f312(f312(f228(a1),f2(a1)),x84813))
% 173.53/173.43 [9375]~P22(f312(f70(x93751),x93752))+~P22(f312(f312(f314(x93751),x93753),x93752))+P22(f312(f312(f228(a852),f312(f53(x93751),f312(f312(f21(f860(x93751,a845)),x93752),f312(f312(f289(x93751),x93753),f189(f860(x93751,a845)))))),f312(f53(x93751),x93752)))
% 173.53/173.43 [9975]P50(x99751,x99752,x99753)+~P22(f312(f312(f249(x99751,x99751,a845),f312(f312(f7(x99751,f860(x99751,a845),f860(x99751,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x99751,a845),f860(x99751,a845)),x99751),f8(a845,a845,x99751)),f312(f312(f8(a845,f860(a845,a845),x99751),a310),f312(f312(f7(x99751,f860(x99751,a845),a845),f314(x99751)),x99752)))),f312(f312(f7(x99751,f860(x99751,a845),a845),f314(x99751)),x99752))),f420(x99753,x99752,x99751)))+P22(f312(f312(f314(x99751),f419(x99753,x99752,x99751)),x99752))
% 173.53/173.43 [5402]~P114(x54022)+E(x54021,f2(x54022))+E(f312(f312(f268(x54022),x54023),f312(f88(x54022),x54021)),f312(f88(x54022),f312(f312(f268(x54022),x54023),x54021)))
% 173.53/173.43 [5538]~E(x55383,f189(f860(x55381,a845)))+~E(x55382,f189(f860(x55381,a845)))+E(f312(f312(f124(f860(x55381,a845)),x55382),x55383),f189(f860(x55381,a845)))
% 173.53/173.43 [5729]~P67(x57292)+E(x57291,f2(x57292))+E(f312(f312(f268(x57292),f312(f84(x57292),x57293)),f312(f84(x57292),x57291)),f312(f84(x57292),f312(f312(f268(x57292),x57293),x57291)))
% 173.53/173.43 [5893]~P22(f312(f70(x58931),x58933))+E(f312(f53(x58931),f312(f312(f289(x58931),x58932),x58933)),f312(a126,f312(f53(x58931),x58933)))+P22(f312(f312(f314(x58931),x58932),x58933))
% 173.53/173.43 [5985]~P22(f312(f70(x59851),x59853))+E(f312(f53(x59851),f312(f312(f289(x59851),x59852),x59853)),f312(f53(x59851),x59853))+~P22(f312(f312(f314(x59851),x59852),x59853))
% 173.53/173.43 [6016]~P22(f312(f70(x60161),x60163))+E(f312(f53(x60161),f312(f312(f289(x60161),x60162),x60163)),f312(f312(f89(a852),f87(a852)),f312(f53(x60161),x60163)))+P22(f312(f312(f314(x60161),x60162),x60163))
% 173.53/173.43 [6133]E(f312(f312(f89(a852),x61331),f822(x61331,x61332,x61333)),x61332)+~P22(f312(x61333,f2(a852)))+P22(f312(x61333,f312(f312(f21(a852),x61332),x61331)))
% 173.53/173.43 [6134]E(f312(f312(f89(a852),x61341),f826(x61341,x61342,x61343)),x61342)+~P22(f312(x61343,f2(a852)))+P22(f312(x61343,f312(f312(f21(a852),x61342),x61341)))
% 173.53/173.43 [6181]~P31(x61811)+~P22(f312(f70(x61811),x61813))+E(f312(f312(f73(x61811,x61811,f124(x61811)),x61812),x61813),f312(f312(f124(x61811),x61812),f48(x61811,x61813)))
% 173.53/173.43 [6182]~P31(x61821)+~P22(f312(f70(x61821),x61823))+E(f312(f312(f73(x61821,x61821,f115(x61821)),x61822),x61823),f312(f312(f115(x61821),x61822),f49(x61821,x61823)))
% 173.53/173.43 [6189]~P90(x61891)+~E(f312(f117(x61891),x61892),f312(f117(x61891),x61893))+P35(x61891,f312(f117(x61891),f312(f312(f89(a1),x61892),f312(f88(a1),x61893))))
% 173.53/173.43 [6196]~P111(x61961)+E(f312(f312(f21(x61961),f312(f114(x61961),x61962)),f312(f114(x61961),x61963)),f312(f114(x61961),f312(f312(f21(a852),x61962),x61963)))+~P22(f312(f312(f227(a852),x61963),x61962))
% 173.53/173.43 [6279]E(f312(f312(f89(a852),x62791),f822(x62791,x62792,x62793)),x62792)+P22(f312(f312(f228(a852),x62792),x62791))+P22(f312(x62793,f312(f312(f21(a852),x62792),x62791)))
% 173.53/173.43 [6280]E(f312(f312(f89(a852),x62801),f826(x62801,x62802,x62803)),x62802)+P22(f312(f312(f228(a852),x62802),x62801))+P22(f312(x62803,f312(f312(f21(a852),x62802),x62801)))
% 173.53/173.43 [6296]~P112(x62961)+E(f312(f312(f90(x62961),f312(f84(x62961),x62962)),x62963),f312(f84(x62961),f312(f312(f90(x62961),x62962),x62963)))+~P22(f312(f312(f227(x62961),f2(x62961)),x62963))
% 173.53/173.43 [6297]~P66(x62971)+E(f312(f312(f268(x62971),f312(f84(x62971),x62972)),x62973),f312(f84(x62971),f312(f312(f268(x62971),x62972),x62973)))+~P22(f312(f312(f228(x62971),f2(x62971)),x62973))
% 173.53/173.43 [6350]E(x63501,f127(x63502))+~E(f175(x63502,x63503),f127(f853(x63502)))+~P22(f312(f312(f314(f853(x63502)),x63501),f312(f168(f853(x63502)),x63503)))
% 173.53/173.43 [6392]~P22(f312(f133(x63921),x63923))+P22(f312(f312(f314(x63921),x63922),f312(f168(x63921),x63923)))+P22(f312(f133(x63921),f312(f312(f147(x63921),x63922),x63923)))
% 173.53/173.43 [6426]P22(f312(x64261,f2(a852)))+~P22(f312(f312(f228(a852),x64262),x64263))+~P22(f312(x64261,f312(f312(f21(a852),x64262),x64263)))
% 173.53/173.43 [6443]~P112(x64431)+P22(f312(f312(f228(x64431),x64432),x64433))+~P22(f312(f312(f228(x64431),f312(f84(x64431),x64432)),x64433))
% 173.53/173.43 [6445]~P83(x64451)+P22(f312(f312(f227(x64451),x64452),x64453))+~P22(f312(f312(f227(x64451),f312(f84(x64451),x64452)),x64453))
% 173.53/173.43 [6462]E(x64621,f127(x64622))+E(f312(f137(x64622),f312(f312(f134(x64622),x64623),x64621)),f312(f312(f161(x64622),x64621),x64623))+~P22(f312(f312(f228(a852),x64623),f312(f190(f853(x64622)),x64621)))
% 173.53/173.43 [6513]~P22(f312(x65131,x65133))+P22(f312(x65131,f484(x65131,x65132)))+~P22(f312(f312(f314(a852),x65133),f312(f282(a852,f2(a852)),x65132)))
% 173.53/173.43 [6534]P22(f312(x65341,x65342))+~P22(f312(f312(f228(a852),x65342),x65343))+P22(f312(f312(f314(a852),f463(x65341,x65343)),f312(f282(a852,f2(a852)),x65343)))
% 173.53/173.43 [6551]~P117(x65511)+~P22(f312(f312(f228(x65511),f2(x65511)),x65512))+P22(f312(f312(f228(x65511),f2(x65511)),f312(f312(f240(x65511),x65512),x65513)))
% 173.53/173.43 [6553]~P117(x65531)+~P22(f312(f312(f227(x65531),f2(x65531)),x65532))+P22(f312(f312(f227(x65531),f2(x65531)),f312(f312(f240(x65531),x65532),x65533)))
% 173.53/173.43 [6554]~P117(x65541)+~P22(f312(f312(f227(x65541),f87(x65541)),x65542))+P22(f312(f312(f227(x65541),f87(x65541)),f312(f312(f240(x65541),x65542),x65543)))
% 173.53/173.43 [6579]~P22(f312(x65791,x65793))+~P22(f312(f312(f228(a852),x65793),x65792))+P22(f312(f312(f314(a852),f462(x65791,x65792)),f312(f282(a852,f2(a852)),x65792)))
% 173.53/173.43 [6587]P22(f312(f70(x65871),x65872))+~P22(f312(f70(x65871),x65873))+~P22(f312(f312(f227(f860(x65871,a845)),x65872),x65873))
% 173.53/173.43 [6597]P22(f312(x65971,x65972))+~P22(f312(x65971,f464(x65971,x65973)))+~P22(f312(f312(f314(a852),x65972),f312(f282(a852,f2(a852)),x65973)))
% 173.53/173.43 [6611]~P118(x66112)+E(x66111,f2(x66112))+~E(f312(f312(f89(x66112),f312(f312(f90(x66112),x66113),x66113)),f312(f312(f90(x66112),x66111),x66111)),f2(x66112))
% 173.53/173.43 [6612]~P118(x66122)+E(x66121,f2(x66122))+~E(f312(f312(f89(x66122),f312(f312(f90(x66122),x66121),x66121)),f312(f312(f90(x66122),x66123),x66123)),f2(x66122))
% 173.53/173.43 [6663]~P103(x66631)+~P33(x66631,x66633)+P33(x66631,f312(f312(f145(x66631,x66631,f5(x66631)),x66632),x66633))
% 173.53/173.43 [6707]~P90(x67071)+E(f312(f117(x67071),x67072),f312(f117(x67071),x67073))+~P35(x67071,f312(f117(x67071),f312(f312(f89(a1),x67072),f312(f88(a1),x67073))))
% 173.53/173.43 [6770]E(x67701,f2(a1))+E(x67702,f2(a1))+~P22(f312(f57(x67702,x67702),f312(f312(f239(a1,a1),x67703),x67701)))
% 173.53/173.43 [6771]E(x67711,f87(a1))+E(x67712,f2(a1))+~P22(f312(f57(x67712,x67712),f312(f312(f239(a1,a1),x67711),x67713)))
% 173.53/173.43 [6782]P22(f312(x67821,x67822))+P22(f312(f312(f228(a852),f464(x67821,x67823)),x67823))+~P22(f312(f312(f314(a852),x67822),f312(f282(a852,f2(a852)),x67823)))
% 173.53/173.43 [6806]~P22(f312(x68061,f822(x68063,x68062,x68061)))+~P22(f312(x68061,f2(a852)))+P22(f312(x68061,f312(f312(f21(a852),x68062),x68063)))
% 173.53/173.43 [6807]~P22(f312(x68071,f826(x68073,x68072,x68071)))+~P22(f312(x68071,f2(a852)))+P22(f312(x68071,f312(f312(f21(a852),x68072),x68073)))
% 173.53/173.43 [6828]~P22(f312(x68281,x68283))+P22(f312(f312(f228(a852),f484(x68281,x68282)),x68282))+~P22(f312(f312(f314(a852),x68283),f312(f282(a852,f2(a852)),x68282)))
% 173.53/173.43 [6829]E(f312(f312(f21(a852),f312(f312(f21(a852),x68291),x68292)),f312(f312(f21(a852),x68293),x68292)),f312(f312(f21(a852),x68291),x68293))+~P22(f312(f312(f227(a852),x68292),x68291))+~P22(f312(f312(f227(a852),x68292),x68293))
% 173.53/173.43 [6865]~P76(x68651)+~P22(f312(f312(f228(x68651),f312(f88(x68651),x68653)),x68652))+P22(f312(f312(f228(x68651),f312(f88(x68651),x68652)),x68653))
% 173.53/173.43 [6866]~P112(x68661)+~P22(f312(f312(f228(x68661),f312(f84(x68661),x68662)),x68663))+P22(f312(f312(f228(x68661),f312(f88(x68661),x68662)),x68663))
% 173.53/173.43 [6868]~P76(x68681)+~P22(f312(f312(f227(x68681),f312(f88(x68681),x68683)),x68682))+P22(f312(f312(f227(x68681),f312(f88(x68681),x68682)),x68683))
% 173.53/173.43 [6870]~P83(x68701)+~P22(f312(f312(f227(x68701),f312(f84(x68701),x68702)),x68703))+P22(f312(f312(f227(x68701),f312(f88(x68701),x68702)),x68703))
% 173.53/173.43 [6910]~P22(f312(x69103,f822(x69102,x69101,x69103)))+P22(f312(f312(f228(a852),x69101),x69102))+P22(f312(x69103,f312(f312(f21(a852),x69101),x69102)))
% 173.53/173.43 [6911]~P22(f312(x69113,f826(x69112,x69111,x69113)))+P22(f312(f312(f228(a852),x69111),x69112))+P22(f312(x69113,f312(f312(f21(a852),x69111),x69112)))
% 173.53/173.43 [6959]~E(f679(x69593,x69592,x69591),f680(x69593,x69592,x69591))+E(f312(f312(f115(f860(x69591,a845)),x69592),f48(f860(x69591,a845),x69593)),f189(f860(x69591,a845)))+P22(f312(f312(f314(f860(x69591,a845)),x69592),x69593))
% 173.53/173.43 [6969]~P22(f312(f70(x69691),x69693))+P22(f312(f70(x69691),f49(f860(x69691,a845),x69692)))+~P22(f312(f312(f314(f860(x69691,a845)),x69693),x69692))
% 173.53/173.43 [7029]~P103(x70291)+E(f312(f312(f124(f860(x70291,a845)),f312(f282(x70291,x70292),x70293)),f312(f312(f289(x70291),x70293),f189(f860(x70291,a845)))),f283(x70291,x70292,x70293))+~P22(f312(f312(f227(x70291),x70292),x70293))
% 173.53/173.43 [7066]E(x70661,x70662)+~P22(f312(f312(f227(f860(x70663,a845)),x70661),x70662))+P22(f312(f312(f228(f860(x70663,a845)),x70661),x70662))
% 173.53/173.43 [7079]E(x70791,x70792)+~E(f312(f190(f853(x70793)),x70791),f312(f190(f853(x70793)),x70792))+P22(f312(f312(f228(a852),f586(x70793,x70791,x70792)),f312(f190(f853(x70793)),x70792)))
% 173.53/173.43 [7125]P3(x71251,x71252,x71253)+~E(f312(f238(x71251,x71251),x71253),x71252)+~E(f312(f312(f267(x71251,x71251,x71251),f312(f265(x71251,x71251),x71253)),x71253),x71253)
% 173.53/173.43 [7194]~P103(x71941)+E(f312(f312(f124(f860(x71941,a845)),f285(x71941,x71942,x71943)),f312(f312(f289(x71941),x71943),f189(f860(x71941,a845)))),f284(x71941,x71942,x71943))+~P22(f312(f312(f228(x71941),x71942),x71943))
% 173.53/173.43 [7297]~P22(f312(f70(x72971),x72973))+P22(f312(f312(f228(a852),f312(f53(x72971),x72972)),f312(f53(x72971),x72973)))+~P22(f312(f312(f228(f860(x72971,a845)),x72972),x72973))
% 173.53/173.43 [7298]~P22(f312(f70(x72981),x72983))+P22(f312(f312(f227(a852),f312(f53(x72981),x72982)),f312(f53(x72981),x72983)))+~P22(f312(f312(f227(f860(x72981,a845)),x72982),x72983))
% 173.53/173.43 [7334]~P22(f312(x73343,x73342))+P22(f312(f312(f195(x73341),x73342),f813(x73342,x73341,x73343)))+~P22(f312(f312(f195(f35(x73343,x73341)),x73342),x73342))
% 173.53/173.43 [7430]E(x74301,x74302)+~P22(f312(f312(f227(f860(x74303,a845)),x74302),x74301))+~P22(f312(f312(f227(f860(x74303,a845)),x74301),x74302))
% 173.53/173.43 [7433]~P103(x74331)+P33(x74331,x74332)+~P33(x74331,f312(f312(f145(x74331,x74331,f5(x74331)),x74333),x74332))
% 173.53/173.43 [7501]~P22(f312(f312(f228(a852),x75013),x75012))+~P22(f312(f312(f228(a852),x75013),x75011))+P22(f312(f312(f228(a852),f312(f312(f21(a852),x75011),x75012)),f312(f312(f21(a852),x75011),x75013)))
% 173.53/173.43 [7502]~P22(f312(f312(f228(a852),x75021),x75023))+~P22(f312(f312(f227(a852),x75022),x75021))+P22(f312(f312(f228(a852),f312(f312(f21(a852),x75021),x75022)),f312(f312(f21(a852),x75023),x75022)))
% 173.53/173.43 [7539]~P22(f312(f312(f228(a852),f2(a852)),x75392))+~P22(f312(f312(f228(a852),x75391),x75393))+P22(f312(f312(f228(a852),f312(f312(f90(a852),x75391),x75392)),f312(f312(f90(a852),x75393),x75392)))
% 173.53/173.43 [7540]~P22(f312(f312(f228(a852),f2(a852)),x75401))+~P22(f312(f312(f228(a852),x75402),x75403))+P22(f312(f312(f228(a852),f312(f312(f90(a852),x75401),x75402)),f312(f312(f90(a852),x75401),x75403)))
% 173.53/173.43 [7541]~P22(f312(f312(f228(a1),f2(a1)),x75411))+~P22(f312(f312(f228(a1),x75412),x75413))+P22(f312(f312(f228(a1),f312(f312(f90(a1),x75411),x75412)),f312(f312(f90(a1),x75411),x75413)))
% 173.53/173.43 [7669]~P22(f312(f70(x76691),x76693))+P22(f312(f312(f314(x76691),f398(x76692,x76693,x76691)),x76693))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f9(x76691,a852),x76692),x76693)))
% 173.53/173.43 [7670]~P22(f312(f70(x76701),x76703))+P22(f312(f312(f314(x76701),f542(x76702,x76703,x76701)),x76703))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f9(x76701,a852),x76702),x76703)))
% 173.53/173.43 [7954]E(x79541,f189(f860(x79542,a845)))+E(x79541,f312(f312(f289(x79542),x79543),f189(f860(x79542,a845))))+~P22(f312(f312(f227(f860(x79542,a845)),x79541),f312(f312(f289(x79542),x79543),f189(f860(x79542,a845)))))
% 173.53/173.43 [7972]~P63(x79721)+P8(x79721,x79722,x79723)+P22(f312(f312(f314(f853(x79721)),f667(x79723,x79722,x79721)),f312(f168(f853(x79721)),f63(x79721,x79723,f64(x79721)))))
% 173.53/173.43 [7990]~P22(f312(f312(f228(a852),f2(a852)),x79903))+P22(f312(f312(f228(a852),x79901),x79902))+~P22(f312(f312(f228(a852),f312(f312(f240(a852),x79903),x79901)),f312(f312(f240(a852),x79903),x79902)))
% 173.53/173.43 [7992]~P22(f312(f312(f228(a852),f2(a852)),x79923))+P22(f312(f312(f227(a852),x79921),x79922))+~P22(f312(f312(f227(a852),f312(f312(f90(a852),x79923),x79921)),f312(f312(f90(a852),x79923),x79922)))
% 173.53/173.43 [7993]~P22(f312(f312(f228(a852),f2(a852)),x79933))+P22(f312(f312(f227(a852),x79931),x79932))+~P22(f312(f312(f227(a852),f312(f312(f90(a852),x79931),x79933)),f312(f312(f90(a852),x79932),x79933)))
% 173.53/173.43 [8023]~P63(x80231)+~P7(x80231,x80233,x80232)+P22(f312(f312(f314(f853(x80231)),f666(x80232,x80233,x80231)),f312(f168(f853(x80231)),f63(x80231,x80232,f64(x80231)))))
% 173.53/173.43 [8031]~P22(f312(x80311,x80313))+P22(f312(f312(f195(f35(x80311,x80312)),f813(x80313,x80312,x80311)),x80313))+~P22(f312(f312(f195(f35(x80311,x80312)),x80313),x80313))
% 173.53/173.43 [8040]~E(f312(f312(f115(f860(x80401,a845)),f680(x80403,x80402,x80401)),f679(x80403,x80402,x80401)),f189(f860(x80401,a845)))+E(f312(f312(f115(f860(x80401,a845)),x80402),f48(f860(x80401,a845),x80403)),f189(f860(x80401,a845)))+P22(f312(f312(f314(f860(x80401,a845)),x80402),x80403))
% 173.53/173.43 [8058]E(x80581,f127(x80582))+~E(f312(f138(f853(x80582),f853(x80582),f129(x80582),f127(x80582)),x80583),f127(x80582))+~P22(f312(f312(f314(f853(x80582)),x80581),f312(f168(f853(x80582)),x80583)))
% 173.53/173.43 [8114]E(x81141,f189(f860(f860(x81142,a845),a845)))+P22(f312(f312(f314(f860(x81142,a845)),f697(x81143,x81141,x81142)),x81141))+P22(f312(f312(f227(f860(x81142,a845)),f49(f860(x81142,a845),x81141)),x81143))
% 173.53/173.43 [8121]~P26(x81211)+~P72(x81211)+E(f312(f312(f9(a1,x81211),f312(f312(f8(a852,x81211,a1),x81212),a118)),f312(f290(a852,a1,f114(a1)),x81213)),f312(f312(f9(a852,x81211),x81212),x81213))
% 173.53/173.43 [8122]~P26(x81221)+~P72(x81221)+E(f312(f312(f6(a1,x81221),f312(f312(f8(a852,x81221,a1),x81222),a118)),f312(f290(a852,a1,f114(a1)),x81223)),f312(f312(f6(a852,x81221),x81222),x81223))
% 173.53/173.43 [8162]~P22(f312(f70(x81621),x81623))+~P22(f312(f312(f228(a852),f2(a852)),f312(x81622,f398(x81622,x81623,x81621))))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f9(x81621,a852),x81622),x81623)))
% 173.53/173.43 [8163]~P22(f312(f70(x81631),x81633))+~P22(f312(f312(f228(a852),f2(a852)),f312(x81632,f542(x81632,x81633,x81631))))+P22(f312(f312(f228(a852),f2(a852)),f312(f312(f9(x81631,a852),x81632),x81633)))
% 173.53/173.43 [8199]~P65(x81992)+E(x81991,f87(x81992))+E(f312(f312(f268(x81992),f312(f312(f21(x81992),f312(f312(f240(x81992),x81991),x81993)),f87(x81992))),f312(f312(f21(x81992),x81991),f87(x81992))),f312(f312(f6(a852,x81992),f312(f240(x81992),x81991)),f312(f282(a852,f2(a852)),x81993)))
% 173.53/173.43 [8228]E(x82281,f2(a852))+~P22(f312(x82283,f312(f47(a852,x82282),x82281)))+P22(f312(f312(f228(a852),x82282),f312(f312(f90(a852),x82281),f312(a126,f330(x82281,x82282,x82283)))))
% 173.53/173.43 [8255]P22(f312(x82551,f2(a852)))+~P22(f312(x82551,f312(f47(a852,x82552),x82553)))+P22(f312(f312(f228(a852),x82552),f312(f312(f90(a852),x82553),f312(a126,f330(x82553,x82552,x82551)))))
% 173.53/173.43 [8274]E(x82741,f2(a852))+~P22(f312(x82743,f312(f47(a852,x82742),x82741)))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x82741),f330(x82741,x82742,x82743))),x82742))
% 173.53/173.43 [8294]P22(f312(x82941,f2(a852)))+~P22(f312(x82941,f312(f47(a852,x82943),x82942)))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x82942),f330(x82942,x82943,x82941))),x82943))
% 173.53/173.43 [8364]~P103(x83641)+E(f312(f312(f145(x83641,x83641,f5(x83641)),x83642),x83643),f146(x83641,x83641,f5(x83641),x83642,x83643))+P22(f312(f312(f314(x83641),x83642),f312(f168(x83641),x83643)))
% 173.53/173.43 [8405]~E(f312(x84053,f703(x84052,x84053,x84051)),f312(x84053,f710(x84052,x84053,x84051)))+~P59(x84051,f312(x84053,f704(x84052,x84053,x84051)))+P59(x84051,f312(f312(f50(x84052,f860(x84051,f860(x84051,a845))),f235(f860(x84052,a845))),x84053))
% 173.53/173.43 [8412]E(x84121,f189(f860(f860(x84122,a845),a845)))+~P22(f312(f312(f227(f860(x84122,a845)),f697(x84123,x84121,x84122)),x84123))+P22(f312(f312(f227(f860(x84122,a845)),f49(f860(x84122,a845),x84121)),x84123))
% 173.53/173.43 [8474]~P67(x84741)+~P22(f312(f312(f228(x84741),x84742),x84743))+P22(f312(f312(f228(x84741),x84742),f312(f312(f268(x84741),f312(f312(f89(x84741),x84742),x84743)),f312(f312(f89(x84741),f87(x84741)),f87(x84741)))))
% 173.53/173.43 [8526]~P22(f312(f312(x85261,f347(x85261,x85263,x85262)),f348(x85261,x85263,x85262)))+P22(f312(f312(x85261,x85262),x85263))+~P22(f312(f300(f859(a1,a1),a60),f312(f312(f239(a1,a1),x85262),x85263)))
% 173.53/173.43 [8527]~P22(f312(f312(x85271,f349(x85271,x85273,x85272)),f354(x85271,x85273,x85272)))+P22(f312(f312(x85271,x85272),x85273))+~P22(f312(f300(f859(a1,a1),a65),f312(f312(f239(a1,a1),x85272),x85273)))
% 173.53/173.43 [8528]~P22(f312(f312(x85281,f355(x85281,x85283,x85282)),f356(x85281,x85283,x85282)))+P22(f312(f312(x85281,x85282),x85283))+~P22(f312(f300(f859(a1,a1),a212),f312(f312(f239(a1,a1),x85282),x85283)))
% 173.53/173.43 [8529]~P22(f312(f312(x85291,f357(x85291,x85293,x85292)),f358(x85291,x85293,x85292)))+P22(f312(f312(x85291,x85292),x85293))+~P22(f312(f300(f859(a852,a852),a211),f312(f312(f239(a852,a852),x85292),x85293)))
% 173.53/173.43 [8530]~P22(f312(f312(x85301,f616(x85301,x85303,x85302)),f618(x85301,x85303,x85302)))+P22(f312(f312(x85301,x85302),x85303))+~P22(f312(f300(f859(a1,a1),a178),f312(f312(f239(a1,a1),x85302),x85303)))
% 173.53/173.43 [8779]P22(f312(f312(x87791,x87792),x87793))+P22(f312(f300(f859(a852,a852),a211),f312(f312(f239(a852,a852),f357(x87791,x87793,x87792)),f358(x87791,x87793,x87792))))+~P22(f312(f300(f859(a852,a852),a211),f312(f312(f239(a852,a852),x87792),x87793)))
% 173.53/173.43 [8780]P22(f312(f312(x87801,x87802),x87803))+P22(f312(f300(f859(a1,a1),a60),f312(f312(f239(a1,a1),f347(x87801,x87803,x87802)),f348(x87801,x87803,x87802))))+~P22(f312(f300(f859(a1,a1),a60),f312(f312(f239(a1,a1),x87802),x87803)))
% 173.53/173.43 [8781]P22(f312(f312(x87811,x87812),x87813))+P22(f312(f300(f859(a1,a1),a65),f312(f312(f239(a1,a1),f349(x87811,x87813,x87812)),f354(x87811,x87813,x87812))))+~P22(f312(f300(f859(a1,a1),a65),f312(f312(f239(a1,a1),x87812),x87813)))
% 173.53/173.43 [8782]P22(f312(f312(x87821,x87822),x87823))+P22(f312(f300(f859(a1,a1),a212),f312(f312(f239(a1,a1),f355(x87821,x87823,x87822)),f356(x87821,x87823,x87822))))+~P22(f312(f300(f859(a1,a1),a212),f312(f312(f239(a1,a1),x87822),x87823)))
% 173.53/173.43 [8783]P22(f312(f312(x87831,x87832),x87833))+P22(f312(f300(f859(a1,a1),a178),f312(f312(f239(a1,a1),f616(x87831,x87833,x87832)),f618(x87831,x87833,x87832))))+~P22(f312(f300(f859(a1,a1),a178),f312(f312(f239(a1,a1),x87832),x87833)))
% 173.53/173.43 [9125]~P22(f312(f70(x91251),x91253))+P22(f312(f312(f314(f859(f860(x91251,a845),f860(x91251,a845))),f312(f312(f239(f860(x91251,a845),f860(x91251,a845)),x91252),x91253)),f286(x91251)))+~P22(f312(f312(f228(f860(x91251,a845)),x91252),x91253))
% 173.53/173.43 [9198]~P59(x91981,f312(x91983,f704(x91982,x91983,x91981)))+P59(x91981,f312(f312(f50(x91982,f860(x91981,f860(x91981,a845))),f235(f860(x91982,a845))),x91983))+~E(f312(f312(f115(f860(x91981,a845)),f244(x91981,x91981,f312(x91983,f703(x91982,x91983,x91981)))),f245(x91981,x91981,f312(x91983,f710(x91982,x91983,x91981)))),f189(f860(x91981,a845)))
% 173.53/173.43 [9394]P50(x93941,x93942,x93943)+P22(f312(f312(f314(f859(x93941,x93941)),f420(x93943,x93942,x93941)),x93943))+~P22(f312(f312(f314(f859(x93941,x93941)),f312(f312(f239(x93941,x93941),f419(x93943,x93942,x93941)),f419(x93943,x93942,x93941))),x93943))
% 173.53/173.43 [9976]P50(x99761,x99762,x99763)+~P22(f312(f312(f249(x99761,x99761,a845),f312(f312(f7(x99761,f860(x99761,a845),f860(x99761,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x99761,a845),f860(x99761,a845)),x99761),f8(a845,a845,x99761)),f312(f312(f8(a845,f860(a845,a845),x99761),a310),f312(f312(f7(x99761,f860(x99761,a845),a845),f314(x99761)),x99762)))),f312(f312(f7(x99761,f860(x99761,a845),a845),f314(x99761)),x99762))),f420(x99763,x99762,x99761)))+~P22(f312(f312(f314(f859(x99761,x99761)),f312(f312(f239(x99761,x99761),f419(x99763,x99762,x99761)),f419(x99763,x99762,x99761))),x99763))
% 173.53/173.43 [5529]~P60(x55292)+E(x55291,f2(x55292))+E(f312(f47(x55292,f312(f312(f90(x55292),x55293),x55291)),x55291),x55293)
% 173.53/173.43 [5530]~P60(x55302)+E(x55301,f2(x55302))+E(f312(f47(x55302,f312(f312(f90(x55302),x55301),x55303)),x55301),x55303)
% 173.53/173.43 [6309]~P60(x63092)+E(x63091,f2(x63092))+E(f312(f47(x63092,f312(f312(f89(x63092),x63093),x63091)),x63091),f312(f312(f89(x63092),f312(f47(x63092,x63093),x63091)),f87(x63092)))
% 173.53/173.43 [6310]~P60(x63102)+E(x63101,f2(x63102))+E(f312(f47(x63102,f312(f312(f89(x63102),x63101),x63103)),x63101),f312(f312(f89(x63102),f312(f47(x63102,x63103),x63101)),f87(x63102)))
% 173.53/173.43 [6349]~P26(x63491)+~E(f312(x63492,f2(a852)),f2(x63491))+E(f312(f312(f6(a852,x63491),x63492),f312(f282(a852,f312(a126,f2(a852))),x63493)),f312(f312(f6(a852,x63491),x63492),f312(f282(a852,f2(a852)),x63493)))
% 173.53/173.43 [6693]~P22(f312(x66933,f2(a1)))+P22(f312(f312(f227(a852),x66931),x66932))+P22(f312(x66933,f312(f114(a1),f312(f312(f21(a852),x66932),x66931))))
% 173.53/173.43 [6788]P22(f312(f312(f227(a852),x67882),x67881))+P22(f312(f312(f228(a852),x67881),x67882))+P22(f312(x67883,f312(f114(a1),f312(f312(f21(a852),x67881),x67882))))
% 173.53/173.43 [6863]E(f312(f312(f89(a852),f312(f117(a852),x68631)),f312(f312(f89(a852),f312(f117(a852),x68632)),x68633)),f312(f312(f89(a852),f312(f117(a852),x68631)),x68633))+P22(f312(a194,f312(f117(a1),x68631)))+~P22(f312(a194,f312(f117(a1),x68632)))
% 173.53/173.43 [6896]~E(x68962,f312(f47(a852,x68963),x68961))+~P22(f312(f312(f228(a852),f2(a852)),x68961))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x68961),x68962)),x68963))
% 173.53/173.43 [7064]~P22(f312(f70(x70641),x70643))+~P22(f312(f70(x70641),x70642))+P22(f312(f70(x70641),f312(f312(f124(f860(x70641,a845)),x70642),x70643)))
% 173.53/173.43 [7346]~P103(x73461)+~P22(f312(f70(x73461),x73462))+E(f135(x73461,f312(f312(f21(f860(x73461,a845)),x73462),f312(f312(f289(x73461),x73463),f189(f860(x73461,a845))))),f166(x73461,x73463,f135(x73461,x73462)))
% 173.53/173.43 [7410]P22(f312(x74101,f2(a1)))+~P22(f312(f312(f228(a852),x74102),x74103))+~P22(f312(x74101,f312(f114(a1),f312(f312(f21(a852),x74102),x74103))))
% 173.53/173.43 [7427]~P22(f312(f70(x74271),x74272))+E(f312(f53(x74271),f312(f312(f21(f860(x74271,a845)),x74272),f312(f312(f289(x74271),x74273),f189(f860(x74271,a845))))),f312(f53(x74271),x74272))+P22(f312(f312(f314(x74271),x74273),x74272))
% 173.53/173.43 [7557]~P117(x75571)+~P22(f312(f312(f228(x75571),f87(x75571)),x75572))+P22(f312(f312(f228(x75571),f87(x75571)),f312(f312(f90(x75571),x75572),f312(f312(f240(x75571),x75572),x75573))))
% 173.53/173.43 [7602]~P22(f312(f70(x76021),x76023))+E(f312(f312(f21(a852),f312(f53(x76021),x76022)),f312(f53(x76021),x76023)),f312(f53(x76021),f312(f312(f21(f860(x76021,a845)),x76022),x76023)))+~P22(f312(f312(f227(f860(x76021,a845)),x76023),x76022))
% 173.53/173.43 [7660]~P22(f312(f312(f227(a852),x76602),x76603))+~P22(f312(f312(f227(a852),x76601),f312(f312(f21(a852),x76603),x76602)))+P22(f312(f312(f227(a852),f312(f312(f89(a852),x76601),x76602)),x76603))
% 173.53/173.43 [7714]P22(f312(f70(x77141),x77142))+~P22(f312(f70(x77141),x77143))+~P22(f312(f70(x77141),f312(f312(f21(f860(x77141,a845)),x77142),x77143)))
% 173.53/173.43 [7720]~P22(f312(f70(x77201),x77202))+E(f312(f53(x77201),f312(f312(f21(f860(x77201,a845)),x77202),f312(f312(f289(x77201),x77203),f189(f860(x77201,a845))))),f312(f312(f21(a852),f312(f53(x77201),x77202)),f87(a852)))+~P22(f312(f312(f314(x77201),x77203),x77202))
% 173.53/173.43 [7794]P59(x77941,x77942)+~P59(x77941,x77943)+~P22(f312(f312(f227(f860(x77941,f860(x77941,a845))),x77942),x77943))
% 173.53/173.43 [7830]~P22(f312(f312(f227(a852),x78303),x78302))+P22(f312(f312(f227(a852),x78301),f312(f312(f21(a852),x78302),x78303)))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),x78301),x78303)),x78302))
% 173.53/173.43 [7847]P41(x78471,x78472)+~P41(x78471,x78473)+~P22(f312(f312(f227(f860(f859(x78471,x78471),a845)),x78472),x78473))
% 173.53/173.43 [7848]P57(x78481,x78482)+~P57(x78481,x78483)+~P22(f312(f312(f227(f860(f859(x78481,x78481),a845)),x78482),x78483))
% 173.53/173.43 [8091]~P117(x80911)+~P22(f312(f312(f228(x80911),f87(x80911)),x80912))+P22(f312(f312(f228(x80911),f312(f312(f240(x80911),x80912),x80913)),f312(f312(f90(x80911),x80912),f312(f312(f240(x80911),x80912),x80913))))
% 173.53/173.43 [8182]~P22(f312(x81821,f2(a1)))+~P22(f312(x81821,f312(f312(f21(a1),f312(f114(a1),x81822)),f312(f114(a1),x81823))))+P22(f312(x81821,f312(f114(a1),f312(f312(f21(a852),x81822),x81823))))
% 173.53/173.43 [8195]~P22(f312(f312(f227(a852),x81953),x81952))+P22(f312(x81951,f312(f312(f21(a1),f312(f114(a1),x81952)),f312(f114(a1),x81953))))+~P22(f312(x81951,f312(f114(a1),f312(f312(f21(a852),x81952),x81953))))
% 173.53/173.43 [8213]P22(f312(f312(f228(a852),x82131),x82132))+~P22(f312(x82133,f312(f312(f21(a1),f312(f114(a1),x82131)),f312(f114(a1),x82132))))+P22(f312(x82133,f312(f114(a1),f312(f312(f21(a852),x82131),x82132))))
% 173.53/173.43 [8269]~P118(x82692)+E(x82691,f2(x82692))+P22(f312(f312(f228(x82692),f2(x82692)),f312(f312(f89(x82692),f312(f312(f90(x82692),x82693),x82693)),f312(f312(f90(x82692),x82691),x82691))))
% 173.53/173.43 [8270]~P118(x82702)+E(x82701,f2(x82702))+P22(f312(f312(f228(x82702),f2(x82702)),f312(f312(f89(x82702),f312(f312(f90(x82702),x82701),x82701)),f312(f312(f90(x82702),x82703),x82703))))
% 173.53/173.43 [8385]~P22(f312(f312(f228(a852),f2(a852)),x83851))+~P22(f312(f312(f228(a1),x83852),x83853))+P22(f312(f312(f228(a1),f312(f312(f90(a1),f312(f114(a1),x83851)),x83852)),f312(f312(f90(a1),f312(f114(a1),x83851)),x83853)))
% 173.53/173.43 [8441]E(f312(f312(f115(f860(x84411,a845)),x84412),f48(f860(x84411,a845),x84413)),f189(f860(x84411,a845)))+P22(f312(f312(f314(f860(x84411,a845)),x84412),x84413))+P22(f312(f312(f314(f860(x84411,a845)),f680(x84413,x84412,x84411)),f312(f312(f289(f860(x84411,a845)),x84412),x84413)))
% 173.53/173.43 [8442]E(f312(f312(f115(f860(x84421,a845)),x84422),f48(f860(x84421,a845),x84423)),f189(f860(x84421,a845)))+P22(f312(f312(f314(f860(x84421,a845)),x84422),x84423))+P22(f312(f312(f314(f860(x84421,a845)),f679(x84423,x84422,x84421)),f312(f312(f289(f860(x84421,a845)),x84422),x84423)))
% 173.53/173.43 [8473]E(x84731,x84732)+~E(f312(f190(f853(x84733)),x84731),f312(f190(f853(x84733)),x84732))+P22(f312(f312(f314(f859(x84733,x84733)),f587(x84733,x84731,x84732)),f312(f168(f859(x84733,x84733)),f312(f312(f177(x84733,x84733),x84732),x84731))))
% 173.53/173.43 [8698]E(f287(x86981,x86982),f287(x86981,x86983))+~P22(f312(f312(f227(f860(f859(x86981,x86981),a845)),x86983),f287(x86981,x86982)))+~P22(f312(f312(f227(f860(f859(x86981,x86981),a845)),x86982),x86983))
% 173.53/173.43 [8757]~P50(x87571,f235(f860(x87571,a845)),x87573)+P22(f312(f312(f227(f860(f859(f853(x87571),f853(x87571)),a845)),f153(x87571,x87572)),f154(x87571,x87573)))+~P22(f312(f312(f227(f860(f859(x87571,x87571),a845)),x87572),x87573))
% 173.53/173.43 [8996]~P22(f312(f70(x89961),x89962))+P22(f312(f70(f860(x89961,a845)),f312(f312(f69(x89961),x89962),x89963)))+~P22(f312(f312(f227(f860(f859(x89961,x89961),a845)),x89963),f312(f312(f247(x89961,x89961),x89962),f312(f16(f860(x89961,a845),x89961),x89962))))
% 173.53/173.43 [9032]P50(x90321,x90322,x90323)+P22(f312(f312(f314(x90321),f515(x90323,x90322,x90321)),x90322))+~P22(f312(f312(f227(f860(f859(x90321,x90321),a845)),x90323),f312(f312(f247(x90321,x90321),x90322),f312(f16(f860(x90321,a845),x90321),x90322))))
% 173.53/173.43 [9033]P50(x90331,x90332,x90333)+P22(f312(f312(f314(x90331),f526(x90332,x90333,x90331)),x90332))+~P22(f312(f312(f227(f860(f859(x90331,x90331),a845)),x90333),f312(f312(f247(x90331,x90331),x90332),f312(f16(f860(x90331,a845),x90331),x90332))))
% 173.53/173.43 [9065]~P67(x90651)+~P22(f312(f312(f228(x90651),x90652),x90653))+P22(f312(f312(f228(x90651),f312(f312(f268(x90651),f312(f312(f89(x90651),x90652),x90653)),f312(f312(f89(x90651),f87(x90651)),f87(x90651)))),x90653))
% 173.53/173.43 [9094]~P66(x90941)+P22(f312(f312(f227(x90941),x90942),x90943))+~P22(f312(f312(f227(x90941),f312(f312(f90(x90941),f505(x90943,x90942,x90941)),x90942)),x90943))
% 173.53/173.43 [9232]E(f312(f190(f853(f853(x92321))),f312(f132(f853(x92321),f312(f312(f8(a852,a845,f853(x92321)),f312(f228(a852),x92322)),f190(f853(x92321)))),f175(x92321,x92323))),f312(f190(f853(x92321)),f312(f312(f161(f853(x92321)),x92323),x92322)))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x92321),a852),f190(f853(x92321))),x92323)))+~P22(f312(f312(f228(a852),x92322),f312(f190(f853(f853(x92321))),x92323)))
% 173.53/173.43 [9339]~P41(x93391,x93392)+P20(x93391,f312(f312(f239(f860(f859(x93391,x93391),a845),f860(f859(x93391,x93391),a845)),x93392),x93393))+~P22(f312(f312(f227(f860(f859(x93391,x93391),a845)),f312(f312(f267(x93391,x93391,x93391),x93392),x93393)),x93392))
% 173.53/173.43 [9346]E(f312(f312(f150(f853(x93461),x93461),f312(f312(f7(f853(x93461),a852,x93461),f161(x93461)),x93462)),f312(f132(f853(x93461),f312(f312(f8(a852,a845,f853(x93461)),f312(f228(a852),x93462)),f190(f853(x93461)))),f175(x93461,x93463))),f312(f312(f161(f853(x93461)),x93463),x93462))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x93461),a852),f190(f853(x93461))),x93463)))+~P22(f312(f312(f228(a852),x93462),f312(f190(f853(f853(x93461))),x93463)))
% 173.53/173.43 [9478]P50(x94781,x94782,x94783)+~P22(f312(f312(f314(f859(x94781,x94781)),f312(f312(f239(x94781,x94781),f515(x94783,x94782,x94781)),f515(x94783,x94782,x94781))),x94783))+~P22(f312(f312(f227(f860(f859(x94781,x94781),a845)),x94783),f312(f312(f247(x94781,x94781),x94782),f312(f16(f860(x94781,a845),x94781),x94782))))
% 173.53/173.43 [9479]P50(x94791,x94792,x94793)+~P22(f312(f312(f314(f859(x94791,x94791)),f312(f312(f239(x94791,x94791),f526(x94792,x94793,x94791)),f526(x94792,x94793,x94791))),x94793))+~P22(f312(f312(f227(f860(f859(x94791,x94791),a845)),x94793),f312(f312(f247(x94791,x94791),x94792),f312(f16(f860(x94791,a845),x94791),x94792))))
% 173.53/173.43 [9852]~E(x98523,f2(a852))+~E(f312(f190(f853(x98521)),f312(f312(f161(f853(x98521)),x98522),f659(x98523,x98521,x98522))),x98523)+E(f312(f312(f150(a852,f853(x98521)),f312(f312(f7(a852,f853(a852),f853(x98521)),f312(f312(f8(f860(a852,x98521),f860(f853(a852),f853(x98521)),a852),f150(a852,x98521)),f312(f7(a852,a852,x98521),f312(f312(f8(f853(x98521),f860(a852,x98521),a852),f161(x98521)),f312(f161(f853(x98521)),x98522))))),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(f853(x98521))),x98522))))),f135(a852,f312(f282(a852,f2(a852)),x98523))),f175(x98521,x98522))
% 173.53/173.43 [9853]E(x98531,f127(f853(x98532)))+~E(f312(f190(f853(x98532)),f312(f312(f161(f853(x98532)),x98531),f659(x98533,x98532,x98531))),x98533)+E(f312(f312(f150(a852,f853(x98532)),f312(f312(f7(a852,f853(a852),f853(x98532)),f312(f312(f8(f860(a852,x98532),f860(f853(a852),f853(x98532)),a852),f150(a852,x98532)),f312(f7(a852,a852,x98532),f312(f312(f8(f853(x98532),f860(a852,x98532),a852),f161(x98532)),f312(f161(f853(x98532)),x98531))))),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(f853(x98532))),x98531))))),f135(a852,f312(f282(a852,f2(a852)),x98533))),f175(x98532,x98531))
% 173.53/173.43 [9854]~E(x98543,f2(a852))+E(f312(f312(f150(a852,f853(x98541)),f312(f312(f7(a852,f853(a852),f853(x98541)),f312(f312(f8(f860(a852,x98541),f860(f853(a852),f853(x98541)),a852),f150(a852,x98541)),f312(f7(a852,a852,x98541),f312(f312(f8(f853(x98541),f860(a852,x98541),a852),f161(x98541)),f312(f161(f853(x98541)),x98542))))),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(f853(x98541))),x98542))))),f135(a852,f312(f282(a852,f2(a852)),x98543))),f175(x98541,x98542))+P22(f312(f312(f228(a852),f659(x98543,x98541,x98542)),f312(f190(f853(f853(x98541))),x98542)))
% 173.53/173.43 [9855]E(x98551,f127(f853(x98552)))+E(f312(f312(f150(a852,f853(x98552)),f312(f312(f7(a852,f853(a852),f853(x98552)),f312(f312(f8(f860(a852,x98552),f860(f853(a852),f853(x98552)),a852),f150(a852,x98552)),f312(f7(a852,a852,x98552),f312(f312(f8(f853(x98552),f860(a852,x98552),a852),f161(x98552)),f312(f161(f853(x98552)),x98551))))),f135(a852,f312(f282(a852,f2(a852)),f312(f190(f853(f853(x98552))),x98551))))),f135(a852,f312(f282(a852,f2(a852)),x98553))),f175(x98552,x98551))+P22(f312(f312(f228(a852),f659(x98553,x98552,x98551)),f312(f190(f853(f853(x98552))),x98551)))
% 173.53/173.43 [7599]E(f312(f312(f89(a852),f312(f117(a852),x75991)),f312(f312(f89(a852),f312(f117(a852),x75992)),x75993)),f312(f312(f89(a852),f312(f117(a852),f312(f312(f89(a1),x75991),x75992))),x75993))+P22(f312(a194,f312(f117(a1),x75991)))+P22(f312(a194,f312(f117(a1),x75992)))
% 173.53/173.43 [8376]~P22(f312(f70(x83761),x83762))+~P22(f312(f312(f314(x83761),x83763),x83762))+E(f312(a126,f312(f53(x83761),f312(f312(f21(f860(x83761,a845)),x83762),f312(f312(f289(x83761),x83763),f189(f860(x83761,a845)))))),f312(f53(x83761),x83762))
% 173.53/173.43 [8395]~P22(f312(f70(x83951),x83952))+~P22(f312(f312(f314(x83951),x83953),x83952))+E(f312(f312(f89(a852),f87(a852)),f312(f53(x83951),f312(f312(f21(f860(x83951,a845)),x83952),f312(f312(f289(x83951),x83953),f189(f860(x83951,a845)))))),f312(f53(x83951),x83952))
% 173.53/173.43 [8484]~P103(x84841)+~P22(f312(f70(x84841),x84843))+E(f312(f312(f145(x84841,x84841,f5(x84841)),x84842),f135(x84841,f312(f312(f21(f860(x84841,a845)),x84843),f312(f312(f289(x84841),x84842),f189(f860(x84841,a845)))))),f135(x84841,f312(f312(f289(x84841),x84842),x84843)))
% 173.53/173.43 [8628]~P22(f312(f70(x86281),x86283))+~P22(f312(f70(x86281),x86282))+E(f312(f312(f89(a852),f312(f53(x86281),f312(f312(f124(f860(x86281,a845)),x86282),x86283))),f312(f53(x86281),f312(f312(f115(f860(x86281,a845)),x86282),x86283))),f312(f312(f89(a852),f312(f53(x86281),x86282)),f312(f53(x86281),x86283)))
% 173.53/173.43 [9800]~P19(x98001,f860(f860(x98001,a845),a845),f312(f312(f7(x98001,f860(f859(x98001,x98001),a845),f860(f860(x98001,a845),a845)),f312(f312(f8(f860(x98001,a845),f860(f860(f859(x98001,x98001),a845),f860(f860(x98001,a845),a845)),x98001),f69(x98001)),f312(f312(f7(x98001,f860(x98001,a845),f860(x98001,a845)),f289(x98001)),f189(f860(x98001,a845))))),x98003),x98002)+~P22(f312(f70(x98001),x98002))+E(f312(f53(f860(x98001,a845)),f312(f312(f69(x98001),x98002),x98003)),f312(f53(x98001),x98002))
% 173.53/173.43 [10072]~P49(f860(x100721,a845),f860(x100721,a845),x100722)+~P22(f312(f312(f227(f860(x100721,a845)),x100723),f312(x100722,f109(f860(x100721,a845),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),x100722)),x100723))),f110(f860(x100721,a845),x100722))))))+P22(f312(f312(f227(f860(x100721,a845)),f109(f860(x100721,a845),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),x100722)),x100723))),f110(f860(x100721,a845),x100722)))),f312(x100722,f109(f860(x100721,a845),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),f312(f312(f7(f860(x100721,a845),f860(x100721,a845),f860(x100721,a845)),f312(f312(f8(f860(x100721,a845),f860(f860(x100721,a845),f860(x100721,a845)),f860(x100721,a845)),f124(f860(x100721,a845))),x100722)),x100723))),f110(f860(x100721,a845),x100722))))))
% 173.53/173.43 [7863]~P90(x78631)+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x78633)))+E(f312(f312(f240(x78631),x78632),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x78633),x78633)),a111))),f87(x78631))
% 173.53/173.43 [9322]~P90(x93221)+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x93223)))+E(f312(f312(f240(x93221),x93222),f312(f117(a852),f312(f312(f21(a1),f312(f312(f89(a1),x93223),x93223)),a111))),f312(f312(f95(x93221,x93221),f312(f312(f240(x93221),x93222),f312(f117(a852),x93223))),f312(f312(f18(x93221,x93221,x93221),f312(f312(f8(x93221,f860(x93221,x93221),x93221),f90(x93221)),f312(f90(x93221),x93222))),f5(x93221))))
% 173.53/173.43 [9704]~P22(f312(f133(x97041),x97043))+~P22(f312(f312(f314(x97041),x97042),f312(f168(x97041),x97043)))+E(f312(f312(f134(x97041),f312(f190(f853(x97041)),f172(x97041,f312(f312(f8(a845,a845,x97041),a307),f312(f312(f7(x97041,x97041,a845),a309),x97042)),f312(f165(x97041),x97043)))),f312(f165(x97041),x97043)),f312(f312(f147(x97041),x97042),f312(f165(x97041),f172(x97041,f312(f312(f8(a845,a845,x97041),a307),f312(f312(f7(x97041,x97041,a845),a309),x97042)),x97043))))
% 173.53/173.43 [9776]P22(f312(f312(f227(f860(f859(x97761,x97761),a845)),f287(x97761,x97762)),x97763))+~P22(f312(f312(f227(f860(f859(x97761,x97761),a845)),f287(x97761,f189(f860(f859(x97761,x97761),a845)))),x97763))+~P22(f312(f312(f227(f860(f859(x97761,x97761),a845)),f312(f312(f267(x97761,x97761,x97761),f312(f312(f115(f860(f859(x97761,x97761),a845)),f287(x97761,x97762)),x97763)),x97762)),x97763))
% 173.53/173.43 [9620]~P22(f312(f70(x96201),f312(f233(x96201),x96203)))+~P22(f312(f70(x96201),f312(f233(x96201),x96202)))+P22(f312(f70(x96201),f312(f233(x96201),f312(f312(f18(x96201,a845,a845),f312(f312(f8(a845,f860(a845,a845),x96201),a311),x96202)),x96203))))
% 173.53/173.43 [9919]P22(f312(f312(f227(f860(f859(x99191,x99191),a845)),f312(f312(f267(x99191,x99191,x99191),x99192),f287(x99191,x99192))),x99193))+~P22(f312(f312(f227(f860(f859(x99191,x99191),a845)),x99192),x99193))+~P22(f312(f312(f227(f860(f859(x99191,x99191),a845)),f312(f312(f267(x99191,x99191,x99191),f312(f312(f115(f860(f859(x99191,x99191),a845)),f312(f312(f267(x99191,x99191,x99191),x99192),f287(x99191,x99192))),x99193)),x99192)),x99193))
% 173.53/173.43 [9870]~P112(x98702)+E(x98701,f2(x98702))+~E(f312(f312(f89(x98702),f312(f312(f240(x98702),x98703),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x98702),x98701),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f2(x98702))
% 173.53/173.43 [9871]~P112(x98712)+E(x98711,f2(x98712))+~E(f312(f312(f89(x98712),f312(f312(f240(x98712),x98711),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x98712),x98713),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f2(x98712))
% 173.53/173.43 [9877]~P22(f312(f133(x98771),x98773))+~P22(f312(f312(f314(x98771),x98772),f312(f168(x98771),x98773)))+E(f312(f165(x98771),f312(f167(x98771),f312(f312(f134(x98771),f312(f190(f853(x98771)),f172(x98771,f312(f312(f8(a845,a845,x98771),a307),f312(f312(f7(x98771,x98771,a845),a309),x98772)),x98773))),x98773))),f172(x98771,f312(f312(f8(a845,a845,x98771),a307),f312(f312(f7(x98771,x98771,a845),a309),x98772)),f312(f165(x98771),x98773)))
% 173.53/173.43 [9965]~P112(x99652)+E(x99651,f2(x99652))+P22(f312(f312(f228(x99652),f2(x99652)),f312(f312(f89(x99652),f312(f312(f240(x99652),x99653),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99652),x99651),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))))
% 173.53/173.43 [9966]~P112(x99662)+E(x99661,f2(x99662))+P22(f312(f312(f228(x99662),f2(x99662)),f312(f312(f89(x99662),f312(f312(f240(x99662),x99661),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99662),x99663),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))))
% 173.53/173.43 [10009]~P112(x100091)+P22(f312(f312(f227(x100091),f2(x100091)),x100092))+~P22(f312(f312(f227(x100091),f2(x100091)),f312(f312(f240(x100091),x100092),f312(a126,f312(f312(f90(a852),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),x100093)))))
% 173.53/173.43 [5415]~P18(x54151,x54154,x54153)+P18(x54151,x54152,x54153)+~P18(x54151,x54152,x54154)
% 173.53/173.43 [7148]~P36(x71483,x71484,x71481,x71482)+E(x71481,x71482)+~P36(x71483,x71484,x71482,x71481)
% 173.53/173.43 [4890]~E(x48902,f99(x48903,x48901))+P22(f312(x48901,x48902))+~P22(f312(x48901,x48904))
% 173.53/173.43 [6604]~P41(x66042,x66044)+~P41(x66041,x66043)+P41(f859(x66041,x66042),f304(x66041,x66042,x66043,x66044))
% 173.53/173.43 [5067]~P2(x50674,x50671)+~E(f312(x50671,x50672),f312(x50671,x50673))+P22(f312(f312(x50671,x50672),x50673))
% 173.53/173.43 [5235]~P2(x52354,x52351)+E(f312(x52351,x52352),f312(x52351,x52353))+~P22(f312(f312(x52351,x52352),x52353))
% 173.53/173.43 [5321]~P13(x53213,x53214,x53211)+E(f312(x53211,x53212),f312(f72(x53213,x53214),x53212))+~P22(f312(f70(x53213),x53212))
% 173.53/173.43 [5322]~P5(x53223,x53224,x53221)+E(f312(x53221,x53222),f312(f72(x53223,x53224),x53222))+~P22(f312(f70(x53223),x53222))
% 173.53/173.43 [5447]~P2(x54474,x54471)+~P22(f312(f312(x54471,x54473),x54472))+P22(f312(f312(x54471,x54472),x54473))
% 173.53/173.43 [5517]E(x55171,x55172)+~E(f312(f246(x55173,x55174),x55171),f312(f246(x55173,x55174),x55172))+~E(f312(f248(x55173,x55174),x55171),f312(f248(x55173,x55174),x55172))
% 173.53/173.43 [5546]E(x55461,x55462)+~P22(f312(f56(x55463,x55464),x55462))+~P22(f312(f56(x55463,x55464),x55461))
% 173.53/173.43 [5728]~P26(x57282)+E(f217(x57281,x57282,x57283,x57284),f2(x57282))+P22(f312(f70(x57281),x57284))
% 173.53/173.43 [5859]~P22(f312(f300(x58591,x58592),x58594))+P22(f312(f300(x58591,x58592),x58593))+~P22(f312(f312(x58592,x58593),x58594))
% 173.53/173.43 [7789]~P103(x77892)+~P22(f312(f133(x77891),x77894))+P22(f312(f133(x77891),f144(x77891,x77892,x77893,x77894)))
% 173.53/173.43 [8010]~P22(f312(f70(x80102),x80104))+~P22(f312(f70(x80101),x80103))+P22(f312(f70(f858(x80101,x80102)),f298(x80101,x80102,x80103,x80104)))
% 173.53/173.43 [8011]~P22(f312(f133(x80112),x80114))+~P22(f312(f133(x80111),x80113))+P22(f312(f133(f859(x80111,x80112)),f68(x80111,x80112,x80113,x80114)))
% 173.53/173.43 [8015]P22(f312(f312(f314(f853(x80151)),f312(f312(f129(x80151),x80152),x80153)),f157(x80151,x80154)))+~P22(f312(f312(f314(f853(x80151)),x80153),f157(x80151,x80154)))+~P22(f312(f312(f314(f853(x80151)),x80152),f157(x80151,x80154)))
% 173.53/173.43 [8342]P22(f312(x83421,x83422))+~E(x83423,f312(f219(x83424),x83422))+~P22(f312(x83421,f762(x83422,x83421,x83423,x83424)))
% 173.53/173.43 [8353]~P103(x83533)+~P22(f312(f133(x83531),f144(x83531,x83533,x83534,x83532)))+P22(f312(f133(x83531),x83532))
% 173.53/173.43 [8619]~P22(f312(f312(f314(f859(x86191,x86191)),f312(f312(f239(x86191,x86191),x86192),x86194)),f287(x86191,x86193)))+P22(f312(f312(f314(x86191),x86192),f301(x86191,x86193)))+~P22(f312(f312(f314(x86191),x86194),f301(x86191,x86193)))
% 173.53/173.43 [8640]~E(x86404,f312(f219(x86403),x86402))+P22(f312(x86401,x86402))+P22(f312(f312(f314(x86403),f762(x86402,x86401,x86404,x86403)),f218(x86403,x86404)))
% 173.53/173.43 [5049]~P72(x50492)+E(f312(f312(f9(x50491,x50492),x50493),x50494),f87(x50492))+P22(f312(f70(x50491),x50494))
% 173.53/173.43 [5052]~P26(x50522)+E(f312(f312(f6(x50521,x50522),x50523),x50524),f2(x50522))+P22(f312(f70(x50521),x50524))
% 173.53/173.43 [5201]~P27(x52013)+E(x52011,x52012)+~E(f312(f312(f89(x52013),x52014),x52011),f312(f312(f89(x52013),x52014),x52012))
% 173.53/173.43 [5202]~P28(x52023)+E(x52021,x52022)+~E(f312(f312(f89(x52023),x52024),x52021),f312(f312(f89(x52023),x52024),x52022))
% 173.53/173.43 [5204]~P27(x52043)+E(x52041,x52042)+~E(f312(f312(f89(x52043),x52041),x52044),f312(f312(f89(x52043),x52042),x52044))
% 173.53/173.43 [5317]~P31(x53173)+E(x53171,f189(f860(x53172,a845)))+E(f312(f312(f50(x53172,x53173),x53171),f312(f16(x53173,x53172),x53174)),x53174)
% 173.53/173.43 [5318]~P31(x53183)+E(x53181,f189(f860(x53182,a845)))+E(f312(f312(f51(x53182,x53183),x53181),f312(f16(x53183,x53182),x53184)),x53184)
% 173.53/173.43 [5533]~P105(x55333)+E(x55331,x55332)+~E(f283(x55333,x55334,x55331),f312(f312(f289(x55333),x55332),f189(f860(x55333,a845))))
% 173.53/173.43 [5534]~P105(x55343)+E(x55341,x55342)+~E(f283(x55343,x55341,x55342),f312(f312(f289(x55343),x55344),f189(f860(x55343,a845))))
% 173.53/173.43 [5817]P22(f312(x58171,x58172))+~P22(f312(f243(x58173,x58171),x58174))+~P22(f312(f312(f314(x58173),x58172),x58174))
% 173.53/173.43 [5835]P38(x58351,x58352,x58353)+~P38(x58351,x58352,f312(f312(f147(x58351),x58354),x58353))+P22(f312(x58352,x58354))
% 173.53/173.43 [5848]E(x58481,x58482)+~P22(f312(f312(f195(x58483),x58484),x58482))+~P22(f312(f312(f195(x58483),x58484),x58481))
% 173.53/173.43 [5921]P38(x59211,x59212,x59213)+P38(x59211,x59212,x59214)+~P38(x59211,x59212,f312(f312(f129(x59211),x59214),x59213))
% 173.53/173.43 [5940]~P26(x59401)+E(f312(f312(f6(a852,x59401),x59402),f312(f282(a852,x59403),f312(a126,x59404))),f2(x59401))+~P22(f312(f312(f228(a852),x59404),x59403))
% 173.53/173.43 [5944]~P61(x59441)+~E(f54(x59441,x59442,x59443),f54(x59441,x59444,x59443))+E(f54(x59441,f312(f88(x59441),x59442),x59443),f54(x59441,f312(f88(x59441),x59444),x59443))
% 173.53/173.43 [6006]P22(f312(x60061,x60062))+~E(f312(f132(x60063,x60061),x60064),x60064)+~P22(f312(f312(f314(x60063),x60062),f312(f168(x60063),x60064)))
% 173.53/173.43 [6023]~E(f312(f312(f89(a852),x60233),x60232),f312(f312(f89(a852),x60231),x60234))+~P22(f312(f312(f228(a852),x60233),x60234))+P22(f312(f312(f228(a852),x60231),x60232))
% 173.53/173.43 [6027]P38(x60271,x60272,x60273)+~P22(f312(x60272,x60274))+~P22(f312(f312(f314(x60271),x60274),f312(f168(x60271),x60273)))
% 173.53/173.43 [6062]~E(f312(f132(x60621,x60622),x60623),f127(x60621))+~P22(f312(x60622,x60624))+~P22(f312(f312(f314(x60621),x60624),f312(f168(x60621),x60623)))
% 173.53/173.43 [6063]~E(f172(x60633,x60631,x60634),x60634)+P22(f312(x60631,x60632))+~P22(f312(f312(f314(x60633),x60632),f312(f168(x60633),x60634)))
% 173.53/173.43 [6096]~E(x60964,f189(f860(x60962,a845)))+~E(x60963,f189(f860(x60961,a845)))+E(f298(x60961,x60962,x60963,x60964),f189(f860(f858(x60961,x60962),a845)))
% 173.53/173.43 [6240]P22(f312(x62401,x62402))+~P22(f312(f156(x62403,x62401),x62404))+~P22(f312(f312(f314(x62403),x62402),f312(f168(x62403),x62404)))
% 173.53/173.43 [6503]~P26(x65031)+E(f312(f312(f6(a852,x65031),x65032),f283(a852,x65033,f312(a126,x65034))),f2(x65031))+~P22(f312(f312(f228(a852),f312(a126,x65034)),x65033))
% 173.53/173.43 [6645]~P103(x66451)+E(f312(f312(f21(f860(x66451,a845)),f312(f282(x66451,x66452),x66453)),f312(f282(x66451,x66452),x66454)),f312(f282(x66451,x66454),x66453))+~P22(f312(f312(f227(x66451),x66452),x66454))
% 173.53/173.43 [6996]~P22(f312(f312(f314(f853(x69961)),x69964),f157(x69961,x69963)))+P22(f312(f312(f314(x69961),x69962),x69963))+~P22(f312(f312(f314(x69961),x69962),f312(f168(x69961),x69964)))
% 173.53/173.43 [7057]~P72(x70571)+E(f312(f312(f312(f74(x70571,x70572,f90(x70571)),x70573),f87(x70571)),x70574),f312(f312(f9(x70572,x70571),x70573),x70574))+~P22(f312(f70(x70572),x70574))
% 173.53/173.43 [7059]~P26(x70591)+E(f312(f312(f312(f74(x70591,x70592,f89(x70591)),x70593),f2(x70591)),x70594),f312(f312(f6(x70592,x70591),x70593),x70594))+~P22(f312(f70(x70592),x70594))
% 173.53/173.43 [7089]P19(x70891,x70892,x70893,x70894)+~E(f312(f53(x70892),f312(f290(x70891,x70892,x70893),x70894)),f312(f53(x70891),x70894))+~P22(f312(f70(x70891),x70894))
% 173.53/173.43 [7264]~P26(x72641)+E(f312(f312(f89(x72641),f312(x72642,x72643)),f312(f312(f6(a852,x72641),x72642),f284(a852,x72643,x72644))),f312(f312(f6(a852,x72641),x72642),f283(a852,x72643,x72644)))+~P22(f312(f312(f227(a852),x72643),x72644))
% 173.53/173.43 [7275]~P72(x72751)+~P19(x72752,x72751,x72753,x72754)+E(f312(f312(f9(x72751,x72751),f39(x72751)),f312(f290(x72752,x72751,x72753),x72754)),f312(f312(f9(x72752,x72751),x72753),x72754))
% 173.53/173.43 [7276]~P26(x72761)+~P19(x72762,x72761,x72763,x72764)+E(f312(f312(f6(x72761,x72761),f39(x72761)),f312(f290(x72762,x72761,x72763),x72764)),f312(f312(f6(x72762,x72761),x72763),x72764))
% 173.53/173.43 [7327]E(f312(f53(f858(x73271,x73272)),f298(x73271,x73272,x73273,x73274)),f312(f312(f89(a852),f312(f53(x73271),x73273)),f312(f53(x73272),x73274)))+~P22(f312(f70(x73272),x73274))+~P22(f312(f70(x73271),x73273))
% 173.53/173.43 [7411]E(x74111,x74112)+P22(f312(f312(f314(x74113),x74111),f312(f168(x74113),f166(x74113,x74112,x74114))))+~P22(f312(f312(f314(x74113),x74111),f312(f168(x74113),x74114)))
% 173.53/173.43 [7550]~P22(f312(f312(f227(f860(x75501,a845)),x75504),f312(x75503,x75504)))+~P22(f312(f312(f314(x75501),x75502),x75504))+P22(f312(f312(f314(x75501),x75502),f110(f860(x75501,a845),x75503)))
% 173.53/173.43 [7636]~P26(x76361)+E(f312(f312(f89(x76361),f312(f312(f6(a852,x76361),x76362),f312(f282(a852,x76363),x76364))),f312(x76362,x76364)),f312(f312(f6(a852,x76361),x76362),f312(f282(a852,x76363),f312(a126,x76364))))+P22(f312(f312(f228(a852),x76364),x76363))
% 173.53/173.43 [7690]~P19(x76901,x76902,x76903,f235(f860(x76901,a845)))+~P22(f312(f70(x76902),x76904))+P22(f312(f70(x76901),f312(f291(x76901,x76902,x76903),x76904)))
% 173.53/173.43 [7799]P22(f312(f312(f314(f853(x77991)),f312(f312(f147(x77991),x77992),x77993)),f157(x77991,x77994)))+~P22(f312(f312(f314(f853(x77991)),x77993),f157(x77991,x77994)))+~P22(f312(f312(f314(x77991),x77992),x77994))
% 173.53/173.43 [7886]~E(f312(f290(x78863,x78861,x78864),f235(f860(x78863,a845))),f235(f860(x78861,a845)))+P22(f312(f70(x78861),x78862))+~P22(f312(f70(x78863),f312(f291(x78863,x78861,x78864),x78862)))
% 173.53/173.43 [7980]~P19(x79801,x79803,x79804,x79802)+P22(f312(f70(x79801),x79802))+~P22(f312(f70(x79803),f312(f290(x79801,x79803,x79804),x79802)))
% 173.53/173.43 [8001]~E(x80012,x80013)+P22(f312(f312(f314(f859(x80011,x80011)),f312(f312(f239(x80011,x80011),x80012),x80013)),f237(x80011,x80014)))+~P22(f312(f312(f314(x80011),x80012),x80014))
% 173.53/173.43 [8042]~P26(x80421)+E(f312(f312(f89(x80421),f312(f312(f6(a852,x80421),x80422),f283(a852,x80423,x80424))),f312(x80422,f312(a126,x80424))),f312(f312(f6(a852,x80421),x80422),f283(a852,x80423,f312(a126,x80424))))+P22(f312(f312(f228(a852),f312(a126,x80424)),x80423))
% 173.53/173.43 [8106]P22(f312(x81061,x81062))+~P22(f312(x81061,f312(f312(f161(x81063),x81064),f597(x81061,x81064,x81063))))+~P22(f312(f312(f314(x81063),x81062),f312(f168(x81063),x81064)))
% 173.53/173.43 [8251]~P22(f312(f312(f314(x82511),x82512),f301(x82511,x82514)))+P22(f312(f312(f314(f853(x82511)),f312(f312(f147(x82511),x82512),x82513)),f301(f853(x82511),f153(x82511,x82514))))+~P22(f312(f312(f314(f853(x82511)),x82513),f301(f853(x82511),f153(x82511,x82514))))
% 173.53/173.43 [8262]~P19(x82622,x82623,x82624,f698(x82624,x82623,x82622,x82621))+P19(x82622,x82623,x82624,f49(f860(x82622,a845),x82621))+E(x82621,f189(f860(f860(x82622,a845),a845)))
% 173.53/173.43 [8540]E(x85401,x85402)+~P22(f312(f312(f314(f859(x85403,x85403)),f312(f312(f239(x85403,x85403),x85401),x85402)),f287(x85403,x85404)))+P22(f312(f312(f314(x85403),x85401),f312(f238(x85403,x85403),x85404)))
% 173.53/173.43 [8814]P19(x88142,x88143,x88144,f49(f860(x88142,a845),x88141))+E(x88141,f189(f860(f860(x88142,a845),a845)))+P22(f312(f312(f314(f860(x88142,a845)),f698(x88144,x88143,x88142,x88141)),x88141))
% 173.53/173.43 [8955]P22(f312(f70(x89551),x89552))+~P22(f312(f70(x89554),f312(f290(x89551,x89554,x89553),x89552)))+P22(f312(f312(f314(x89551),f578(x89553,x89554,x89552,x89551)),x89552))
% 173.53/173.43 [9128]P22(f312(x91281,x91282))+~P22(f312(x91281,f312(f312(f161(x91283),x91284),f699(x91282,x91281,x91284,x91283))))+~P22(f312(f312(f314(x91283),x91282),f312(f168(x91283),x91284)))
% 173.53/173.43 [9149]E(x91491,x91492)+~P22(f312(f312(f314(f859(x91493,x91493)),f312(f312(f239(x91493,x91493),x91491),x91492)),f287(x91493,x91494)))+P22(f312(f312(f314(f859(x91493,x91493)),f312(f312(f239(x91493,x91493),x91491),x91492)),f312(f312(f267(x91493,x91493,x91493),x91494),f287(x91493,x91494))))
% 173.53/173.43 [9199]~E(f312(f190(f853(x91991)),x91992),f312(f190(f853(x91991)),x91993))+~P22(f312(f312(f314(f859(f853(x91991),f853(x91991))),f312(f312(f239(f853(x91991),f853(x91991)),x91992),x91993)),f143(x91991,x91994)))+P22(f312(f312(f314(f859(f853(x91991),f853(x91991))),f312(f312(f239(f853(x91991),f853(x91991)),x91992),x91993)),f141(x91991,x91994)))
% 173.53/173.43 [9623]~P30(x96231)+E(f312(f312(f6(a852,x96231),f312(f312(f18(a852,x96231,x96231),f312(f312(f8(x96231,f860(x96231,x96231),a852),f21(x96231)),x96232)),f312(f312(f8(a852,x96231,a852),x96232),f312(f312(f7(a852,a852,a852),f89(a852)),f87(a852))))),f283(a852,x96233,x96234)),f2(x96231))+P22(f312(f312(f227(a852),x96233),x96234))
% 173.53/173.43 [9868]~P41(x98682,x98684)+~P19(x98682,x98681,x98683,f235(f860(x98682,a845)))+P41(x98681,f312(f290(f859(x98682,x98682),f859(x98681,x98681),f250(x98682,x98681,x98682,x98681,x98683,x98683)),x98684))
% 173.53/173.43 [10035]~E(f312(f190(f853(x100351)),x100353),f312(f190(f853(x100351)),x100352))+P22(f312(f312(f314(f859(f853(x100351),f853(x100351))),f312(f312(f239(f853(x100351),f853(x100351)),x100352),x100353)),f154(x100351,x100354)))+~P22(f312(f312(f249(x100351,x100351,a845),f312(f312(f7(x100351,f860(f859(x100351,x100351),a845),f860(x100351,a845)),f312(f312(f8(f860(x100351,f860(f860(f859(x100351,x100351),a845),a845)),f860(f860(f859(x100351,x100351),a845),f860(x100351,a845)),x100351),f7(x100351,f860(f859(x100351,x100351),a845),a845)),f312(f312(f8(f860(x100351,f859(x100351,x100351)),f860(x100351,f860(f860(f859(x100351,x100351),a845),a845)),x100351),f312(f8(f859(x100351,x100351),f860(f860(f859(x100351,x100351),a845),a845),x100351),f314(f859(x100351,x100351)))),f239(x100351,x100351)))),x100354)),f590(x100354,x100353,x100352,x100351)))
% 173.53/173.43 [5903]~E(x59034,x59032)+P22(f312(x59031,x59032))+P22(f312(f312(f195(f35(x59031,x59033)),x59032),x59034))
% 173.53/173.43 [5951]~P60(x59511)+~E(x59512,f2(x59511))+E(f312(f47(x59511,f312(f312(f90(x59511),x59512),x59513)),f312(f312(f90(x59511),x59512),x59514)),f2(x59511))
% 173.53/173.43 [6026]E(x60261,f127(x60262))+E(x60263,f312(f312(f21(a852),f312(f190(f853(x60262)),x60261)),f87(a852)))+E(f140(x60262,f312(f312(f155(x60262,x60261),x60263),x60264)),f140(x60262,x60261))
% 173.53/173.43 [6041]~P60(x60412)+E(x60411,f2(x60412))+E(f312(f47(x60412,f312(f312(f90(x60412),x60413),x60411)),f312(f312(f90(x60412),x60414),x60411)),f312(f47(x60412,x60413),x60414))
% 173.53/173.43 [6043]~P60(x60432)+E(x60431,f2(x60432))+E(f312(f47(x60432,f312(f312(f90(x60432),x60431),x60433)),f312(f312(f90(x60432),x60431),x60434)),f312(f47(x60432,x60433),x60434))
% 173.53/173.43 [6054]E(x60541,x60542)+P22(f312(x60543,x60542))+~P22(f312(f312(f312(f289(x60544),x60541),x60543),x60542))
% 173.53/173.43 [6067]~P26(x60671)+~P22(f312(f133(x60672),x60674))+E(f312(f162(x60671),f312(f312(f150(x60672,x60671),x60673),x60674)),f312(f312(f6(x60672,x60671),x60673),f312(f168(x60672),x60674)))
% 173.53/173.43 [6089]~P72(x60892)+~P22(f312(f70(x60891),x60894))+E(f312(f312(f9(x60891,x60892),f312(f16(x60892,x60891),x60893)),x60894),f312(f312(f240(x60892),x60893),f312(f53(x60891),x60894)))
% 173.53/173.43 [6149]~P64(x61492)+E(x61491,f2(x61492))+E(f312(f312(f268(x61492),f312(f312(f90(x61492),x61493),x61491)),f312(f312(f90(x61492),x61494),x61491)),f312(f312(f268(x61492),x61493),x61494))
% 173.53/173.43 [6150]~P64(x61502)+E(x61501,f2(x61502))+E(f312(f312(f268(x61502),f312(f312(f90(x61502),x61501),x61503)),f312(f312(f90(x61502),x61501),x61504)),f312(f312(f268(x61502),x61503),x61504))
% 173.53/173.43 [6213]P22(f312(x62131,x62132))+~E(x62133,f312(f312(f89(a852),x62134),x62132))+~P22(f312(x62131,f312(f312(f21(a852),x62133),x62134)))
% 173.53/173.43 [6293]P21(x62931,x62932,x62933)+P34(x62931,f644(x62933,x62932,x62931),x62934)+~P22(f312(f312(f314(f851(x62931)),x62934),x62932))
% 173.53/173.43 [6295]~P22(f312(x62952,x62953))+~P22(f312(f156(x62951,x62952),x62954))+P22(f312(f156(x62951,x62952),f312(f312(f147(x62951),x62953),x62954)))
% 173.53/173.43 [6333]E(x63331,f127(x63332))+~E(x63333,f312(f312(f21(a852),f312(f190(f853(x63332)),x63331)),f87(a852)))+E(f140(x63332,f312(f312(f155(x63332,x63331),x63333),x63334)),x63334)
% 173.53/173.43 [6355]~P98(x63551)+~P22(f312(f312(f228(x63551),x63552),x63554))+P22(f312(f312(f228(x63551),x63552),f312(f312(f124(x63551),x63553),x63554)))
% 173.53/173.43 [6356]~P98(x63561)+~P22(f312(f312(f228(x63561),x63562),x63563))+P22(f312(f312(f228(x63561),x63562),f312(f312(f124(x63561),x63563),x63564)))
% 173.53/173.43 [6358]~P103(x63581)+~P22(f312(f312(f228(x63581),x63582),x63584))+P22(f312(f312(f228(x63581),x63582),f312(f312(f226(x63581),x63583),x63584)))
% 173.53/173.43 [6360]~P103(x63601)+~P22(f312(f312(f228(x63601),x63602),x63603))+P22(f312(f312(f228(x63601),x63602),f312(f312(f226(x63601),x63603),x63604)))
% 173.53/173.43 [6361]~P98(x63611)+~P22(f312(f312(f227(x63611),x63612),x63614))+P22(f312(f312(f227(x63611),x63612),f312(f312(f124(x63611),x63613),x63614)))
% 173.53/173.43 [6362]~P98(x63621)+~P22(f312(f312(f227(x63621),x63622),x63623))+P22(f312(f312(f227(x63621),x63622),f312(f312(f124(x63621),x63623),x63624)))
% 173.53/173.43 [6364]~P103(x63641)+~P22(f312(f312(f227(x63641),x63642),x63644))+P22(f312(f312(f227(x63641),x63642),f312(f312(f226(x63641),x63643),x63644)))
% 173.53/173.43 [6366]~P103(x63661)+~P22(f312(f312(f227(x63661),x63662),x63663))+P22(f312(f312(f227(x63661),x63662),f312(f312(f226(x63661),x63663),x63664)))
% 173.53/173.43 [6449]~E(f312(f312(f161(x64491),x64492),x64493),x64494)+E(f312(f312(f155(x64491,x64492),x64493),x64494),x64492)+~P22(f312(f312(f228(a852),x64493),f312(f190(f853(x64491)),x64492)))
% 173.53/173.43 [6468]E(x64681,x64682)+P22(f312(x64683,x64681))+~P22(f312(f312(f195(f35(x64683,x64684)),x64681),x64682))
% 173.53/173.43 [6489]P22(f312(x64891,x64892))+~P22(f312(x64893,x64892))+~P22(f312(f312(f227(f860(x64894,a845)),x64893),x64891))
% 173.53/173.43 [6521]~E(f312(f312(f155(x65211,x65212),x65213),x65214),x65212)+E(f312(f312(f161(x65211),x65212),x65213),x65214)+~P22(f312(f312(f228(a852),x65213),f312(f190(f853(x65211)),x65212)))
% 173.53/173.43 [6535]~P22(f312(f156(x65351,x65352),x65354))+~P22(f312(f156(x65351,x65352),x65353))+P22(f312(f156(x65351,x65352),f312(f312(f129(x65351),x65353),x65354)))
% 173.53/173.43 [6633]P34(x66331,x66332,x66333)+~P34(x66331,f312(a126,x66332),f615(x66332,x66334,x66331))+~P22(f312(f312(f314(f851(x66331)),x66333),x66334))
% 173.53/173.43 [6642]E(x66421,f189(f860(x66422,a845)))+E(x66423,f189(f860(x66424,a845)))+~E(f312(f312(f247(x66424,x66422),x66423),f312(f16(f860(x66422,a845),x66424),x66421)),f189(f860(f859(x66424,x66422),a845)))
% 173.53/173.43 [6660]E(x66601,x66602)+P22(f312(f312(f314(x66603),x66601),x66604))+~P22(f312(f312(f314(x66603),x66601),f312(f312(f289(x66603),x66602),x66604)))
% 173.53/173.43 [6676]~P103(x66761)+P22(f312(f312(f228(x66761),x66762),x66763))+~P22(f312(f312(f228(x66761),x66762),f312(f312(f225(x66761),x66764),x66763)))
% 173.53/173.43 [6677]~P103(x66771)+P22(f312(f312(f228(x66771),x66772),x66773))+~P22(f312(f312(f228(x66771),x66772),f312(f312(f225(x66771),x66773),x66774)))
% 173.53/173.43 [6679]~P99(x66791)+P22(f312(f312(f227(x66791),x66792),x66793))+~P22(f312(f312(f227(x66791),x66792),f312(f312(f115(x66791),x66794),x66793)))
% 173.53/173.43 [6681]~P99(x66811)+P22(f312(f312(f227(x66811),x66812),x66813))+~P22(f312(f312(f227(x66811),x66812),f312(f312(f115(x66811),x66813),x66814)))
% 173.53/173.43 [6683]~P103(x66831)+P22(f312(f312(f227(x66831),x66832),x66833))+~P22(f312(f312(f227(x66831),x66832),f312(f312(f225(x66831),x66834),x66833)))
% 173.53/173.43 [6685]~P103(x66851)+P22(f312(f312(f227(x66851),x66852),x66853))+~P22(f312(f312(f227(x66851),x66852),f312(f312(f225(x66851),x66853),x66854)))
% 173.53/173.43 [6703]~E(f312(f312(f161(x67031),x67033),x67034),x67032)+P22(f312(f312(f314(x67031),x67032),f312(f168(x67031),x67033)))+~P22(f312(f312(f228(a852),x67034),f312(f190(f853(x67031)),x67033)))
% 173.53/173.43 [6715]~P103(x67151)+~P33(x67151,f312(f312(f147(x67151),x67152),f312(f312(f147(x67151),x67153),x67154)))+P22(f312(f312(f227(x67151),x67152),x67153))
% 173.53/173.43 [6846]E(x68461,f2(a1))+E(f312(f47(a1,x68462),x68461),x68463)+~P22(f312(f57(x68462,x68461),f312(f312(f239(a1,a1),x68463),x68464)))
% 173.53/173.43 [6894]E(f54(a1,x68942,x68941),x68943)+E(x68941,f2(a1))+~P22(f312(f57(x68942,x68941),f312(f312(f239(a1,a1),x68944),x68943)))
% 173.53/173.43 [7014]P22(f312(f312(f314(x70141),x70142),x70143))+~P22(f312(f312(f314(x70141),x70142),x70144))+~P22(f312(f312(f228(f860(x70141,a845)),x70144),x70143))
% 173.53/173.43 [7018]P22(f312(f312(f314(x70181),x70182),x70183))+~P22(f312(f312(f314(x70181),x70182),x70184))+~P22(f312(f312(f227(f860(x70181,a845)),x70184),x70183))
% 173.53/173.43 [7128]P38(x71281,x71282,x71283)+~P22(f312(x71282,f312(f312(f161(x71281),x71283),x71284)))+~P22(f312(f312(f228(a852),x71284),f312(f190(f853(x71281)),x71283)))
% 173.53/173.43 [7231]~P104(x72312)+~P22(f312(f312(f228(f860(x72311,x72312)),x72313),x72314))+P22(f312(f312(f227(f860(x72311,x72312)),x72313),x72314))
% 173.53/173.43 [7315]~P18(x73151,x73152,x73154)+P18(x73151,x73152,f312(f312(f289(f851(x73151)),x73153),x73154))+~P18(x73151,x73152,f312(f312(f289(f851(x73151)),x73153),f189(f860(f851(x73151),a845))))
% 173.53/173.43 [7358]~P22(f312(f312(f314(x73581),x73582),x73584))+P22(f312(f312(f314(x73581),x73582),f48(f860(x73581,a845),x73583)))+~P22(f312(f312(f314(f860(x73581,a845)),x73584),x73583))
% 173.53/173.43 [7372]P34(x73721,x73722,x73723)+P22(f312(f312(f314(f851(x73721)),f615(x73722,x73724,x73721)),x73724))+~P22(f312(f312(f314(f851(x73721)),x73723),x73724))
% 173.53/173.43 [7389]~P80(x73891)+~P22(f312(f312(f228(x73891),x73893),x73894))+P22(f312(f312(f228(x73891),f312(f312(f89(x73891),x73892),x73893)),f312(f312(f89(x73891),x73892),x73894)))
% 173.53/173.43 [7390]~P81(x73901)+~P22(f312(f312(f228(x73901),x73903),x73904))+P22(f312(f312(f228(x73901),f312(f312(f89(x73901),x73902),x73903)),f312(f312(f89(x73901),x73902),x73904)))
% 173.53/173.43 [7391]~P80(x73911)+~P22(f312(f312(f228(x73911),x73912),x73914))+P22(f312(f312(f228(x73911),f312(f312(f89(x73911),x73912),x73913)),f312(f312(f89(x73911),x73914),x73913)))
% 173.53/173.43 [7392]~P81(x73921)+~P22(f312(f312(f228(x73921),x73922),x73924))+P22(f312(f312(f228(x73921),f312(f312(f89(x73921),x73922),x73923)),f312(f312(f89(x73921),x73924),x73923)))
% 173.53/173.43 [7393]~P81(x73931)+~P22(f312(f312(f227(x73931),x73933),x73934))+P22(f312(f312(f227(x73931),f312(f312(f89(x73931),x73932),x73933)),f312(f312(f89(x73931),x73932),x73934)))
% 173.53/173.43 [7394]~P82(x73941)+~P22(f312(f312(f227(x73941),x73943),x73944))+P22(f312(f312(f227(x73941),f312(f312(f89(x73941),x73942),x73943)),f312(f312(f89(x73941),x73942),x73944)))
% 173.53/173.43 [7395]~P81(x73951)+~P22(f312(f312(f227(x73951),x73952),x73954))+P22(f312(f312(f227(x73951),f312(f312(f89(x73951),x73952),x73953)),f312(f312(f89(x73951),x73954),x73953)))
% 173.53/173.43 [7396]~P82(x73961)+~P22(f312(f312(f227(x73961),x73962),x73964))+P22(f312(f312(f227(x73961),f312(f312(f89(x73961),x73962),x73963)),f312(f312(f89(x73961),x73964),x73963)))
% 173.53/173.43 [7405]~P132(x74051)+~P91(x74051)+E(f312(f312(f89(x74051),f312(f312(f90(x74051),x74052),f312(f117(x74051),x74053))),f312(f312(f90(x74051),x74054),f312(f117(x74051),x74053))),f312(f312(f90(x74051),f312(f312(f89(x74051),x74052),x74054)),f312(f117(x74051),x74053)))
% 173.53/173.43 [7406]~P120(x74061)+~P91(x74061)+E(f312(f312(f21(x74061),f312(f312(f90(x74061),x74062),f312(f117(x74061),x74063))),f312(f312(f90(x74061),x74064),f312(f117(x74061),x74063))),f312(f312(f90(x74061),f312(f312(f21(x74061),x74062),x74064)),f312(f117(x74061),x74063)))
% 173.53/173.43 [7441]~P26(x74411)+E(f312(f312(f89(x74411),f312(x74412,x74413)),f312(f312(f6(a852,x74411),x74412),f283(a852,f312(a126,x74413),x74414))),f312(f312(f6(a852,x74411),x74412),f283(a852,x74413,x74414)))+~P22(f312(f312(f227(a852),x74413),x74414))
% 173.53/173.43 [7453]~P19(x74532,x74531,x74533,f312(f168(x74532),x74534))+~P22(f312(f133(x74532),x74534))+P22(f312(f133(x74531),f312(f312(f150(x74532,x74531),x74533),x74534)))
% 173.53/173.43 [7500]~P22(f312(f312(f228(a852),x75002),x75004))+~P22(f312(f312(f228(a852),x75001),x75003))+P22(f312(f312(f228(a852),f312(f312(f89(a852),x75001),x75002)),f312(f312(f89(a852),x75003),x75004)))
% 173.53/173.43 [7503]~P22(f312(f312(f228(a1),x75031),x75033))+~P22(f312(f312(f227(a1),x75032),x75034))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x75031),x75032)),f312(f312(f89(a1),x75033),x75034)))
% 173.53/173.43 [7504]~P22(f312(f312(f227(a852),x75042),x75044))+~P22(f312(f312(f227(a852),x75041),x75043))+P22(f312(f312(f227(a852),f312(f312(f89(a852),x75041),x75042)),f312(f312(f89(a852),x75043),x75044)))
% 173.53/173.43 [7505]~P22(f312(f312(f227(a852),x75052),x75054))+~P22(f312(f312(f227(a852),x75051),x75053))+P22(f312(f312(f227(a852),f312(f312(f90(a852),x75051),x75052)),f312(f312(f90(a852),x75053),x75054)))
% 173.53/173.43 [7552]P22(f312(f312(f314(x75521),x75522),x75523))+~P22(f312(f312(f314(x75521),x75522),f49(f860(x75521,a845),x75524)))+~P22(f312(f312(f314(f860(x75521,a845)),x75523),x75524))
% 173.53/173.43 [7567]~P22(f312(x75671,f596(x75671,x75673,x75672)))+P22(f312(x75671,f312(f312(f161(x75672),x75673),x75674)))+~P22(f312(f312(f228(a852),x75674),f312(f190(f853(x75672)),x75673)))
% 173.53/173.43 [7573]P22(f312(x75731,x75732))+~P22(f312(f312(f314(x75734),x75732),f312(f168(x75734),x75733)))+P22(f312(f312(f228(a852),f597(x75731,x75733,x75734)),f312(f190(f853(x75734)),x75733)))
% 173.53/173.43 [7592]~P22(f312(f312(f195(x75922),x75923),x75924))+~P22(f312(f312(f195(f35(x75921,x75922)),x75924),x75923))+P22(f312(f312(f195(f35(x75921,x75922)),x75923),x75923))
% 173.53/173.43 [7621]~P104(x76211)+~P22(f312(f312(f227(f860(x76212,x76211)),x76214),x76213))+~P22(f312(f312(f228(f860(x76212,x76211)),x76213),x76214))
% 173.53/173.43 [7667]~P22(f312(x76674,x76672))+~P22(f312(f312(f314(x76671),x76672),x76673))+P22(f312(f312(f314(x76671),x76672),f312(f312(f115(f860(x76671,a845)),x76673),f312(f233(x76671),x76674))))
% 173.53/173.43 [7808]~P22(f312(f312(f314(x78081),x78083),x78084))+~P22(f312(f312(f228(f860(x78081,a845)),x78082),x78084))+P22(f312(f312(f228(f860(x78081,a845)),x78082),f312(f312(f289(x78081),x78083),x78084)))
% 173.53/173.43 [7809]E(f312(f312(f115(f860(x78091,a845)),x78092),x78093),f189(f860(x78091,a845)))+~E(f312(f312(f115(f860(x78091,a845)),f48(f860(x78091,a845),x78094)),x78093),f189(f860(x78091,a845)))+~P22(f312(f312(f314(f860(x78091,a845)),x78092),x78094))
% 173.53/173.43 [7882]P22(f312(f312(f314(x78821),x78822),x78823))+~P22(f312(f312(f227(f860(x78821,a845)),x78823),f312(f312(f289(x78821),x78822),x78824)))+P22(f312(f312(f227(f860(x78821,a845)),x78823),x78824))
% 173.53/173.43 [7902]P22(f312(f312(f314(x79022),f596(x79021,x79023,x79022)),f312(f168(x79022),x79023)))+P22(f312(x79021,f312(f312(f161(x79022),x79023),x79024)))+~P22(f312(f312(f228(a852),x79024),f312(f190(f853(x79022)),x79023)))
% 173.53/173.43 [7910]~P22(f312(f312(f228(f860(x79101,a845)),x79102),x79104))+P22(f312(f312(f228(f860(x79101,a845)),x79102),x79103))+~P22(f312(f312(f228(f860(x79101,a845)),x79104),x79103))
% 173.53/173.43 [7911]~P22(f312(f312(f227(f860(x79111,a845)),x79112),x79114))+P22(f312(f312(f228(f860(x79111,a845)),x79112),x79113))+~P22(f312(f312(f228(f860(x79111,a845)),x79114),x79113))
% 173.53/173.43 [7912]~P22(f312(f312(f227(f860(x79121,a845)),x79124),x79123))+~P22(f312(f312(f228(f860(x79121,a845)),x79122),x79124))+P22(f312(f312(f228(f860(x79121,a845)),x79122),x79123))
% 173.53/173.43 [7913]~P22(f312(f312(f227(f860(x79131,a845)),x79132),x79134))+P22(f312(f312(f227(f860(x79131,a845)),x79132),x79133))+~P22(f312(f312(f227(f860(x79131,a845)),x79134),x79133))
% 173.53/173.43 [7953]~P22(f312(f312(f314(x79531),x79534),x79533))+~P22(f312(f312(f228(f860(x79531,a845)),x79532),f312(f312(f289(x79531),x79534),x79533)))+P22(f312(f312(f228(f860(x79531,a845)),x79532),x79533))
% 173.53/173.43 [7965]~P81(x79651)+P22(f312(f312(f228(x79651),x79652),x79653))+~P22(f312(f312(f228(x79651),f312(f312(f89(x79651),x79654),x79652)),f312(f312(f89(x79651),x79654),x79653)))
% 173.53/173.43 [7967]~P81(x79671)+P22(f312(f312(f228(x79671),x79672),x79673))+~P22(f312(f312(f228(x79671),f312(f312(f89(x79671),x79672),x79674)),f312(f312(f89(x79671),x79673),x79674)))
% 173.53/173.43 [7969]~P81(x79691)+P22(f312(f312(f227(x79691),x79692),x79693))+~P22(f312(f312(f227(x79691),f312(f312(f89(x79691),x79694),x79692)),f312(f312(f89(x79691),x79694),x79693)))
% 173.53/173.43 [7971]~P81(x79711)+P22(f312(f312(f227(x79711),x79712),x79713))+~P22(f312(f312(f227(x79711),f312(f312(f89(x79711),x79712),x79714)),f312(f312(f89(x79711),x79713),x79714)))
% 173.53/173.43 [8022]P22(f312(x80221,x80222))+~E(f312(f312(f134(x80223),f312(f190(f853(x80223)),f172(x80223,x80221,x80224))),x80224),f127(x80223))+~P22(f312(f312(f314(x80223),x80222),f312(f168(x80223),x80224)))
% 173.53/173.43 [8148]P22(f312(x81481,x81482))+~P22(f312(f312(f314(x81483),x81482),f312(f168(x81483),x81484)))+P22(f312(f312(f228(a852),f312(f190(f853(x81483)),f312(f132(x81483,x81481),x81484))),f312(f190(f853(x81483)),x81484)))
% 173.53/173.43 [8277]E(x82771,x82772)+P22(f312(f312(f195(x82773),x82771),f804(x82772,x82771,x82773,x82774)))+~P22(f312(f312(f195(f35(x82774,x82773)),x82771),x82772))
% 173.53/173.43 [8278]E(x82781,x82782)+P22(f312(f312(f195(x82783),x82781),f844(x82782,x82781,x82783,x82784)))+~P22(f312(f312(f195(f35(x82784,x82783)),x82781),x82782))
% 173.53/173.43 [8308]~P22(f312(x83084,x83082))+P22(f312(f312(f195(x83081),x83082),f804(x83083,x83082,x83081,x83084)))+~P22(f312(f312(f195(f35(x83084,x83081)),x83082),x83083))
% 173.53/173.43 [8309]~P22(f312(x83094,x83092))+P22(f312(f312(f195(x83091),x83092),f844(x83093,x83092,x83091,x83094)))+~P22(f312(f312(f195(f35(x83094,x83091)),x83092),x83093))
% 173.53/173.43 [8630]~P22(f312(x86301,f738(x86301,x86303,x86302,x86304)))+P22(f312(x86301,f312(f312(f161(x86302),x86303),x86304)))+~P22(f312(f312(f228(a852),x86304),f312(f190(f853(x86302)),x86303)))
% 173.53/173.43 [8655]~P19(x86554,x86553,x86551,f235(f860(x86554,a845)))+E(f312(x86551,f824(x86552,x86551,x86553,x86554)),x86552)+~P22(f312(f312(f314(x86553),x86552),f312(f290(x86554,x86553,x86551),f235(f860(x86554,a845)))))
% 173.53/173.43 [8718]E(f172(x87181,x87182,x87183),f312(f312(f169(x87181),x87184),x87183))+P22(f312(f312(f228(a852),f682(x87182,x87183,x87181,x87184)),x87184))+P22(f312(f312(f228(a852),x87184),f312(f190(f853(x87181)),x87183)))
% 173.53/173.43 [8721]E(f172(x87211,x87212,x87213),f312(f312(f169(x87211),x87214),x87213))+P22(f312(f312(f228(a852),f682(x87212,x87213,x87211,x87214)),x87214))+P22(f312(x87212,f312(f312(f161(x87211),x87213),x87214)))
% 173.53/173.43 [8750]P22(f312(x87501,x87502))+~P22(f312(f312(f314(x87504),x87502),f312(f168(x87504),x87503)))+P22(f312(f312(f228(a852),f699(x87502,x87501,x87503,x87504)),f312(f190(f853(x87504)),x87503)))
% 173.53/173.43 [8753]E(f172(x87531,x87532,x87533),f312(f312(f169(x87531),x87534),x87533))+P22(f312(f312(f228(a852),x87534),f312(f190(f853(x87531)),x87533)))+P22(f312(f312(f228(a852),f682(x87532,x87533,x87531,x87534)),f312(f190(f853(x87531)),x87533)))
% 173.53/173.43 [8759]E(f172(x87591,x87592,x87593),f312(f312(f169(x87591),x87594),x87593))+P22(f312(x87592,f312(f312(f161(x87591),x87593),x87594)))+P22(f312(f312(f228(a852),f682(x87592,x87593,x87591,x87594)),f312(f190(f853(x87591)),x87593)))
% 173.53/173.43 [8816]~P22(f312(f70(x88161),x88164))+P22(f312(f312(f314(x88161),f525(x88162,x88163,x88164,x88161)),x88164))+P22(f312(f70(f859(x88161,x88163)),f312(f312(f247(x88161,x88163),x88164),x88162)))
% 173.53/173.43 [8851]P22(f312(f312(f314(x88512),f738(x88511,x88513,x88512,x88514)),f312(f168(x88512),x88513)))+P22(f312(x88511,f312(f312(f161(x88512),x88513),x88514)))+~P22(f312(f312(f228(a852),x88514),f312(f190(f853(x88512)),x88513)))
% 173.53/173.43 [8866]E(x88661,x88662)+P22(f312(f312(f195(f35(x88663,x88664)),f804(x88661,x88662,x88664,x88663)),x88661))+~P22(f312(f312(f195(f35(x88663,x88664)),x88662),x88661))
% 173.53/173.43 [8867]E(x88671,x88672)+P22(f312(f312(f195(f35(x88673,x88674)),f844(x88671,x88672,x88674,x88673)),x88671))+~P22(f312(f312(f195(f35(x88673,x88674)),x88672),x88671))
% 173.53/173.43 [8889]~P22(f312(x88891,x88894))+P22(f312(f312(f195(f35(x88891,x88892)),f804(x88893,x88894,x88892,x88891)),x88893))+~P22(f312(f312(f195(f35(x88891,x88892)),x88894),x88893))
% 173.53/173.43 [8890]~P22(f312(x88901,x88904))+P22(f312(f312(f195(f35(x88901,x88902)),f844(x88903,x88904,x88902,x88901)),x88903))+~P22(f312(f312(f195(f35(x88901,x88902)),x88904),x88903))
% 173.53/173.43 [8982]P22(f312(f312(f227(a852),x89824),f312(f190(f853(x89822)),f172(x89822,x89823,x89821))))+P22(f312(f312(f228(a852),f683(x89821,x89822,x89823,x89824)),x89824))+~P22(f312(f312(f227(a852),x89824),f312(f190(f853(x89822)),x89821)))
% 173.53/173.43 [9084]~E(f312(f312(f173(x90841,x90842),x90843),f706(x90844,x90843,x90842,x90841)),f312(f312(f173(x90841,x90842),x90844),f706(x90844,x90843,x90842,x90841)))+E(f312(f173(x90841,x90842),x90843),f312(f173(x90841,x90842),x90844))+~E(f312(f168(x90841),f312(f312(f150(f859(x90841,x90842),x90841),f246(x90841,x90842)),x90843)),f312(f168(x90841),f312(f312(f150(f859(x90841,x90842),x90841),f246(x90841,x90842)),x90844)))
% 173.53/173.43 [9131]E(f172(x91311,x91312,x91313),f312(f312(f169(x91311),x91314),x91313))+~P22(f312(x91312,f312(f312(f161(x91311),x91313),f682(x91312,x91313,x91311,x91314))))+P22(f312(f312(f228(a852),x91314),f312(f190(f853(x91311)),x91313)))
% 173.53/173.43 [9136]E(f172(x91361,x91362,x91363),f312(f312(f169(x91361),x91364),x91363))+~P22(f312(x91362,f312(f312(f161(x91361),x91363),f682(x91362,x91363,x91361,x91364))))+P22(f312(x91362,f312(f312(f161(x91361),x91363),x91364)))
% 173.53/173.43 [9143]~P22(f312(f70(x91431),x91433))+~P22(f312(f70(x91432),f312(x91434,f525(x91434,x91432,x91433,x91431))))+P22(f312(f70(f859(x91431,x91432)),f312(f312(f247(x91431,x91432),x91433),x91434)))
% 173.53/173.43 [9157]~E(f312(f190(f853(x91574)),x91572),f312(f190(f853(x91574)),x91573))+P22(f312(f312(f314(f859(f853(x91574),f853(x91574))),f312(f312(f239(f853(x91574),f853(x91574)),x91573),x91572)),f154(x91574,x91571)))+P22(f312(f312(f228(a852),f601(x91571,x91572,x91573,x91574)),f312(f190(f853(x91574)),x91573)))
% 173.53/173.43 [9212]~P22(f312(x92123,f312(f312(f161(x92122),x92124),f683(x92124,x92122,x92123,x92121))))+P22(f312(f312(f227(a852),x92121),f312(f190(f853(x92122)),f172(x92122,x92123,x92124))))+~P22(f312(f312(f227(a852),x92121),f312(f190(f853(x92122)),x92124)))
% 173.53/173.43 [9286]E(f312(f312(f169(x92861),f602(x92862,x92863,x92864,x92861)),x92863),f312(f312(f169(x92861),f602(x92862,x92863,x92864,x92861)),x92864))+~P22(f312(f312(f314(f859(f853(x92861),f853(x92861))),f312(f312(f239(f853(x92861),f853(x92861)),x92864),x92863)),f143(x92861,x92862)))+P22(f312(f312(f228(a852),f312(f190(f853(x92861)),x92864)),f312(f190(f853(x92861)),x92863)))
% 173.53/173.43 [9342]~P22(f312(f312(f228(a852),f2(a852)),x93423))+~P22(f312(f312(f228(a852),x93424),x93421))+P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),x93421),f54(a852,x93422,x93423))),x93424)),f312(f312(f90(a852),x93421),x93423)))
% 173.53/173.43 [9528]~P104(x95282)+~P22(f312(f312(f227(x95282),f312(x95283,f814(x95284,x95283,x95281,x95282))),f312(x95284,f814(x95284,x95283,x95281,x95282))))+P22(f312(f312(f227(f860(x95281,x95282)),x95283),x95284))
% 173.53/173.43 [9631]~P30(x96311)+E(f312(f312(f6(a852,x96311),f312(f312(f18(a852,x96311,x96311),f312(f312(f8(x96311,f860(x96311,x96311),a852),f21(x96311)),x96312)),f312(f312(f8(a852,x96311,a852),x96312),f312(f312(f7(a852,a852,a852),f89(a852)),f87(a852))))),f283(a852,x96313,x96314)),f312(f312(f21(x96311),f312(x96312,x96313)),f312(x96312,f312(f312(f89(a852),x96314),f87(a852)))))+~P22(f312(f312(f227(a852),x96313),x96314))
% 173.53/173.43 [6706]E(f312(f312(f129(x67061),x67062),x67063),x67064)+~E(x67063,f312(f312(f134(x67061),f312(f190(f853(x67061)),x67062)),x67064))+~E(f312(f312(f169(x67061),f312(f190(f853(x67061)),x67062)),x67064),x67062)
% 173.53/173.43 [6760]~P65(x67602)+E(x67601,f2(x67602))+E(f312(f312(f268(x67602),f312(f312(f240(x67602),x67603),x67604)),f312(f312(f240(x67602),x67601),x67604)),f312(f312(f240(x67602),f312(f312(f268(x67602),x67603),x67601)),x67604))
% 173.53/173.43 [6898]~E(f312(f190(f853(x68981)),x68983),f312(f190(f853(x68982)),x68984))+~P22(f312(f133(x68981),x68983))+E(f179(x68981,x68982,f312(f173(x68981,x68982),f312(f312(f177(x68981,x68982),x68983),x68984))),f312(f168(x68981),x68983))
% 173.53/173.43 [6918]~P99(x69181)+~P22(f312(f312(f228(x69181),x69183),x69184))+P22(f312(f312(f228(x69181),f312(f312(f115(x69181),x69182),x69183)),x69184))
% 173.53/173.43 [6919]~P99(x69191)+~P22(f312(f312(f228(x69191),x69192),x69194))+P22(f312(f312(f228(x69191),f312(f312(f115(x69191),x69192),x69193)),x69194))
% 173.53/173.43 [6921]~P103(x69211)+~P22(f312(f312(f228(x69211),x69213),x69214))+P22(f312(f312(f228(x69211),f312(f312(f225(x69211),x69212),x69213)),x69214))
% 173.53/173.43 [6923]~P103(x69231)+~P22(f312(f312(f228(x69231),x69232),x69234))+P22(f312(f312(f228(x69231),f312(f312(f225(x69231),x69232),x69233)),x69234))
% 173.53/173.43 [6924]~P99(x69241)+~P22(f312(f312(f227(x69241),x69243),x69244))+P22(f312(f312(f227(x69241),f312(f312(f115(x69241),x69242),x69243)),x69244))
% 173.53/173.43 [6925]~P99(x69251)+~P22(f312(f312(f227(x69251),x69252),x69254))+P22(f312(f312(f227(x69251),f312(f312(f115(x69251),x69252),x69253)),x69254))
% 173.53/173.43 [6927]~P103(x69271)+~P22(f312(f312(f227(x69271),x69273),x69274))+P22(f312(f312(f227(x69271),f312(f312(f225(x69271),x69272),x69273)),x69274))
% 173.53/173.43 [6929]~P103(x69291)+~P22(f312(f312(f227(x69291),x69292),x69294))+P22(f312(f312(f227(x69291),f312(f312(f225(x69291),x69292),x69293)),x69294))
% 173.53/173.43 [6948]~P22(f312(x69483,x69484))+~P22(f312(x69482,x69484))+P22(f312(f312(f312(f115(f860(x69481,a845)),x69482),x69483),x69484))
% 173.53/173.43 [7074]P18(x70741,x70742,x70743)+~P18(x70741,x70744,x70743)+~P22(f312(f312(f227(f860(f851(x70741),a845)),x70744),x70742))
% 173.53/173.43 [7075]P18(x70751,x70752,x70753)+~P18(x70751,x70752,x70754)+~P22(f312(f312(f227(f860(f851(x70751),a845)),x70753),x70754))
% 173.53/173.43 [7431]~P26(x74311)+E(f312(f312(f89(x74311),f312(x74312,x74313)),f312(f312(f6(a852,x74311),x74312),f312(f282(a852,f312(a126,x74313)),x74314))),f312(f312(f6(a852,x74311),x74312),f312(f282(a852,x74313),x74314)))+~P22(f312(f312(f228(a852),x74313),x74314))
% 173.53/173.43 [7460]~P103(x74601)+P22(f312(f312(f228(x74601),x74602),x74603))+~P22(f312(f312(f228(x74601),f312(f312(f226(x74601),x74604),x74602)),x74603))
% 173.53/173.43 [7461]~P103(x74611)+P22(f312(f312(f228(x74611),x74612),x74613))+~P22(f312(f312(f228(x74611),f312(f312(f226(x74611),x74612),x74614)),x74613))
% 173.53/173.43 [7463]~P98(x74631)+P22(f312(f312(f227(x74631),x74632),x74633))+~P22(f312(f312(f227(x74631),f312(f312(f124(x74631),x74634),x74632)),x74633))
% 173.53/173.43 [7465]~P98(x74651)+P22(f312(f312(f227(x74651),x74652),x74653))+~P22(f312(f312(f227(x74651),f312(f312(f124(x74651),x74652),x74654)),x74653))
% 173.53/173.43 [7467]~P103(x74671)+P22(f312(f312(f227(x74671),x74672),x74673))+~P22(f312(f312(f227(x74671),f312(f312(f226(x74671),x74674),x74672)),x74673))
% 173.53/173.43 [7469]~P103(x74691)+P22(f312(f312(f227(x74691),x74692),x74693))+~P22(f312(f312(f227(x74691),f312(f312(f226(x74691),x74692),x74694)),x74693))
% 173.53/173.43 [7544]~P22(f312(f312(f314(x75441),x75442),x75444))+P22(f312(f312(f314(x75441),x75442),x75443))+P22(f312(f312(f314(x75441),x75442),f312(f312(f21(f860(x75441,a845)),x75444),x75443)))
% 173.53/173.43 [7628]P22(f312(x76281,x76282))+P22(f312(x76283,x76282))+~P22(f312(f312(f312(f124(f860(x76284,a845)),x76283),x76281),x76282))
% 173.53/173.43 [7639]~P22(f312(f312(f314(x76391),x76392),x76394))+~P22(f312(f312(f314(x76391),x76392),x76393))+P22(f312(f312(f314(x76391),x76392),f312(f312(f115(f860(x76391,a845)),x76393),x76394)))
% 173.53/173.43 [7691]~P98(x76911)+~P22(f312(f70(x76911),x76914))+E(f312(f312(f73(x76911,x76911,f124(x76911)),x76912),f312(f312(f289(x76911),x76913),x76914)),f312(f312(f124(x76911),x76913),f312(f312(f73(x76911,x76911,f124(x76911)),x76912),x76914)))
% 173.53/173.43 [7692]~P99(x76921)+~P22(f312(f70(x76921),x76924))+E(f312(f312(f73(x76921,x76921,f115(x76921)),x76922),f312(f312(f289(x76921),x76923),x76924)),f312(f312(f115(x76921),x76923),f312(f312(f73(x76921,x76921,f115(x76921)),x76922),x76924)))
% 173.53/173.43 [7693]~P103(x76931)+~P22(f312(f70(x76931),x76934))+E(f312(f312(f73(x76931,x76931,f225(x76931)),x76932),f312(f312(f289(x76931),x76933),x76934)),f312(f312(f225(x76931),x76933),f312(f312(f73(x76931,x76931,f225(x76931)),x76932),x76934)))
% 173.53/173.43 [7694]~P103(x76941)+~P22(f312(f70(x76941),x76944))+E(f312(f312(f73(x76941,x76941,f226(x76941)),x76942),f312(f312(f289(x76941),x76943),x76944)),f312(f312(f226(x76941),x76943),f312(f312(f73(x76941,x76941,f226(x76941)),x76942),x76944)))
% 173.53/173.43 [7695]~P132(x76951)+~P91(x76951)+E(f312(f312(f89(x76951),f312(f312(f90(x76951),f312(f117(x76951),x76952)),x76953)),f312(f312(f90(x76951),f312(f117(x76951),x76952)),x76954)),f312(f312(f90(x76951),f312(f117(x76951),x76952)),f312(f312(f89(x76951),x76953),x76954)))
% 173.53/173.43 [7696]~P120(x76961)+~P91(x76961)+E(f312(f312(f21(x76961),f312(f312(f90(x76961),f312(f117(x76961),x76962)),x76963)),f312(f312(f90(x76961),f312(f117(x76961),x76962)),x76964)),f312(f312(f90(x76961),f312(f117(x76961),x76962)),f312(f312(f21(x76961),x76963),x76964)))
% 173.53/173.43 [7806]E(x78061,x78062)+P22(f312(f312(f314(x78063),x78061),f312(f168(x78063),x78064)))+~P22(f312(f312(f314(x78063),x78061),f312(f168(x78063),f312(f312(f147(x78063),x78062),x78064))))
% 173.53/173.43 [7829]~P63(x78291)+~E(f312(f190(f853(x78292)),x78293),f312(f190(f853(x78291)),f64(x78291)))+E(f312(f312(f173(x78291,x78292),f312(f312(f177(x78291,x78292),f64(x78291)),x78293)),x78294),f312(f219(x78292),f671(x78294,x78293,x78292,x78291)))
% 173.53/173.43 [7978]P54(x79781,x79782,x79783)+~P54(x79781,x79782,x79784)+~P22(f312(f312(f227(f860(f859(x79781,x79782),a845)),x79783),x79784))
% 173.53/173.43 [8025]P22(f312(f312(f314(x80251),x80252),x80253))+P22(f312(f312(f314(x80251),x80252),x80254))+~P22(f312(f312(f314(x80251),x80252),f312(f312(f124(f860(x80251,a845)),x80254),x80253)))
% 173.53/173.43 [8036]~P50(x80361,x80364,x80363)+~P22(f312(f312(f314(x80361),x80362),x80364))+P22(f312(f312(f314(f859(x80361,x80361)),f312(f312(f239(x80361,x80361),x80362),x80362)),x80363))
% 173.53/173.43 [8052]~P22(f312(f70(x80522),x80524))+~P22(f312(f70(x80521),x80523))+P22(f312(f70(f859(x80521,x80522)),f312(f312(f247(x80521,x80522),x80523),f312(f16(f860(x80522,a845),x80521),x80524))))
% 173.53/173.43 [8053]~P22(f312(f312(f314(x80531),x80532),x80534))+~P22(f312(f312(f227(f860(x80531,a845)),x80533),x80534))+P22(f312(f312(f227(f860(x80531,a845)),f312(f312(f289(x80531),x80532),x80533)),x80534))
% 173.53/173.43 [8061]~P23(x80612)+~P72(x80612)+E(f312(f312(f9(x80611,x80612),f312(f312(f8(a852,x80612,x80611),f114(x80612)),x80613)),x80614),f312(f114(x80612),f312(f312(f9(x80611,a852),x80613),x80614)))
% 173.53/173.43 [8062]~P111(x80622)+~P72(x80622)+E(f312(f312(f9(x80621,x80622),f312(f312(f8(a1,x80622,x80621),f116(x80622)),x80623)),x80624),f312(f116(x80622),f312(f312(f9(x80621,a1),x80623),x80624)))
% 173.53/173.43 [8086]E(f312(f312(f21(f860(x80861,a845)),x80862),f312(f312(f21(f860(x80861,a845)),x80863),x80864)),x80864)+~P22(f312(f312(f227(f860(x80861,a845)),x80862),x80863))+~P22(f312(f312(f227(f860(x80861,a845)),x80864),x80862))
% 173.53/173.43 [8183]~P22(f312(f70(x81831),x81834))+E(f312(f312(f21(a852),f312(f312(f6(x81831,a852),x81832),x81833)),f312(f312(f6(x81831,a852),x81832),x81834)),f312(f312(f6(x81831,a852),x81832),f312(f312(f21(f860(x81831,a845)),x81833),x81834)))+~P22(f312(f312(f227(f860(x81831,a845)),x81834),x81833))
% 173.53/173.43 [8346]~P3(x83461,x83464,x83463)+~P22(f312(f312(f314(x83461),x83462),x83464))+P22(f312(f312(f314(x83461),x83462),f312(f264(x83461,x83461,x83463),f312(f312(f289(x83461),x83462),f189(f860(x83461,a845))))))
% 173.53/173.43 [8411]~P22(f312(f312(f227(f860(x84111,a845)),x84112),x84113))+~P22(f312(f312(f227(f860(x84111,a845)),x84112),x84114))+P22(f312(f312(f227(f860(x84111,a845)),x84112),f312(f312(f115(f860(x84111,a845)),x84113),x84114)))
% 173.53/173.43 [8511]E(x85111,f189(f860(x85112,a845)))+P22(f312(f70(x85113),x85114))+~P22(f312(f70(f859(x85113,x85112)),f312(f312(f247(x85113,x85112),x85114),f312(f16(f860(x85112,a845),x85113),x85111))))
% 173.53/173.43 [8512]E(x85121,f189(f860(x85122,a845)))+P22(f312(f70(x85123),x85124))+~P22(f312(f70(f859(x85122,x85123)),f312(f312(f247(x85122,x85123),x85121),f312(f16(f860(x85123,a845),x85122),x85124))))
% 173.53/173.43 [8573]P22(f312(f312(f314(x85731),x85732),f301(x85731,x85733)))+~P22(f312(f312(f314(x85731),x85734),f301(x85731,x85733)))+~P22(f312(f312(f314(f859(x85731,x85731)),f312(f312(f239(x85731,x85731),x85732),x85734)),x85733))
% 173.53/173.43 [8625]~P41(x86251,x86254)+P22(f312(f312(f314(f859(x86251,x86251)),f312(f312(f239(x86251,x86251),x86253),x86252)),f287(x86251,x86254)))+P41(x86251,f312(f312(f289(f859(x86251,x86251)),f312(f312(f239(x86251,x86251),x86252),x86253)),x86254))
% 173.53/173.43 [8626]~P57(x86261,x86264)+P22(f312(f312(f314(f859(x86261,x86261)),f312(f312(f239(x86261,x86261),x86263),x86262)),f287(x86261,x86264)))+P57(x86261,f312(f312(f289(f859(x86261,x86261)),f312(f312(f239(x86261,x86261),x86262),x86263)),x86264))
% 173.53/173.43 [8703]~E(x87032,x87033)+~P22(f312(f312(f314(x87031),x87032),f312(f168(x87031),x87034)))+P22(f312(f312(f314(f859(x87031,x87031)),f312(f312(f239(x87031,x87031),x87032),x87033)),f312(f168(f859(x87031,x87031)),f312(f312(f177(x87031,x87031),x87034),x87034))))
% 173.53/173.43 [8726]~P49(f860(x87261,a845),f860(x87261,a845),x87263)+~P22(f312(f312(f314(x87261),x87262),f110(f860(x87261,a845),x87263)))+P22(f312(f312(f314(x87261),x87262),f312(x87263,f312(f312(f124(f860(x87261,a845)),x87264),f110(f860(x87261,a845),x87263)))))
% 173.53/173.43 [8784]~E(x87843,x87844)+P22(f312(f312(f249(x87841,x87841,a845),a309),x87842))+~P22(f312(f312(f314(f859(x87841,x87841)),x87842),f312(f168(f859(x87841,x87841)),f312(f312(f177(x87841,x87841),x87843),x87844))))
% 173.53/173.43 [8807]~P22(f312(x88074,x88072))+P22(f312(f312(f312(f312(a198,x88071),x88072),x88073),f350(x88073,x88072,x88071,x88074)))+~P22(f312(f312(f312(f312(a198,f35(x88074,x88071)),x88072),x88073),x88072))
% 173.53/173.43 [8834]P22(f312(f312(f314(f859(f853(x88341),f853(x88341))),f312(f312(f239(f853(x88341),f853(x88341)),x88342),x88343)),f143(x88341,x88344)))+~E(f312(f312(f169(x88341),f312(f190(f853(x88341)),x88342)),x88343),x88342)+~P22(f312(f312(f228(a852),f312(f190(f853(x88341)),x88342)),f312(f190(f853(x88341)),x88343)))
% 173.53/173.43 [8937]~P22(f312(f70(x89371),x89374))+P22(f312(f312(f314(x89371),f403(x89372,x89373,x89374,x89371)),x89374))+P22(f312(f70(x89373),f312(f312(f50(x89371,f860(x89373,a845)),x89374),x89372)))
% 173.53/173.43 [8938]~P22(f312(f70(x89381),x89384))+P22(f312(f312(f314(x89381),f705(x89382,x89383,x89384,x89381)),x89384))+P22(f312(f70(x89383),f312(f312(f50(x89381,f860(x89383,a845)),x89384),x89382)))
% 173.53/173.43 [9017]P22(f312(f312(f314(f859(x90171,x90171)),x90172),f312(f312(f267(x90171,x90171,x90171),x90173),f287(x90171,x90173))))+~P22(f312(f312(f228(a852),f2(a852)),x90174))+~P22(f312(f312(f314(f859(x90171,x90171)),x90172),f312(f312(f184(f859(x90171,x90171),a845),x90174),x90173)))
% 173.53/173.43 [9025]~P41(x90251,x90252)+~P22(f312(f312(f314(f859(x90251,x90251)),f312(f312(f239(x90251,x90251),x90254),x90253)),x90252))+~P22(f312(f312(f314(f859(x90251,x90251)),f312(f312(f239(x90251,x90251),x90253),x90254)),x90252))
% 173.53/173.43 [9151]~P22(f312(f70(x91511),x91514))+E(f312(f312(f6(x91511,a852),f312(f312(f8(f860(x91512,a845),a852,x91511),f53(x91512)),x91513)),x91514),f312(f53(f859(x91511,x91512)),f312(f312(f247(x91511,x91512),x91514),x91513)))+P22(f312(f312(f314(x91511),f527(x91513,x91512,x91514,x91511)),x91514))
% 173.53/173.43 [9153]~P22(f312(f133(x91531),x91532))+P22(f312(f133(x91531),f312(f312(f155(x91531,x91532),x91533),x91534)))+P22(f312(f312(f314(x91531),x91534),f312(f312(f21(f860(x91531,a845)),f312(f168(x91531),x91532)),f312(f312(f289(x91531),f312(f312(f161(x91531),x91532),x91533)),f189(f860(x91531,a845))))))
% 173.53/173.43 [9171]~P22(f312(f70(x91712),x91713))+~P22(f312(f70(x91711),f312(x91714,f403(x91714,x91711,x91713,x91712))))+P22(f312(f70(x91711),f312(f312(f50(x91712,f860(x91711,a845)),x91713),x91714)))
% 173.53/173.43 [9172]~P22(f312(f70(x91722),x91723))+~P22(f312(f70(x91721),f312(x91724,f705(x91724,x91721,x91723,x91722))))+P22(f312(f70(x91721),f312(f312(f50(x91722,f860(x91721,a845)),x91723),x91724)))
% 173.53/173.43 [9248]~P22(f312(f312(f314(f859(x92481,x92481)),x92482),f312(f312(f267(x92481,x92481,x92481),x92484),f287(x92481,x92484))))+P22(f312(f312(f314(f859(x92481,x92481)),x92482),f312(f312(f267(x92481,x92481,x92481),x92483),f287(x92481,x92483))))+~P22(f312(f312(f227(f860(f859(x92481,x92481),a845)),x92484),x92483))
% 173.53/173.43 [9254]E(f312(f312(f169(x92541),f602(x92544,x92543,x92542,x92541)),x92543),f312(f312(f169(x92541),f602(x92544,x92543,x92542,x92541)),x92542))+~P22(f312(f312(f314(f859(f853(x92541),f853(x92541))),f312(f312(f239(f853(x92541),f853(x92541)),x92542),x92543)),f143(x92541,x92544)))+E(f312(f312(f169(x92541),f312(f190(f853(x92541)),x92542)),x92543),x92542)
% 173.53/173.43 [9271]~P22(f312(f70(x92711),x92714))+E(f312(f312(f6(x92711,a852),f312(f312(f8(f860(x92712,a845),a852,x92711),f53(x92712)),x92713)),x92714),f312(f53(f859(x92711,x92712)),f312(f312(f247(x92711,x92712),x92714),x92713)))+~P22(f312(f70(x92712),f312(x92713,f527(x92713,x92712,x92714,x92711))))
% 173.53/173.43 [9275]~E(f312(f190(f853(x92751)),x92753),f312(f190(f853(x92751)),x92752))+P22(f312(f312(f314(f859(f853(x92751),f853(x92751))),f312(f312(f239(f853(x92751),f853(x92751)),x92752),x92753)),f154(x92751,x92754)))+P22(f312(f312(f314(f859(x92751,x92751)),f590(x92754,x92753,x92752,x92751)),f312(f168(f859(x92751,x92751)),f312(f312(f177(x92751,x92751),x92752),x92753))))
% 173.53/173.43 [9354]~P22(f312(f312(f314(f859(f853(x93541),f853(x93541))),f312(f312(f239(f853(x93541),f853(x93541)),x93542),x93543)),f143(x93541,x93544)))+E(f312(f312(f169(x93541),f312(f190(f853(x93541)),x93542)),x93543),x93542)+P22(f312(f312(f228(a852),f602(x93544,x93543,x93542,x93541)),f312(f312(f225(a852),f312(f190(f853(x93541)),x93542)),f312(f190(f853(x93541)),x93543))))
% 173.53/173.43 [9355]E(f312(f173(x93551,x93552),x93553),f312(f173(x93551,x93552),x93554))+~E(f312(f168(x93551),f312(f312(f150(f859(x93551,x93552),x93551),f246(x93551,x93552)),x93553)),f312(f168(x93551),f312(f312(f150(f859(x93551,x93552),x93551),f246(x93551,x93552)),x93554)))+P22(f312(f312(f314(x93551),f706(x93553,x93554,x93552,x93551)),f312(f168(x93551),f312(f312(f150(f859(x93551,x93552),x93551),f246(x93551,x93552)),x93554))))
% 173.53/173.43 [9368]~P22(f312(x93681,x93684))+P22(f312(f312(f312(f312(a198,f35(x93681,x93682)),f350(x93683,x93684,x93682,x93681)),x93683),x93684))+~P22(f312(f312(f312(f312(a198,f35(x93681,x93682)),x93684),x93683),x93684))
% 173.53/173.43 [9373]~P22(f312(f312(f314(f859(f853(x93731),f853(x93731))),f312(f312(f239(f853(x93731),f853(x93731)),x93732),x93733)),f143(x93731,x93734)))+P22(f312(f312(f228(a852),f312(f190(f853(x93731)),x93732)),f312(f190(f853(x93731)),x93733)))+P22(f312(f312(f228(a852),f602(x93734,x93733,x93732,x93731)),f312(f312(f225(a852),f312(f190(f853(x93731)),x93732)),f312(f190(f853(x93731)),x93733))))
% 173.53/173.43 [9666]~P22(f312(f312(f312(x96661,f351(x96661,x96664,x96663,x96662)),f352(x96661,x96664,x96663,x96662)),f353(x96661,x96664,x96663,x96662)))+P22(f312(f312(f312(x96661,x96662),x96663),x96664))+~P22(f312(f300(f859(f860(a1,f856(f853(a308))),f859(a1,a1)),a297),f312(f312(f239(f860(a1,f856(f853(a308))),f859(a1,a1)),x96662),f312(f312(f239(a1,a1),x96663),x96664))))
% 173.53/173.43 [9744]P22(f312(f312(f312(x97441,x97442),x97443),x97444))+P22(f312(f300(f859(f860(a1,f856(f853(a308))),f859(a1,a1)),a297),f312(f312(f239(f860(a1,f856(f853(a308))),f859(a1,a1)),f351(x97441,x97444,x97443,x97442)),f312(f312(f239(a1,a1),f352(x97441,x97444,x97443,x97442)),f353(x97441,x97444,x97443,x97442)))))+~P22(f312(f300(f859(f860(a1,f856(f853(a308))),f859(a1,a1)),a297),f312(f312(f239(f860(a1,f856(f853(a308))),f859(a1,a1)),x97442),f312(f312(f239(a1,a1),x97443),x97444))))
% 173.53/173.43 [9783]~P22(f312(f312(f314(f859(f853(x97831),f853(x97831))),f312(f312(f239(f853(x97831),f853(x97831)),x97832),x97833)),f143(x97831,x97834)))+E(f312(f312(f169(x97831),f312(f190(f853(x97831)),x97832)),x97833),x97832)+P22(f312(f312(f314(f859(x97831,x97831)),f312(f312(f239(x97831,x97831),f312(f312(f161(x97831),x97832),f602(x97834,x97833,x97832,x97831))),f312(f312(f161(x97831),x97833),f602(x97834,x97833,x97832,x97831)))),x97834))
% 173.53/173.43 [9786]~P22(f312(f312(f314(f859(f853(x97861),f853(x97861))),f312(f312(f239(f853(x97861),f853(x97861)),x97862),x97863)),f143(x97861,x97864)))+P22(f312(f312(f228(a852),f312(f190(f853(x97861)),x97862)),f312(f190(f853(x97861)),x97863)))+P22(f312(f312(f314(f859(x97861,x97861)),f312(f312(f239(x97861,x97861),f312(f312(f161(x97861),x97862),f602(x97864,x97863,x97862,x97861))),f312(f312(f161(x97861),x97863),f602(x97864,x97863,x97862,x97861)))),x97864))
% 173.53/173.43 [9845]~E(f312(f190(f853(x98451)),x98452),f312(f190(f853(x98451)),x98453))+P22(f312(f312(f314(f859(f853(x98451),f853(x98451))),f312(f312(f239(f853(x98451),f853(x98451)),x98452),x98453)),f154(x98451,x98454)))+~P22(f312(f312(f314(f859(x98451,x98451)),f312(f312(f239(x98451,x98451),f312(f312(f161(x98451),x98452),f601(x98454,x98453,x98452,x98451))),f312(f312(f161(x98451),x98453),f601(x98454,x98453,x98452,x98451)))),x98454))
% 173.53/173.43 [9984]~P26(x99841)+~P22(f312(f70(x99842),x99844))+E(f312(f162(x99841),f312(f312(f150(x99842,x99841),x99843),f99(f853(x99842),f312(f312(f18(f853(x99842),a845,a845),f312(f312(f8(a845,f860(a845,a845),f853(x99842)),a310),f312(f312(f7(f853(x99842),f860(x99842,a845),a845),f312(f312(f8(f860(x99842,a845),f860(f860(x99842,a845),a845),f853(x99842)),a309),f168(x99842))),x99844))),f133(x99842))))),f217(x99842,x99841,x99843,x99844))
% 173.53/173.43 [7199]~P60(x71992)+E(x71991,f2(x71992))+E(f312(f47(x71992,f312(f312(f89(x71992),x71993),f312(f312(f90(x71992),x71994),x71991))),x71991),f312(f312(f89(x71992),x71994),f312(f47(x71992,x71993),x71991)))
% 173.53/173.43 [7200]~P60(x72002)+E(x72001,f2(x72002))+E(f312(f47(x72002,f312(f312(f89(x72002),x72003),f312(f312(f90(x72002),x72001),x72004))),x72001),f312(f312(f89(x72002),x72004),f312(f47(x72002,x72003),x72001)))
% 173.53/173.43 [7277]~P64(x72772)+E(x72771,f2(x72772))+E(f312(f312(f268(x72772),f312(f312(f89(x72772),x72773),f312(f312(f90(x72772),x72774),x72771))),x72771),f312(f312(f89(x72772),x72774),f312(f312(f268(x72772),x72773),x72771)))
% 173.53/173.43 [7508]~P64(x75082)+E(x75081,f2(x75082))+E(f312(f312(f268(x75082),f312(f312(f89(x75082),x75083),f312(f312(f90(x75082),x75084),x75081))),x75081),f312(f312(f89(x75082),f312(f312(f268(x75082),x75083),x75081)),x75084))
% 173.53/173.43 [7509]~P65(x75092)+E(x75091,f2(x75092))+E(f312(f312(f268(x75092),f312(f312(f89(x75092),x75093),f312(f312(f90(x75092),x75091),x75094))),x75091),f312(f312(f89(x75092),f312(f312(f268(x75092),x75093),x75091)),x75094))
% 173.53/173.43 [7510]~P65(x75102)+E(x75101,f2(x75102))+E(f312(f312(f268(x75102),f312(f312(f21(x75102),x75103),f312(f312(f90(x75102),x75101),x75104))),x75101),f312(f312(f21(x75102),f312(f312(f268(x75102),x75103),x75101)),x75104))
% 173.53/173.43 [8212]~P22(f312(f156(x82121,x82123),x82124))+~P22(f312(f156(x82121,x82122),x82124))+P22(f312(f156(x82121,f312(f312(f115(f860(x82121,a845)),x82122),x82123)),x82124))
% 173.53/173.43 [8587]~E(f312(f312(f267(x85871,x85871,x85871),x85872),x85874),f189(f860(f859(x85871,x85871),a845)))+~E(f312(f312(f267(x85871,x85871,x85871),x85872),x85873),f189(f860(f859(x85871,x85871),a845)))+E(f312(f312(f267(x85871,x85871,x85871),x85872),f312(f312(f124(f860(f859(x85871,x85871),a845)),x85873),x85874)),f189(f860(f859(x85871,x85871),a845)))
% 173.53/173.43 [8704]~P22(f312(f312(f227(f860(x87041,a845)),x87043),x87044))+~P22(f312(f312(f227(f860(x87041,a845)),x87042),x87044))+P22(f312(f312(f227(f860(x87041,a845)),f312(f312(f124(f860(x87041,a845)),x87042),x87043)),x87044))
% 173.53/173.43 [9078]~P22(f312(f70(x90781),x90784))+~P22(f312(f70(x90781),x90783))+E(f312(f312(f21(a852),f312(f312(f89(a852),f312(f312(f6(x90781,a852),x90782),x90783)),f312(f312(f6(x90781,a852),x90782),x90784))),f312(f312(f6(x90781,a852),x90782),f312(f312(f115(f860(x90781,a845)),x90783),x90784))),f312(f312(f6(x90781,a852),x90782),f312(f312(f124(f860(x90781,a845)),x90783),x90784)))
% 173.53/173.43 [9166]~P22(f312(f312(f314(x91661),x91663),x91662))+~P22(f312(f312(f227(f860(x91661,a845)),x91662),f312(f312(f289(x91661),x91663),x91664)))+P22(f312(f312(f227(f860(x91661,a845)),f312(f312(f21(f860(x91661,a845)),x91662),f312(f312(f289(x91661),x91663),f189(f860(x91661,a845))))),x91664))
% 173.53/173.43 [9326]~P22(f312(f312(f314(x93261),x93263),x93262))+P22(f312(f312(f227(f860(x93261,a845)),x93262),f312(f312(f289(x93261),x93263),x93264)))+~P22(f312(f312(f227(f860(x93261,a845)),f312(f312(f21(f860(x93261,a845)),x93262),f312(f312(f289(x93261),x93263),f189(f860(x93261,a845))))),x93264))
% 173.53/173.43 [9415]~P22(f312(f312(f228(a852),x94152),x94154))+~P22(f312(f312(f227(a852),x94151),x94153))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x94151),x94152)),f312(f312(f239(a852,a852),x94153),x94154))),a45))
% 173.53/173.43 [9416]~P22(f312(f312(f227(a852),x94162),x94164))+~P22(f312(f312(f227(a852),x94161),x94163))+P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),f312(f312(f239(a852,a852),x94161),x94162)),f312(f312(f239(a852,a852),x94163),x94164))),a79))
% 173.53/173.43 [9702]~P22(f312(f312(f314(f853(x97021)),x97024),f157(x97021,x97023)))+~P22(f312(f312(f314(f853(x97021)),x97024),f157(x97021,x97022)))+P22(f312(f156(x97021,f312(f312(f115(f860(x97021,a845)),f312(f312(f7(x97021,f860(x97021,a845),a845),f314(x97021)),x97022)),f312(f312(f7(x97021,f860(x97021,a845),a845),f314(x97021)),x97023))),x97024))
% 173.53/173.43 [9810]~P19(x98101,f860(f860(x98101,a845),a845),f312(f312(f7(x98101,f860(f859(x98101,x98101),a845),f860(f860(x98101,a845),a845)),f312(f312(f8(f860(x98101,a845),f860(f860(f859(x98101,x98101),a845),f860(f860(x98101,a845),a845)),x98101),f69(x98101)),f312(f312(f7(x98101,f860(x98101,a845),f860(x98101,a845)),f289(x98101)),f189(f860(x98101,a845))))),x98103),x98102)+~P22(f312(f312(f314(x98101),x98104),x98102))+E(f312(f312(f21(f860(f860(x98101,a845),a845)),f312(f312(f69(x98101),x98102),x98103)),f312(f312(f69(x98101),f312(f312(f289(x98101),x98104),f189(f860(x98101,a845)))),x98103)),f312(f312(f69(x98101),f312(f312(f21(f860(x98101,a845)),x98102),f312(f312(f289(x98101),x98104),f189(f860(x98101,a845))))),x98103))
% 173.53/173.43 [9949]~P50(x99491,x99492,x99494)+~P22(f312(f312(f314(f859(x99491,x99491)),x99493),x99494))+P22(f312(f312(f249(x99491,x99491,a845),f312(f312(f7(x99491,f860(x99491,a845),f860(x99491,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x99491,a845),f860(x99491,a845)),x99491),f8(a845,a845,x99491)),f312(f312(f8(a845,f860(a845,a845),x99491),a310),f312(f312(f7(x99491,f860(x99491,a845),a845),f314(x99491)),x99492)))),f312(f312(f7(x99491,f860(x99491,a845),a845),f314(x99491)),x99492))),x99493))
% 173.53/173.43 [9962]P22(f312(f70(x99621),x99622))+~P22(f312(f70(x99623),f312(f290(x99621,x99623,x99624),x99622)))+~P22(f312(f70(x99621),f312(f233(x99621),f312(f312(f18(x99621,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99621),a310),f312(f312(f7(x99621,f860(x99621,a845),a845),f314(x99621)),x99622))),f312(f312(f7(x99621,x99623,a845),f312(f312(f8(x99623,f860(x99623,a845),x99621),a309),x99624)),f312(x99624,f578(x99624,x99623,x99622,x99621)))))))
% 173.53/173.43 [7960]~P65(x79602)+E(x79601,f2(x79602))+E(f312(f312(f268(x79602),f312(f312(f89(x79602),f312(f312(f90(x79602),x79601),x79603)),x79604)),x79601),f312(f312(f89(x79602),x79603),f312(f312(f268(x79602),x79604),x79601)))
% 173.53/173.43 [7961]~P65(x79612)+E(x79611,f2(x79612))+E(f312(f312(f268(x79612),f312(f312(f21(x79612),f312(f312(f90(x79612),x79611),x79613)),x79614)),x79611),f312(f312(f21(x79612),x79613),f312(f312(f268(x79612),x79614),x79611)))
% 173.53/173.43 [8865]~E(f312(f312(f267(x88651,x88651,x88651),x88653),x88654),f189(f860(f859(x88651,x88651),a845)))+~E(f312(f312(f267(x88651,x88651,x88651),x88652),x88654),f189(f860(f859(x88651,x88651),a845)))+E(f312(f312(f267(x88651,x88651,x88651),f312(f312(f124(f860(f859(x88651,x88651),a845)),x88652),x88653)),x88654),f189(f860(f859(x88651,x88651),a845)))
% 173.53/173.43 [9893]~P138(x98931)+~P138(x98932)+E(f312(f312(f296(x98931),f312(f312(f7(x98931,a113,f856(f853(a308))),f312(f312(f8(f860(x98932,f856(f853(a308))),f860(a113,f856(f853(a308))),x98931),f296(x98932)),f312(f312(f8(f860(x98932,f859(x98931,x98932)),f860(x98932,f856(f853(a308))),x98931),f312(f8(f859(x98931,x98932),f856(f853(a308)),x98932),x98933)),f239(x98931,x98932)))),x98934)),x98934),f312(f312(f296(f859(x98931,x98932)),x98933),x98934))
% 173.53/173.43 [9615]~P22(f312(f156(x96151,x96153),x96154))+~P22(f312(f156(x96151,x96152),x96154))+P22(f312(f156(x96151,f312(f312(f18(x96151,a845,a845),f312(f312(f8(a845,f860(a845,a845),x96151),a310),x96152)),x96153)),x96154))
% 173.53/173.43 [9885]P22(f312(x98851,f560(x98852,x98853,x98851,x98854)))+~P22(f312(f70(x98854),f312(f233(x98854),x98851)))+P22(f312(f70(x98853),f312(f233(x98853),f312(f312(f8(f860(x98854,a845),a845,x98853),f96(x98854)),f312(f312(f8(f860(x98854,a845),f860(x98854,a845),x98853),f312(f18(x98854,a845,a845),f312(f312(f8(a845,f860(a845,a845),x98854),a310),x98851))),x98852)))))
% 173.53/173.43 [9904]~P22(f312(f70(x99042),f312(f233(x99042),x99043)))+~P22(f312(f70(x99041),f312(f233(x99041),f312(f312(f7(x99041,x99042,a845),x99044),f560(x99044,x99041,x99043,x99042)))))+P22(f312(f70(x99041),f312(f233(x99041),f312(f312(f8(f860(x99042,a845),a845,x99041),f96(x99042)),f312(f312(f8(f860(x99042,a845),f860(x99042,a845),x99041),f312(f18(x99042,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99042),a310),x99043))),x99044)))))
% 173.53/173.43 [7650]~P36(x76501,x76502,x76503,x76505)+P36(x76501,x76502,x76503,x76504)+~P36(x76501,x76502,x76505,x76504)
% 173.53/173.43 [6429]E(x64291,x64292)+~E(f312(x64293,x64291),f312(x64293,x64292))+~P19(x64294,x64295,x64293,f235(f860(x64294,a845)))
% 173.53/173.43 [6593]~E(f312(x65933,x65935),f192(x65932))+~E(f312(x65934,x65935),f192(x65932))+E(f312(f180(x65931,x65932,x65933,x65934),x65935),f192(x65932))
% 173.53/173.43 [7311]E(x73111,x73112)+~P19(x73113,x73114,x73115,f235(f860(x73113,a845)))+~E(f312(f290(x73113,x73114,x73115),x73111),f312(f290(x73113,x73114,x73115),x73112))
% 173.53/173.43 [7452]~P36(x74524,x74525,x74521,x74523)+E(f312(x74521,x74522),f312(x74523,x74522))+~P22(f312(f312(f314(x74524),x74522),f179(x74524,x74525,x74521)))
% 173.53/173.43 [7561]P19(x75612,x75613,f828(x75614,x75613,x75612,x75611),x75611)+~E(f312(f290(x75613,x75612,x75615),x75614),x75611)+E(x75611,f189(f860(x75612,a845)))
% 173.53/173.43 [8098]~P22(f312(f312(x80983,x80982),x80985))+~P22(f312(f312(x80983,x80984),x80982))+P22(f312(f312(f314(x80981),x80982),f277(x80981,x80983,x80984,x80985)))
% 173.53/173.43 [8099]~P22(f312(f312(x80993,x80992),x80995))+~P22(f312(f312(x80993,x80994),x80992))+P22(f312(f312(f314(x80991),x80992),f274(x80991,x80993,x80994,x80995)))
% 173.53/173.43 [8664]~P19(x86641,x86643,x86645,f235(f860(x86641,a845)))+~P19(x86643,x86642,x86644,f235(f860(x86643,a845)))+P19(x86641,x86642,f312(f82(x86643,x86642,x86641,x86644),x86645),f235(f860(x86641,a845)))
% 173.53/173.43 [9226]P22(f312(f312(f314(f859(x92261,x92261)),f312(f312(f239(x92261,x92261),x92262),x92263)),f287(x92261,x92264)))+~P22(f312(f312(f314(f859(x92261,x92261)),f312(f312(f239(x92261,x92261),x92262),x92265)),f287(x92261,x92264)))+~P22(f312(f312(f314(f859(x92261,x92261)),f312(f312(f239(x92261,x92261),x92265),x92263)),f287(x92261,x92264)))
% 173.53/173.43 [9261]~P103(x92612)+~P22(f312(f133(x92611),x92615))+P22(f312(f133(x92611),f146(x92611,x92612,x92613,x92614,x92615)))
% 173.53/173.43 [5287]~E(x52872,f127(x52871))+E(f312(f312(f129(x52871),x52872),x52873),f312(f312(f147(x52871),x52874),x52875))+~E(x52873,f312(f312(f147(x52871),x52874),x52875))
% 173.53/173.43 [5288]~E(x52882,f127(x52881))+E(f312(f312(f129(x52881),x52882),x52883),f312(f312(f147(x52881),x52884),x52885))+~E(f312(f312(f147(x52881),x52884),x52885),x52883)
% 173.53/173.43 [6390]~E(f312(f190(f853(x63901)),x63905),f312(f190(f853(x63902)),x63904))+E(f312(f312(f150(f859(x63901,x63902),x63902),f248(x63901,x63902)),x63903),x63904)+~E(f312(f312(f177(x63901,x63902),x63905),x63904),x63903)
% 173.53/173.43 [6391]~E(f312(f190(f853(x63911)),x63914),f312(f190(f853(x63912)),x63915))+E(f312(f312(f150(f859(x63911,x63912),x63911),f246(x63911,x63912)),x63913),x63914)+~E(f312(f312(f177(x63911,x63912),x63914),x63915),x63913)
% 173.53/173.43 [6851]~P103(x68511)+~P33(x68511,f312(f312(f150(x68512,x68511),x68513),x68515))+P33(x68511,f312(f312(f150(x68512,x68511),x68513),f312(f132(x68512,x68514),x68515)))
% 173.53/173.43 [6904]~P22(f312(x69043,x69045))+~P22(f312(f312(x69042,x69044),x69045))+P22(f312(f312(f103(x69041,x69042,x69043),x69044),x69045))
% 173.53/173.43 [7003]~P103(x70031)+P33(x70031,f312(f312(f150(x70032,x70031),x70033),f166(x70032,x70034,x70035)))+~P33(x70031,f312(f312(f150(x70032,x70031),x70033),x70035))
% 173.53/173.43 [7024]~P54(x70243,x70242,x70245)+~P54(x70241,x70243,x70244)+P54(x70241,x70242,f312(f312(f267(x70241,x70243,x70242),x70244),x70245))
% 173.53/173.43 [7118]E(x71181,x71182)+~P19(x71183,x71184,x71185,f235(f860(x71183,a845)))+~E(f312(f312(f150(x71183,x71184),x71185),x71181),f312(f312(f150(x71183,x71184),x71185),x71182))
% 173.53/173.43 [7262]~P22(f312(f312(f228(a852),x72621),f312(x72623,x72625)))+P22(f312(f312(f228(a852),x72621),f151(x72622,x72623,x72624)))+~P22(f312(f312(f314(x72622),x72625),f312(f168(x72622),x72624)))
% 173.53/173.43 [7263]~P22(f312(f312(f227(a852),x72631),f312(x72633,x72635)))+P22(f312(f312(f227(a852),x72631),f151(x72632,x72633,x72634)))+~P22(f312(f312(f314(x72632),x72635),f312(f168(x72632),x72634)))
% 173.53/173.43 [7666]~P105(x76661)+P22(f312(f312(f227(f860(x76661,a845)),f283(x76661,x76662,x76663)),f283(x76661,x76664,x76665)))+P22(f312(f312(f227(x76661),x76662),x76663))
% 173.53/173.43 [7689]~P31(x76891)+P22(f312(f312(f227(x76891),f312(f312(f51(x76892,x76891),x76893),x76894)),f312(x76894,x76895)))+~P22(f312(f312(f314(x76892),x76895),x76893))
% 173.53/173.43 [7757]~P19(x77571,x77572,x77574,x77573)+E(f312(f86(x77571,x77572,x77573,x77574),f312(x77574,x77575)),x77575)+~P22(f312(f312(f314(x77571),x77575),x77573))
% 173.53/173.43 [7948]~P22(f312(x79481,x79485))+P22(f312(x79481,f805(x79481,x79482,x79483,x79484)))+~P22(f312(f312(f314(x79484),x79485),x79483))
% 173.53/173.43 [7949]~P22(f312(x79491,x79495))+P22(f312(x79491,f805(x79491,x79492,x79493,x79494)))+~P22(f312(f312(f314(x79494),x79495),x79492))
% 173.53/173.43 [8049]P22(f312(f70(x80491),x80492))+~P22(f312(f70(x80493),x80494))+~P22(f312(f312(f227(f860(x80491,a845)),x80492),f312(f290(x80493,x80491,x80495),x80494)))
% 173.53/173.43 [8215]E(x82151,x82152)+~P19(x82153,x82154,x82155,f312(f312(f124(f860(x82153,a845)),f312(f168(x82153),x82151)),f312(f168(x82153),x82152)))+~E(f312(f312(f150(x82153,x82154),x82155),x82151),f312(f312(f150(x82153,x82154),x82155),x82152))
% 173.53/173.43 [8271]~P105(x82711)+~P22(f312(f312(f228(f860(x82711,a845)),f283(x82711,x82714,x82715)),f283(x82711,x82712,x82713)))+P22(f312(f312(f227(x82711),x82712),x82713))
% 173.53/173.43 [8344]~P19(x83441,x83444,x83445,f235(f860(x83441,a845)))+~P22(f312(f312(f314(x83444),f312(x83445,x83442)),f312(f290(x83441,x83444,x83445),x83443)))+P22(f312(f312(f314(x83441),x83442),x83443))
% 173.53/173.43 [8423]P22(f312(x84231,x84232))+~P22(f312(x84231,f808(x84231,x84233,x84234,x84235)))+~P22(f312(f312(f314(x84235),x84232),x84234))
% 173.53/173.43 [8424]P22(f312(x84241,x84242))+~P22(f312(x84241,f808(x84241,x84243,x84244,x84245)))+~P22(f312(f312(f314(x84245),x84242),x84243))
% 173.53/173.43 [8701]~P19(x87012,x87013,x87011,x87014)+E(f312(x87011,f312(f86(x87012,x87013,x87014,x87011),x87015)),x87015)+~P22(f312(f312(f314(x87013),x87015),f312(f290(x87012,x87013,x87011),x87014)))
% 173.53/173.43 [8802]E(x88021,f127(x88022))+E(f312(f312(f147(x88022),x88023),f620(x88024,x88023,x88025,x88021,x88022)),x88021)+~E(f312(f312(f129(x88022),x88021),x88025),f312(f312(f147(x88022),x88023),x88024))
% 173.53/173.43 [8803]E(x88031,f127(x88032))+E(f312(f312(f147(x88032),x88033),f621(x88034,x88031,x88035,x88033,x88032)),x88031)+~E(f312(f312(f129(x88032),x88031),x88034),f312(f312(f147(x88032),x88033),x88035))
% 173.53/173.43 [8820]E(f312(f312(f147(x88202),x88203),f620(x88204,x88203,x88201,x88205,x88202)),x88205)+~E(f312(f312(f129(x88202),x88205),x88201),f312(f312(f147(x88202),x88203),x88204))+E(x88201,f312(f312(f147(x88202),x88203),x88204))
% 173.53/173.43 [8821]E(f312(f312(f147(x88211),x88212),f621(x88214,x88215,x88213,x88212,x88211)),x88215)+~E(f312(f312(f129(x88211),x88215),x88214),f312(f312(f147(x88211),x88212),x88213))+E(f312(f312(f147(x88211),x88212),x88213),x88214)
% 173.53/173.43 [8907]~E(f312(f290(x89073,x89072,x89074),f235(f860(x89073,a845))),f235(f860(x89072,a845)))+~E(f312(f290(x89071,x89073,x89075),f235(f860(x89071,a845))),f235(f860(x89073,a845)))+E(f312(f290(x89071,x89072,f312(f82(x89073,x89072,x89071,x89074),x89075)),f235(f860(x89071,a845))),f235(f860(x89072,a845)))
% 173.53/173.43 [9268]E(x92681,f127(x92682))+~E(f312(f312(f129(x92682),x92681),x92683),f312(f312(f147(x92682),x92685),x92684))+E(f312(f312(f129(x92682),f621(x92683,x92681,x92684,x92685,x92682)),x92683),x92684)
% 173.53/173.43 [9269]E(x92691,f127(x92692))+~E(f312(f312(f129(x92692),x92691),x92695),f312(f312(f147(x92692),x92694),x92693))+E(f312(f312(f129(x92692),f620(x92693,x92694,x92695,x92691,x92692)),x92695),x92693)
% 173.53/173.43 [9276]E(f312(f312(f129(x92762),f620(x92764,x92763,x92761,x92765,x92762)),x92761),x92764)+~E(f312(f312(f129(x92762),x92765),x92761),f312(f312(f147(x92762),x92763),x92764))+E(x92761,f312(f312(f147(x92762),x92763),x92764))
% 173.53/173.43 [9277]~E(f312(f312(f129(x92771),x92775),x92774),f312(f312(f147(x92771),x92772),x92773))+E(f312(f312(f129(x92771),f621(x92774,x92775,x92773,x92772,x92771)),x92774),x92773)+E(f312(f312(f147(x92771),x92772),x92773),x92774)
% 173.53/173.43 [9278]E(f312(f312(f129(x92781),x92785),f623(x92783,x92782,x92784,x92785,x92781)),x92782)+E(f312(f312(f129(x92781),x92782),f622(x92783,x92782,x92784,x92785,x92781)),x92785)+~E(f312(f312(f129(x92781),x92785),x92784),f312(f312(f129(x92781),x92782),x92783))
% 173.53/173.43 [9311]~P103(x93111)+P33(x93111,f312(f312(f150(x93112,x93111),x93113),f146(x93112,x93111,x93113,x93114,x93115)))+~P33(x93111,f312(f312(f150(x93112,x93111),x93113),x93115))
% 173.53/173.43 [9323]~P58(x93235,x93231,x93234,x93233)+P22(f312(f312(x93231,x93232),f514(x93233,x93234,x93231,x93235,x93232)))+~P22(f312(f312(f314(x93235),x93232),x93234))
% 173.53/173.43 [9427]~P22(f312(f312(f314(f859(x94271,x94271)),f312(f312(f239(x94271,x94271),x94275),x94273)),f287(x94271,x94274)))+P22(f312(f312(f314(f859(x94271,x94271)),f312(f312(f239(x94271,x94271),x94272),x94273)),f312(f312(f267(x94271,x94271,x94271),x94274),f287(x94271,x94274))))+~P22(f312(f312(f314(f859(x94271,x94271)),f312(f312(f239(x94271,x94271),x94272),x94275)),f312(f312(f267(x94271,x94271,x94271),x94274),f287(x94271,x94274))))
% 173.53/173.43 [9428]~P22(f312(f312(f314(f859(x94281,x94281)),f312(f312(f239(x94281,x94281),x94282),x94285)),f287(x94281,x94284)))+P22(f312(f312(f314(f859(x94281,x94281)),f312(f312(f239(x94281,x94281),x94282),x94283)),f312(f312(f267(x94281,x94281,x94281),x94284),f287(x94281,x94284))))+~P22(f312(f312(f314(f859(x94281,x94281)),f312(f312(f239(x94281,x94281),x94285),x94283)),f312(f312(f267(x94281,x94281,x94281),x94284),f287(x94281,x94284))))
% 173.53/173.43 [9431]P22(f312(f312(f314(f859(f853(x94311),f853(x94311))),f312(f312(f239(f853(x94311),f853(x94311)),x94312),x94313)),f154(x94311,f287(x94311,x94314))))+~P22(f312(f312(f314(f859(f853(x94311),f853(x94311))),f312(f312(f239(f853(x94311),f853(x94311)),x94312),x94315)),f154(x94311,f287(x94311,x94314))))+~P22(f312(f312(f314(f859(f853(x94311),f853(x94311))),f312(f312(f239(f853(x94311),f853(x94311)),x94315),x94313)),f154(x94311,f287(x94311,x94314))))
% 173.53/173.43 [9436]E(f312(f312(f129(x94361),x94362),f622(x94363,x94362,x94364,x94365,x94361)),x94365)+E(f312(f312(f129(x94361),f623(x94363,x94362,x94364,x94365,x94361)),x94363),x94364)+~E(f312(f312(f129(x94361),x94362),x94363),f312(f312(f129(x94361),x94365),x94364))
% 173.53/173.43 [9437]E(f312(f312(f129(x94371),x94372),f623(x94373,x94374,x94375,x94372,x94371)),x94374)+E(f312(f312(f129(x94371),f622(x94373,x94374,x94375,x94372,x94371)),x94375),x94373)+~E(f312(f312(f129(x94371),x94372),x94375),f312(f312(f129(x94371),x94374),x94373))
% 173.53/173.43 [9491]P22(f312(f312(f314(f859(x94911,x94911)),f312(f312(f239(x94911,x94911),x94912),x94913)),f312(f312(f267(x94911,x94911,x94911),x94914),f287(x94911,x94914))))+~P22(f312(f312(f314(f859(x94911,x94911)),f312(f312(f239(x94911,x94911),x94912),x94915)),f312(f312(f267(x94911,x94911,x94911),x94914),f287(x94911,x94914))))+~P22(f312(f312(f314(f859(x94911,x94911)),f312(f312(f239(x94911,x94911),x94915),x94913)),f312(f312(f267(x94911,x94911,x94911),x94914),f287(x94911,x94914))))
% 173.53/173.43 [9517]P39(x95171,x95172,x95173,x95174,x95175)+~E(f312(f190(f853(x95171)),x95174),f312(f190(f853(x95172)),x95175))+~P22(f312(f312(f249(x95171,x95172,a845),x95173),f685(x95175,x95174,x95173,x95172,x95171)))
% 173.53/173.43 [9518]P39(x95181,x95182,x95183,x95184,x95185)+~E(f312(f190(f853(x95181)),x95184),f312(f190(f853(x95182)),x95185))+~P22(f312(f312(f249(x95181,x95182,a845),x95183),f694(x95183,x95185,x95184,x95182,x95181)))
% 173.53/173.43 [9522]E(f312(f312(f129(x95221),f622(x95222,x95223,x95224,x95225,x95221)),x95224),x95222)+~E(f312(f312(f129(x95221),x95223),x95222),f312(f312(f129(x95221),x95225),x95224))+E(f312(f312(f129(x95221),f623(x95222,x95223,x95224,x95225,x95221)),x95222),x95224)
% 173.53/173.43 [9533]~P103(x95332)+E(f312(f312(f145(x95331,x95332,x95333),x95334),x95335),f312(f312(f147(x95331),x95334),x95335))+P22(f312(f312(f314(x95331),f721(x95334,x95333,x95335,x95331,x95332)),f312(f168(x95331),x95335)))
% 173.53/173.43 [9538]~P58(x95381,x95384,x95383,x95382)+~P22(f312(f312(f314(x95381),x95385),x95383))+P22(f312(f312(f314(x95381),f514(x95382,x95383,x95384,x95381,x95385)),x95382))
% 173.53/173.43 [9657]~P22(f312(f312(f314(f859(f860(x96571,a845),f860(x96571,a845))),f312(f312(f239(f860(x96571,a845),f860(x96571,a845)),x96574),x96573)),f303(x96571,x96572)))+~P22(f312(f312(f314(x96571),x96575),x96574))+P22(f312(f312(f314(x96571),f741(x96572,x96573,x96574,x96571,x96575)),x96573))
% 173.53/173.43 [9669]~P103(x96692)+E(f312(f312(f145(x96691,x96692,x96693),x96694),x96695),f312(f312(f147(x96691),x96694),x96695))+~P22(f312(f312(f227(x96692),f312(x96693,x96694)),f312(x96693,f721(x96694,x96693,x96695,x96691,x96692))))
% 173.53/173.43 [9862]P39(x98621,x98622,x98623,x98624,x98625)+~E(f312(f190(f853(x98621)),x98624),f312(f190(f853(x98622)),x98625))+~P22(f312(f312(x98623,f312(f312(f161(x98621),x98624),f695(x98625,x98624,x98623,x98622,x98621))),f312(f312(f161(x98622),x98625),f695(x98625,x98624,x98623,x98622,x98621))))
% 173.53/173.43 [9863]P39(x98631,x98632,x98633,x98634,x98635)+~E(f312(f190(f853(x98631)),x98634),f312(f190(f853(x98632)),x98635))+~P22(f312(f312(x98633,f312(f312(f161(x98631),x98634),f712(x98633,x98635,x98632,x98634,x98631))),f312(f312(f161(x98632),x98635),f712(x98633,x98635,x98632,x98634,x98631))))
% 173.53/173.43 [6458]~P12(x64582,x64585,x64581)+~P22(f312(f70(x64582),x64584))+E(f312(x64581,f312(f312(f289(x64582),x64583),x64584)),f312(f312(f73(x64582,x64582,x64585),x64583),x64584))
% 173.53/173.43 [6459]~E(x64593,x64594)+~E(x64592,x64595)+E(f312(f312(f289(x64591),x64592),f312(f312(f289(x64591),x64593),f189(f860(x64591,a845)))),f312(f312(f289(x64591),x64594),f312(f312(f289(x64591),x64595),f189(f860(x64591,a845)))))
% 173.53/173.43 [6472]P22(f312(x64722,x64725))+E(f172(x64721,x64722,f312(f312(f129(x64721),x64723),x64724)),f172(x64721,x64722,x64723))+~P22(f312(f312(f314(x64721),x64725),f312(f168(x64721),x64723)))
% 173.53/173.43 [6506]E(f312(x65061,x65062),f189(f860(x65063,a845)))+~E(f312(f312(f50(x65064,f860(x65063,a845)),x65065),x65061),f189(f860(x65063,a845)))+~P22(f312(f312(f314(x65064),x65062),x65065))
% 173.53/173.43 [6507]E(f312(x65071,x65072),f235(f860(x65073,a845)))+~E(f312(f312(f51(x65074,f860(x65073,a845)),x65075),x65071),f235(f860(x65073,a845)))+~P22(f312(f312(f314(x65074),x65072),x65075))
% 173.53/173.43 [6800]~P22(f312(f312(f195(x68001),x68003),x68005))+~P22(f312(f312(f195(x68002),x68005),x68004))+P22(f312(f312(f195(f36(x68001,x68002)),x68003),x68004))
% 173.53/173.43 [7011]~E(x70112,x70114)+~P136(x70111)+E(f312(f312(f89(x70111),f312(f312(f90(x70111),x70112),x70113)),f312(f312(f90(x70111),x70114),x70115)),f312(f312(f89(x70111),f312(f312(f90(x70111),x70112),x70115)),f312(f312(f90(x70111),x70114),x70113)))
% 173.53/173.43 [7073]~P31(x70731)+~P22(f312(f312(f314(x70734),x70733),x70735))+P22(f312(f312(f227(x70731),f312(x70732,x70733)),f312(f312(f50(x70734,x70731),x70735),x70732)))
% 173.53/173.43 [7123]~P104(x71231)+P22(f312(f312(f227(x71231),f312(x71232,x71233)),f312(x71234,x71233)))+~P22(f312(f312(f227(f860(x71235,x71231)),x71232),x71234))
% 173.53/173.43 [7232]E(x72321,x72322)+E(x72323,x72321)+~E(f312(f312(f289(x72324),x72321),f312(f312(f289(x72324),x72325),f189(f860(x72324,a845)))),f312(f312(f289(x72324),x72322),f312(f312(f289(x72324),x72323),f189(f860(x72324,a845)))))
% 173.53/173.43 [7233]E(x72331,x72332)+E(x72333,x72331)+~E(f312(f312(f289(x72334),x72333),f312(f312(f289(x72334),x72332),f189(f860(x72334,a845)))),f312(f312(f289(x72334),x72335),f312(f312(f289(x72334),x72331),f189(f860(x72334,a845)))))
% 173.53/173.43 [7234]E(x72341,x72342)+E(x72341,x72343)+~E(f312(f312(f289(x72344),x72343),f312(f312(f289(x72344),x72342),f189(f860(x72344,a845)))),f312(f312(f289(x72344),x72345),f312(f312(f289(x72344),x72341),f189(f860(x72344,a845)))))
% 173.53/173.43 [7235]E(x72351,x72352)+E(x72351,x72353)+~E(f312(f312(f289(x72354),x72351),f312(f312(f289(x72354),x72355),f189(f860(x72354,a845)))),f312(f312(f289(x72354),x72352),f312(f312(f289(x72354),x72353),f189(f860(x72354,a845)))))
% 173.53/173.43 [7766]P19(x77661,x77662,x77663,x77664)+~P19(x77661,x77662,x77663,x77665)+~P22(f312(f312(f227(f860(x77661,a845)),x77664),x77665))
% 173.53/173.43 [7772]~P22(f312(f312(f227(a852),x77725),x77723))+~P22(f312(f312(f312(f312(a198,x77721),x77722),x77725),x77724))+P22(f312(f312(f312(f312(a198,x77721),x77722),x77723),x77724))
% 173.53/173.43 [7862]P22(f312(x78621,x78622))+~P22(f312(f312(f195(x78624),x78622),x78625))+P22(f312(f312(f195(f33(x78621,x78623,x78624)),x78622),x78625))
% 173.53/173.43 [7889]~P22(f312(x78891,x78894))+~P22(f312(f312(f195(x78892),x78894),x78895))+P22(f312(f312(f195(f33(x78891,x78892,x78893)),x78894),x78895))
% 173.53/173.43 [7938]E(x79381,x79382)+~E(f312(f290(x79383,x79384,x79385),x79381),f312(f290(x79383,x79384,x79385),x79382))+~P19(x79383,x79384,x79385,f312(f312(f124(f860(x79383,a845)),x79381),x79382))
% 173.53/173.43 [8014]P22(f312(x80142,x80144))+E(f312(f312(f134(x80141),f312(f190(f853(x80141)),f172(x80141,x80142,x80143))),x80143),f312(f312(f147(x80141),x80144),x80145))+~E(f312(f312(f129(x80141),f172(x80141,x80142,x80143)),f312(f312(f147(x80141),x80144),x80145)),x80143)
% 173.53/173.43 [8046]~P19(x80461,x80462,x80463,x80465)+~P19(x80461,x80462,x80463,x80464)+P19(x80461,x80462,x80463,f312(f312(f115(f860(x80461,a845)),x80464),x80465))
% 173.53/173.43 [8156]~P26(x81561)+E(f312(f312(f89(x81561),f312(x81562,x81563)),f312(f162(x81561),f312(f312(f150(x81564,x81561),x81562),f166(x81564,x81563,x81565)))),f312(f162(x81561),f312(f312(f150(x81564,x81561),x81562),x81565)))+~P22(f312(f312(f314(x81564),x81563),f312(f168(x81564),x81565)))
% 173.53/173.43 [8250]~P103(x82501)+~P33(x82501,f312(f312(f150(x82502,x82501),x82503),x82505))+P33(x82501,f312(f312(f150(x82502,x82501),x82503),f312(f312(f145(x82502,x82501,x82503),x82504),x82505)))
% 173.53/173.43 [8327]P22(f312(x83271,x83272))+P22(f312(f312(f195(x83273),x83272),x83274))+~P22(f312(f312(f195(f33(x83271,x83275,x83273)),x83272),x83274))
% 173.53/173.43 [8338]~P31(x83381)+P22(f312(f312(f227(x83381),f312(f312(f50(x83382,x83381),x83383),x83384)),f312(f312(f50(x83382,x83381),x83385),x83384)))+~P22(f312(f312(f227(f860(x83382,a845)),x83383),x83385))
% 173.53/173.43 [8339]~P31(x83391)+P22(f312(f312(f227(x83391),f312(f312(f51(x83392,x83391),x83393),x83394)),f312(f312(f51(x83392,x83391),x83395),x83394)))+~P22(f312(f312(f227(f860(x83392,a845)),x83395),x83393))
% 173.53/173.43 [8352]~P22(f312(x83524,x83522))+P22(f312(f312(f195(x83521),x83522),x83523))+~P22(f312(f312(f195(f33(x83524,x83521,x83525)),x83522),x83523))
% 173.53/173.43 [8378]~P103(x83783)+P22(f312(f133(x83781),x83782))+~P22(f312(f133(x83781),f312(f312(f145(x83781,x83783,x83784),x83785),x83782)))
% 173.53/173.43 [8388]P22(f312(f312(f195(x83881),x83882),x83883))+P22(f312(f312(f195(x83884),x83882),x83883))+~P22(f312(f312(f195(f33(x83885,x83881,x83884)),x83882),x83883))
% 173.53/173.43 [8520]~P103(x85201)+~P22(f312(f312(f314(x85202),x85203),f312(f168(x85202),x85204)))+~P22(f312(f133(x85202),f312(f312(f145(x85202,x85201,x85205),x85203),x85204)))
% 173.53/173.43 [8597]~P103(x85971)+P33(x85971,f312(f312(f150(x85972,x85971),x85973),x85974))+~P33(x85971,f312(f312(f150(x85972,x85971),x85973),f312(f312(f145(x85972,x85971,x85973),x85975),x85974)))
% 173.53/173.43 [8690]~P103(x86902)+E(f312(f312(f145(x86901,x86902,x86903),x86904),x86905),f146(x86901,x86902,x86903,x86904,x86905))+P22(f312(f312(f314(x86902),f312(x86903,x86904)),f312(f290(x86901,x86902,x86903),f312(f168(x86901),x86905))))
% 173.53/173.43 [8762]~P103(x87622)+E(f146(x87621,x87622,x87623,x87624,x87625),x87625)+~P22(f312(f312(f314(x87622),f312(x87623,x87624)),f312(f290(x87621,x87622,x87623),f312(f168(x87621),x87625))))
% 173.53/173.43 [8778]~P19(x87782,x87781,x87783,x87785)+P22(f312(f312(f228(f860(x87781,a845)),f312(f290(x87782,x87781,x87783),x87784)),f312(f290(x87782,x87781,x87783),x87785)))+~P22(f312(f312(f228(f860(x87782,a845)),x87784),x87785))
% 173.53/173.43 [8948]~P19(x89481,x89482,x89483,f235(f860(x89481,a845)))+~P22(f312(f312(f227(f860(x89482,a845)),x89484),f312(f290(x89481,x89482,x89483),x89485)))+P22(f312(f312(f227(f860(x89481,a845)),f312(f291(x89481,x89482,x89483),x89484)),x89485))
% 173.53/173.43 [8967]~E(f312(f290(x89673,x89671,x89674),f235(f860(x89673,a845))),f235(f860(x89671,a845)))+P22(f312(f312(f227(f860(x89671,a845)),x89672),f312(f290(x89673,x89671,x89674),x89675)))+~P22(f312(f312(f227(f860(x89673,a845)),f312(f291(x89673,x89671,x89674),x89672)),x89675))
% 173.53/173.43 [8990]~E(f312(f219(x89902),x89904),f312(f312(f173(x89901,x89902),x89905),x89903))+~P22(f312(f133(x89901),f312(f312(f150(f859(x89901,x89902),x89901),f246(x89901,x89902)),x89905)))+P22(f312(f312(f314(f859(x89901,x89902)),f312(f312(f239(x89901,x89902),x89903),x89904)),f312(f168(f859(x89901,x89902)),x89905)))
% 173.53/173.43 [9070]~P19(x90701,x90704,x90705,f235(f860(x90701,a845)))+~P22(f312(f312(f227(f860(x90704,a845)),f312(f290(x90701,x90704,x90705),x90702)),f312(f290(x90701,x90704,x90705),x90703)))+P22(f312(f312(f227(f860(x90701,a845)),x90702),x90703))
% 173.53/173.43 [9137]E(f312(f219(x91371),x91372),f312(f312(f173(x91373,x91371),x91374),x91375))+~P22(f312(f133(x91373),f312(f312(f150(f859(x91373,x91371),x91373),f246(x91373,x91371)),x91374)))+~P22(f312(f312(f314(f859(x91373,x91371)),f312(f312(f239(x91373,x91371),x91375),x91372)),f312(f168(f859(x91373,x91371)),x91374)))
% 173.53/173.43 [9139]E(f312(f312(f173(x91391,x91392),x91393),x91394),f312(f219(x91392),x91395))+~P22(f312(f133(x91391),f312(f312(f150(f859(x91391,x91392),x91391),f246(x91391,x91392)),x91393)))+~P22(f312(f312(f314(f859(x91391,x91392)),f312(f312(f239(x91391,x91392),x91394),x91395)),f312(f168(f859(x91391,x91392)),x91393)))
% 173.53/173.43 [9195]~P25(x91951)+~E(f312(x91953,f664(x91953,x91954,x91955,x91952,x91951)),f2(x91951))+E(f312(f162(x91951),f312(f312(f150(x91952,x91951),x91953),f312(f132(x91952,x91954),x91955))),f312(f162(x91951),f312(f312(f150(x91952,x91951),x91953),x91955)))
% 173.53/173.43 [9461]~P25(x94611)+~P22(f312(x94614,f664(x94613,x94614,x94615,x94612,x94611)))+E(f312(f162(x94611),f312(f312(f150(x94612,x94611),x94613),f312(f132(x94612,x94614),x94615))),f312(f162(x94611),f312(f312(f150(x94612,x94611),x94613),x94615)))
% 173.53/173.43 [9536]~P31(x95365)+P22(f312(f312(f314(x95361),f635(x95362,x95363,x95361,x95364,x95365)),x95363))+P22(f312(f312(f227(x95365),x95364),f312(f312(f51(x95361,x95365),x95363),x95362)))
% 173.53/173.43 [9539]~P25(x95391)+E(f312(f162(x95391),f312(f312(f150(x95392,x95391),x95393),f312(f132(x95392,x95394),x95395))),f312(f162(x95391),f312(f312(f150(x95392,x95391),x95393),x95395)))+P22(f312(f312(f314(x95392),f664(x95393,x95394,x95395,x95392,x95391)),f312(f168(x95392),x95395)))
% 173.53/173.43 [9581]P39(x95811,x95812,x95813,x95814,x95815)+~E(f312(f190(f853(x95812)),x95815),f312(f190(f853(x95811)),x95814))+P22(f312(f312(f228(a852),f695(x95815,x95814,x95813,x95812,x95811)),f312(f190(f853(x95811)),x95814)))
% 173.53/173.43 [9582]P39(x95821,x95822,x95823,x95824,x95825)+~E(f312(f190(f853(x95822)),x95825),f312(f190(f853(x95821)),x95824))+P22(f312(f312(f228(a852),f712(x95823,x95825,x95822,x95824,x95821)),f312(f190(f853(x95821)),x95824)))
% 173.53/173.43 [9670]~P31(x96701)+~P22(f312(f312(f227(x96701),x96702),f312(x96705,f635(x96705,x96704,x96703,x96702,x96701))))+P22(f312(f312(f227(x96701),x96702),f312(f312(f51(x96703,x96701),x96704),x96705)))
% 173.53/173.43 [9700]~P72(x97001)+~P22(f312(f70(x97002),x97005))+E(f312(f312(f312(f74(x97001,x97002,f90(x97001)),f312(f312(f18(x97002,x97001,x97001),f312(f312(f8(x97001,f860(x97001,x97001),x97002),f90(x97001)),x97003)),x97004)),f87(x97001)),x97005),f312(f312(f90(x97001),f312(f312(f312(f74(x97001,x97002,f90(x97001)),x97003),f87(x97001)),x97005)),f312(f312(f312(f74(x97001,x97002,f90(x97001)),x97004),f87(x97001)),x97005)))
% 173.53/173.43 [9764]~P22(f312(f312(f314(f859(f860(x97641,a845),f860(x97641,a845))),f312(f312(f239(f860(x97641,a845),f860(x97641,a845)),x97645),x97644)),f303(x97641,x97643)))+~P22(f312(f312(f314(x97641),x97642),x97645))+P22(f312(f312(f314(f859(x97641,x97641)),f312(f312(f239(x97641,x97641),x97642),f741(x97643,x97644,x97645,x97641,x97642))),x97643))
% 173.53/173.43 [9903]~P22(f312(f312(f314(f859(f853(x99031),f853(x99031))),f312(f312(f239(f853(x99031),f853(x99031)),f312(f312(f129(x99031),x99035),x99032)),f312(f312(f129(x99031),x99035),x99033))),f143(x99031,x99034)))+P22(f312(f312(f314(f859(f853(x99031),f853(x99031))),f312(f312(f239(f853(x99031),f853(x99031)),x99032),x99033)),f143(x99031,x99034)))+P22(f312(f312(f314(f859(x99031,x99031)),f312(f312(f239(x99031,x99031),f628(x99034,x99033,x99032,x99035,x99031)),f628(x99034,x99033,x99032,x99035,x99031))),x99034))
% 173.53/173.43 [7052]~E(f312(f190(f853(x70521)),x70523),f312(f190(f853(x70522)),x70524))+E(f312(f312(f173(x70521,x70522),f312(f312(f177(x70521,x70522),x70523),x70524)),x70525),f192(x70522))+P22(f312(f312(f314(x70521),x70525),f312(f168(x70521),x70523)))
% 173.53/173.43 [7126]~E(x71263,x71265)+E(f312(f312(f161(x71261),f312(f312(f155(x71261,x71262),x71263),x71264)),x71265),x71264)+~P22(f312(f312(f228(a852),x71263),f312(f190(f853(x71261)),x71262)))
% 173.53/173.43 [7225]~E(f312(f312(f129(x72251),x72252),x72254),f312(f312(f129(x72251),x72253),x72255))+E(f312(f312(f169(x72251),f312(f190(f853(x72251)),x72252)),x72253),x72252)+P22(f312(f312(f227(a852),f312(f190(f853(x72251)),x72253)),f312(f190(f853(x72251)),x72252)))
% 173.53/173.43 [7244]~E(x72445,x72442)+P22(f312(x72441,x72442))+P22(f312(f312(f312(f312(a198,f35(x72441,x72443)),x72442),x72444),x72445))
% 173.53/173.43 [7729]~E(f312(f312(f129(x77291),x77292),x77294),f312(f312(f129(x77291),x77293),x77295))+E(f312(f312(f169(x77291),f312(f190(f853(x77291)),x77292)),x77293),x77292)+~P22(f312(f312(f227(a852),f312(f190(f853(x77291)),x77292)),f312(f190(f853(x77291)),x77293)))
% 173.53/173.43 [7753]~P22(f312(f70(x77531),f312(x77534,x77535)))+~P22(f312(f312(f314(x77532),x77535),x77533))+P22(f312(f70(x77531),f312(f312(f51(x77532,f860(x77531,a845)),x77533),x77534)))
% 173.53/173.43 [7800]~E(f312(f190(f853(x78001)),x78002),f312(f190(f853(x78003)),x78004))+~E(f312(f312(f173(x78001,x78003),f312(f312(f177(x78001,x78003),x78002),x78004)),x78005),f192(x78003))+~P22(f312(f312(f314(x78001),x78005),f312(f168(x78001),x78002)))
% 173.53/173.43 [7923]~P50(x79231,x79233,x79235)+~P50(x79231,x79232,x79234)+P50(x79231,f312(f312(f124(f860(x79231,a845)),x79232),x79233),f312(f312(f124(f860(f859(x79231,x79231),a845)),x79234),x79235))
% 173.53/173.43 [7924]~P50(x79241,x79243,x79245)+~P50(x79241,x79242,x79244)+P50(x79241,f312(f312(f115(f860(x79241,a845)),x79242),x79243),f312(f312(f115(f860(f859(x79241,x79241),a845)),x79244),x79245))
% 173.53/173.43 [8007]E(x80071,x80072)+P22(f312(x80073,x80071))+~P22(f312(f312(f312(f312(a198,f35(x80073,x80074)),x80071),x80075),x80072))
% 173.53/173.43 [8286]E(f312(f312(f239(x82861,x82862),f312(f312(f161(x82861),x82863),x82864)),f312(f312(f161(x82862),x82865),x82864)),f312(f312(f161(f859(x82861,x82862)),f312(f312(f177(x82861,x82862),x82863),x82865)),x82864))+~P22(f312(f312(f228(a852),x82864),f312(f190(f853(x82861)),x82863)))+~P22(f312(f312(f228(a852),x82864),f312(f190(f853(x82862)),x82865)))
% 173.53/173.43 [8452]~P50(x84521,x84523,x84524)+P22(f312(f312(f314(x84521),x84522),x84523))+~P22(f312(f312(f314(f859(x84521,x84521)),f312(f312(f239(x84521,x84521),x84525),x84522)),x84524))
% 173.53/173.43 [8453]~P50(x84531,x84533,x84534)+P22(f312(f312(f314(x84531),x84532),x84533))+~P22(f312(f312(f314(f859(x84531,x84531)),f312(f312(f239(x84531,x84531),x84532),x84535)),x84534))
% 173.53/173.43 [8454]~P3(x84541,x84543,x84544)+P22(f312(f312(f314(x84541),x84542),x84543))+~P22(f312(f312(f314(f859(x84541,x84541)),f312(f312(f239(x84541,x84541),x84545),x84542)),x84544))
% 173.53/173.43 [8455]~P3(x84551,x84553,x84554)+P22(f312(f312(f314(x84551),x84552),x84553))+~P22(f312(f312(f314(f859(x84551,x84551)),f312(f312(f239(x84551,x84551),x84552),x84555)),x84554))
% 173.53/173.43 [8711]~P3(x87111,x87115,x87112)+E(f312(f264(x87111,x87111,x87112),f312(f312(f289(x87111),x87113),f189(f860(x87111,a845)))),f312(f264(x87111,x87111,x87112),f312(f312(f289(x87111),x87114),f189(f860(x87111,a845)))))+~P22(f312(f312(f314(f859(x87111,x87111)),f312(f312(f239(x87111,x87111),x87113),x87114)),x87112))
% 173.53/173.43 [8790]~P22(f312(f312(f312(f312(a198,x87902),x87903),x87904),x87905))+~P22(f312(f312(f312(f312(a198,f35(x87901,x87902)),x87905),x87904),x87903))+P22(f312(f312(f312(f312(a198,f35(x87901,x87902)),x87903),x87904),x87903))
% 173.53/173.43 [8904]P22(f312(x89041,x89042))+~P22(f312(f312(f314(x89043),x89042),x89045))+P22(f312(f312(f314(x89043),f808(x89041,x89044,x89045,x89043)),f312(f312(f124(f860(x89043,a845)),x89045),x89044)))
% 173.53/173.43 [8905]P22(f312(x89051,x89052))+~P22(f312(f312(f314(x89053),x89052),x89054))+P22(f312(f312(f314(x89053),f808(x89051,x89054,x89055,x89053)),f312(f312(f124(f860(x89053,a845)),x89055),x89054)))
% 173.53/173.43 [8913]~P22(f312(x89132,x89135))+~P22(f312(f312(f314(x89131),x89135),x89134))+P22(f312(f312(f314(x89131),f805(x89132,x89133,x89134,x89131)),f312(f312(f124(f860(x89131,a845)),x89134),x89133)))
% 173.53/173.43 [8914]~P22(f312(x89142,x89145))+~P22(f312(f312(f314(x89141),x89145),x89143))+P22(f312(f312(f314(x89141),f805(x89142,x89143,x89144,x89141)),f312(f312(f124(f860(x89141,a845)),x89144),x89143)))
% 173.53/173.43 [8929]~P22(f312(f312(f227(f860(x89291,a845)),x89295),x89293))+~P22(f312(f312(f227(f860(x89291,a845)),x89292),x89294))+P22(f312(f312(f227(f860(x89291,a845)),f312(f312(f21(f860(x89291,a845)),x89292),x89293)),f312(f312(f21(f860(x89291,a845)),x89294),x89295)))
% 173.53/173.43 [8930]~P22(f312(f312(f227(f860(x89301,a845)),x89303),x89305))+~P22(f312(f312(f227(f860(x89301,a845)),x89302),x89304))+P22(f312(f312(f227(f860(x89301,a845)),f312(f312(f124(f860(x89301,a845)),x89302),x89303)),f312(f312(f124(f860(x89301,a845)),x89304),x89305)))
% 173.53/173.43 [8931]~P22(f312(f312(f227(f860(x89311,a845)),x89313),x89315))+~P22(f312(f312(f227(f860(x89311,a845)),x89312),x89314))+P22(f312(f312(f227(f860(x89311,a845)),f312(f312(f115(f860(x89311,a845)),x89312),x89313)),f312(f312(f115(f860(x89311,a845)),x89314),x89315)))
% 173.53/173.43 [9016]~E(f312(f190(f853(x90161)),x90163),f312(f190(f853(x90162)),x90164))+E(f312(f312(f173(x90161,x90162),f312(f312(f177(x90161,x90162),x90163),x90164)),x90165),f312(f219(x90162),f589(x90165,x90164,x90162,x90163,x90161)))+~P22(f312(f312(f314(x90161),x90165),f312(f168(x90161),x90163)))
% 173.53/173.43 [9020]P22(f312(f312(f314(f859(x90201,x90201)),f312(f312(f239(x90201,x90201),x90202),x90203)),f306(x90201,x90204,x90205)))+~P22(f312(f312(f227(a852),f312(x90204,x90202)),f312(x90204,x90203)))+~P22(f312(f312(f314(f859(x90201,x90201)),f312(f312(f239(x90201,x90201),x90202),x90203)),x90205))
% 173.53/173.43 [9205]P22(f312(f312(f314(f859(x92051,x92051)),f312(f312(f239(x92051,x92051),x92052),x92053)),f287(x92051,x92054)))+~P22(f312(f312(f314(f859(x92051,x92051)),f312(f312(f239(x92051,x92051),x92052),x92055)),f287(x92051,x92054)))+~P22(f312(f312(f314(f859(x92051,x92051)),f312(f312(f239(x92051,x92051),x92055),x92053)),x92054))
% 173.53/173.43 [9206]P22(f312(f312(f314(f859(x92061,x92061)),f312(f312(f239(x92061,x92061),x92062),x92063)),f287(x92061,x92064)))+~P22(f312(f312(f314(f859(x92061,x92061)),f312(f312(f239(x92061,x92061),x92065),x92063)),f287(x92061,x92064)))+~P22(f312(f312(f314(f859(x92061,x92061)),f312(f312(f239(x92061,x92061),x92062),x92065)),x92064))
% 173.53/173.43 [9299]E(x92991,x92992)+E(f312(a126,f765(x92993,x92994,x92991,x92992,x92995)),x92994)+~P22(f312(f312(f314(f859(x92995,x92995)),f312(f312(f239(x92995,x92995),x92992),x92991)),f312(f312(f184(f859(x92995,x92995),a845),x92994),x92993)))
% 173.53/173.43 [9300]E(x93001,x93002)+E(f312(a126,f767(x93003,x93004,x93001,x93002,x93005)),x93004)+~P22(f312(f312(f314(f859(x93005,x93005)),f312(f312(f239(x93005,x93005),x93002),x93001)),f312(f312(f184(f859(x93005,x93005),a845),x93004),x93003)))
% 173.53/173.43 [9301]E(x93011,f2(a852))+E(f312(a126,f765(x93012,x93011,x93013,x93014,x93015)),x93011)+~P22(f312(f312(f314(f859(x93015,x93015)),f312(f312(f239(x93015,x93015),x93014),x93013)),f312(f312(f184(f859(x93015,x93015),a845),x93011),x93012)))
% 173.53/173.43 [9302]E(x93021,f2(a852))+E(f312(a126,f767(x93022,x93021,x93023,x93024,x93025)),x93021)+~P22(f312(f312(f314(f859(x93025,x93025)),f312(f312(f239(x93025,x93025),x93024),x93023)),f312(f312(f184(f859(x93025,x93025),a845),x93021),x93022)))
% 173.53/173.43 [9319]P22(f312(f312(f314(f859(x93191,x93191)),f312(f312(f239(x93191,x93191),x93192),x93193)),f312(f312(f267(x93191,x93191,x93191),x93194),f287(x93191,x93194))))+~P22(f312(f312(f314(f859(x93191,x93191)),f312(f312(f239(x93191,x93191),x93192),x93195)),x93194))+~P22(f312(f312(f314(f859(x93191,x93191)),f312(f312(f239(x93191,x93191),x93195),x93193)),x93194))
% 173.53/173.43 [9327]~P22(f312(f312(f314(f859(x93271,x93271)),f312(f312(f239(x93271,x93271),x93272),x93275)),f287(x93271,x93274)))+P22(f312(f312(f314(f859(x93271,x93271)),f312(f312(f239(x93271,x93271),x93272),x93273)),f312(f312(f267(x93271,x93271,x93271),x93274),f287(x93271,x93274))))+~P22(f312(f312(f314(f859(x93271,x93271)),f312(f312(f239(x93271,x93271),x93275),x93273)),x93274))
% 173.53/173.43 [9364]~P3(x93641,x93645,x93642)+~P22(f312(f312(f314(f859(x93641,x93641)),f312(f312(f239(x93641,x93641),x93643),x93644)),x93642))+P22(f312(f312(f227(f860(x93641,a845)),f312(f264(x93641,x93641,x93642),f312(f312(f289(x93641),x93643),f189(f860(x93641,a845))))),f312(f264(x93641,x93641,x93642),f312(f312(f289(x93641),x93644),f189(f860(x93641,a845))))))
% 173.53/173.43 [9386]E(x93861,x93862)+P22(f312(f312(f312(f312(a198,x93863),x93861),x93864),f341(x93862,x93864,x93861,x93863,x93865)))+~P22(f312(f312(f312(f312(a198,f35(x93865,x93863)),x93861),x93864),x93862))
% 173.53/173.43 [9387]E(x93871,x93872)+P22(f312(f312(f312(f312(a198,x93873),x93871),x93874),f386(x93872,x93874,x93871,x93873,x93875)))+~P22(f312(f312(f312(f312(a198,f35(x93875,x93873)),x93871),x93874),x93872))
% 173.53/173.43 [9392]~P22(f312(x93925,x93922))+P22(f312(f312(f312(f312(a198,x93921),x93922),x93923),f341(x93924,x93923,x93922,x93921,x93925)))+~P22(f312(f312(f312(f312(a198,f35(x93925,x93921)),x93922),x93923),x93924))
% 173.53/173.43 [9393]~P22(f312(x93935,x93932))+P22(f312(f312(f312(f312(a198,x93931),x93932),x93933),f386(x93934,x93933,x93932,x93931,x93935)))+~P22(f312(f312(f312(f312(a198,f35(x93935,x93931)),x93932),x93933),x93934))
% 173.53/173.43 [9420]P22(f312(f312(f314(f859(x94201,x94201)),f312(f312(f239(x94201,x94201),x94202),x94203)),f312(f312(f267(x94201,x94201,x94201),x94204),f287(x94201,x94204))))+~P22(f312(f312(f314(f859(x94201,x94201)),f312(f312(f239(x94201,x94201),x94202),x94205)),f312(f312(f267(x94201,x94201,x94201),x94204),f287(x94201,x94204))))+~P22(f312(f312(f314(f859(x94201,x94201)),f312(f312(f239(x94201,x94201),x94205),x94203)),x94204))
% 173.53/173.43 [9421]P22(f312(f312(f314(f859(x94211,x94211)),f312(f312(f239(x94211,x94211),x94212),x94213)),f312(f312(f267(x94211,x94211,x94211),x94214),f287(x94211,x94214))))+~P22(f312(f312(f314(f859(x94211,x94211)),f312(f312(f239(x94211,x94211),x94215),x94213)),f312(f312(f267(x94211,x94211,x94211),x94214),f287(x94211,x94214))))+~P22(f312(f312(f314(f859(x94211,x94211)),f312(f312(f239(x94211,x94211),x94212),x94215)),x94214))
% 173.53/173.43 [9470]~P22(f312(f75(x94701,x94701,x94704,x94702,x94703),x94705))+P22(f312(f312(f314(x94701),x94702),x94703))+P22(f312(f71(x94701,x94704,f312(f312(f289(x94701),x94702),x94703)),x94705))
% 173.53/173.43 [9511]~E(f312(f290(x95113,x95112,x95115),x95114),x95111)+E(x95111,f189(f860(x95112,a845)))+P22(f312(f312(f227(f860(x95113,a845)),f312(f290(x95112,x95113,f828(x95114,x95113,x95112,x95111)),x95111)),x95114))
% 173.53/173.43 [9551]~P31(x95515)+P22(f312(f312(f314(x95511),f409(x95512,x95513,x95514,x95511,x95515)),x95514))+P22(f312(f312(f227(x95515),f312(f312(f50(x95511,x95515),x95514),x95513)),x95512))
% 173.53/173.43 [9602]P39(x96021,x96022,x96023,x96024,x96025)+~E(f312(f190(f853(x96021)),x96024),f312(f190(f853(x96022)),x96025))+P22(f312(f312(f314(f859(x96021,x96022)),f685(x96025,x96024,x96023,x96022,x96021)),f312(f168(f859(x96021,x96022)),f312(f312(f177(x96021,x96022),x96024),x96025))))
% 173.53/173.43 [9603]P39(x96031,x96032,x96033,x96034,x96035)+~E(f312(f190(f853(x96031)),x96034),f312(f190(f853(x96032)),x96035))+P22(f312(f312(f314(f859(x96031,x96032)),f694(x96033,x96035,x96034,x96032,x96031)),f312(f168(f859(x96031,x96032)),f312(f312(f177(x96031,x96032),x96034),x96035))))
% 173.53/173.43 [9731]E(x97311,x97312)+P22(f312(f312(f312(f312(a198,f35(x97313,x97314)),f341(x97311,x97315,x97312,x97314,x97313)),x97315),x97311))+~P22(f312(f312(f312(f312(a198,f35(x97313,x97314)),x97312),x97315),x97311))
% 173.53/173.43 [9732]E(x97321,x97322)+P22(f312(f312(f312(f312(a198,f35(x97323,x97324)),f386(x97321,x97325,x97322,x97324,x97323)),x97325),x97321))+~P22(f312(f312(f312(f312(a198,f35(x97323,x97324)),x97322),x97325),x97321))
% 173.53/173.43 [9734]~P22(f312(x97341,x97345))+P22(f312(f312(f312(f312(a198,f35(x97341,x97342)),f341(x97343,x97344,x97345,x97342,x97341)),x97344),x97343))+~P22(f312(f312(f312(f312(a198,f35(x97341,x97342)),x97345),x97344),x97343))
% 173.53/173.43 [9735]~P22(f312(x97351,x97355))+P22(f312(f312(f312(f312(a198,f35(x97351,x97352)),f386(x97353,x97354,x97355,x97352,x97351)),x97354),x97353))+~P22(f312(f312(f312(f312(a198,f35(x97351,x97352)),x97355),x97354),x97353))
% 173.53/173.43 [9742]E(x97421,x97422)+P22(f312(f312(f314(f859(x97423,x97423)),f312(f312(f239(x97423,x97423),x97421),f766(x97424,x97425,x97422,x97421,x97423))),x97424))+~P22(f312(f312(f314(f859(x97423,x97423)),f312(f312(f239(x97423,x97423),x97421),x97422)),f312(f312(f184(f859(x97423,x97423),a845),x97425),x97424)))
% 173.53/173.43 [9743]E(x97431,f2(a852))+P22(f312(f312(f314(f859(x97432,x97432)),f312(f312(f239(x97432,x97432),x97433),f766(x97434,x97431,x97435,x97433,x97432))),x97434))+~P22(f312(f312(f314(f859(x97432,x97432)),f312(f312(f239(x97432,x97432),x97433),x97435)),f312(f312(f184(f859(x97432,x97432),a845),x97431),x97434)))
% 173.53/173.43 [9789]~P31(x97891)+~P22(f312(f312(f227(x97891),f312(x97894,f409(x97895,x97894,x97893,x97892,x97891))),x97895))+P22(f312(f312(f227(x97891),f312(f312(f50(x97892,x97891),x97893),x97894)),x97895))
% 173.53/173.43 [9832]E(x98321,x98322)+P22(f312(f312(f314(f859(x98323,x98323)),f312(f312(f239(x98323,x98323),f768(x98324,x98325,x98321,x98322,x98323)),x98321)),x98324))+~P22(f312(f312(f314(f859(x98323,x98323)),f312(f312(f239(x98323,x98323),x98322),x98321)),f312(f312(f184(f859(x98323,x98323),a845),x98325),x98324)))
% 173.53/173.43 [9833]E(x98331,f2(a852))+P22(f312(f312(f314(f859(x98332,x98332)),f312(f312(f239(x98332,x98332),f768(x98333,x98331,x98334,x98335,x98332)),x98334)),x98333))+~P22(f312(f312(f314(f859(x98332,x98332)),f312(f312(f239(x98332,x98332),x98335),x98334)),f312(f312(f184(f859(x98332,x98332),a845),x98331),x98333)))
% 173.53/173.43 [9837]E(x98371,x98372)+P22(f312(f312(f314(f859(x98373,x98373)),f312(f312(f239(x98373,x98373),x98371),f768(x98374,x98375,x98372,x98371,x98373))),f312(f312(f184(f859(x98373,x98373),a845),f767(x98374,x98375,x98372,x98371,x98373)),x98374)))+~P22(f312(f312(f314(f859(x98373,x98373)),f312(f312(f239(x98373,x98373),x98371),x98372)),f312(f312(f184(f859(x98373,x98373),a845),x98375),x98374)))
% 173.53/173.43 [9838]E(x98381,f2(a852))+P22(f312(f312(f314(f859(x98382,x98382)),f312(f312(f239(x98382,x98382),x98383),f768(x98384,x98381,x98385,x98383,x98382))),f312(f312(f184(f859(x98382,x98382),a845),f767(x98384,x98381,x98385,x98383,x98382)),x98384)))+~P22(f312(f312(f314(f859(x98382,x98382)),f312(f312(f239(x98382,x98382),x98383),x98385)),f312(f312(f184(f859(x98382,x98382),a845),x98381),x98384)))
% 173.53/173.43 [9894]E(x98941,x98942)+P22(f312(f312(f314(f859(x98943,x98943)),f312(f312(f239(x98943,x98943),f766(x98944,x98945,x98941,x98942,x98943)),x98941)),f312(f312(f184(f859(x98943,x98943),a845),f765(x98944,x98945,x98941,x98942,x98943)),x98944)))+~P22(f312(f312(f314(f859(x98943,x98943)),f312(f312(f239(x98943,x98943),x98942),x98941)),f312(f312(f184(f859(x98943,x98943),a845),x98945),x98944)))
% 173.53/173.43 [9895]E(x98951,f2(a852))+P22(f312(f312(f314(f859(x98952,x98952)),f312(f312(f239(x98952,x98952),f766(x98953,x98951,x98954,x98955,x98952)),x98954)),f312(f312(f184(f859(x98952,x98952),a845),f765(x98953,x98951,x98954,x98955,x98952)),x98953)))+~P22(f312(f312(f314(f859(x98952,x98952)),f312(f312(f239(x98952,x98952),x98955),x98954)),f312(f312(f184(f859(x98952,x98952),a845),x98951),x98953)))
% 173.53/173.43 [9927]~P26(x99272)+~P22(f312(f70(x99271),x99275))+E(f312(f312(f6(x99271,x99272),f312(f312(f7(x99271,x99272,x99272),f312(f312(f18(x99271,x99272,f860(x99272,x99272)),f312(f312(f8(a845,f860(x99272,f860(x99272,x99272)),x99271),f108(x99272)),f312(f312(f7(x99271,f860(x99271,a845),a845),f314(x99271)),x99273))),x99274)),f2(x99272))),x99275),f312(f312(f6(x99271,x99272),x99274),f312(f312(f115(f860(x99271,a845)),x99275),x99273)))
% 173.53/173.43 [8517]~P72(x85171)+~P22(f312(f70(x85174),x85175))+E(f312(f312(f90(x85171),f312(x85172,x85173)),f312(f312(f9(x85174,x85171),x85172),f312(f312(f21(f860(x85174,a845)),x85175),f312(f312(f289(x85174),x85173),f189(f860(x85174,a845)))))),f312(f312(f9(x85174,x85171),x85172),f312(f312(f289(x85174),x85173),x85175)))
% 173.53/173.43 [8518]~P26(x85181)+~P22(f312(f70(x85184),x85185))+E(f312(f312(f89(x85181),f312(x85182,x85183)),f312(f312(f6(x85184,x85181),x85182),f312(f312(f21(f860(x85184,a845)),x85185),f312(f312(f289(x85184),x85183),f189(f860(x85184,a845)))))),f312(f312(f6(x85184,x85181),x85182),f312(f312(f289(x85184),x85183),x85185)))
% 173.53/173.43 [8830]~P103(x88302)+~P33(x88302,f312(f165(x88302),f312(f312(f150(x88301,x88302),x88304),x88305)))+E(f312(f132(x88301,f312(f312(f8(x88302,a845,x88301),f312(f228(x88302),x88303)),x88304)),x88305),f172(x88301,f312(f312(f8(x88302,a845,x88301),f312(f228(x88302),x88303)),x88304),x88305))
% 173.53/173.43 [8855]~P26(x88551)+E(f312(f312(f89(x88551),f312(f312(f6(a852,x88551),x88552),f283(a852,x88553,x88554))),f312(f312(f6(a852,x88551),x88552),f283(a852,f312(f312(f89(a852),x88554),f87(a852)),f312(f312(f89(a852),x88554),x88555)))),f312(f312(f6(a852,x88551),x88552),f283(a852,x88553,f312(f312(f89(a852),x88554),x88555))))+~P22(f312(f312(f227(a852),x88553),f312(f312(f89(a852),x88554),f87(a852))))
% 173.53/173.43 [8856]~P22(f312(f312(f314(x88561),x88564),x88565))+~P22(f312(f312(f227(f860(x88561,a845)),f312(f168(x88561),x88562)),x88565))+P22(f312(f312(f227(f860(x88561,a845)),f312(f168(x88561),f312(f312(f155(x88561,x88562),x88563),x88564))),x88565))
% 173.53/173.43 [9080]~P31(x90802)+~P22(f312(f70(x90801),x90805))+E(f312(f312(f73(x90801,x90802,f312(f312(f8(x90802,f860(x90802,x90802),x90801),f124(x90802)),x90803)),x90804),x90805),f312(f312(f124(x90802),x90804),f312(f312(f50(x90801,x90802),x90805),x90803)))
% 173.53/173.43 [9081]~P31(x90812)+~P22(f312(f70(x90811),x90815))+E(f312(f312(f73(x90811,x90812,f312(f312(f8(x90812,f860(x90812,x90812),x90811),f115(x90812)),x90813)),x90814),x90815),f312(f312(f115(x90812),x90814),f312(f312(f51(x90811,x90812),x90815),x90813)))
% 173.53/173.43 [9129]E(f312(x91291,x91292),f312(x91291,x91293))+P22(f312(f312(f228(a852),f312(x91291,x91292)),f312(x91291,x91293)))+~P22(f312(f312(f314(f859(x91294,x91294)),f312(f312(f239(x91294,x91294),x91292),x91293)),f149(x91294,f312(f312(f147(f860(x91294,a852)),x91291),x91295))))
% 173.53/173.43 [9160]~E(f312(x91604,x91602),f312(x91604,x91603))+~P22(f312(f312(f314(f859(x91601,x91601)),f312(f312(f239(x91601,x91601),x91602),x91603)),f149(x91601,x91605)))+P22(f312(f312(f314(f859(x91601,x91601)),f312(f312(f239(x91601,x91601),x91602),x91603)),f149(x91601,f312(f312(f147(f860(x91601,a852)),x91604),x91605))))
% 173.53/173.43 [9184]~P19(x91841,x91842,x91843,x91845)+P19(x91841,x91842,x91843,f312(f312(f289(x91841),x91844),x91845))+P22(f312(f312(f314(x91842),f312(x91843,x91844)),f312(f290(x91841,x91842,x91843),f312(f312(f21(f860(x91841,a845)),x91845),f312(f312(f289(x91841),x91844),f189(f860(x91841,a845)))))))
% 173.53/173.43 [9188]P22(f312(x91882,x91885))+~P22(f312(f312(f314(x91881),x91885),f312(f168(x91881),x91883)))+E(f312(f312(f134(x91881),f312(f190(f853(x91881)),f172(x91881,x91882,f312(f312(f129(x91881),x91883),x91884)))),f312(f312(f129(x91881),x91883),x91884)),f312(f312(f129(x91881),f312(f312(f134(x91881),f312(f190(f853(x91881)),f172(x91881,x91882,x91883))),x91883)),x91884))
% 173.53/173.43 [9191]~P22(f312(f312(f314(f859(x91911,x91911)),f312(f312(f239(x91911,x91911),x91912),x91913)),f149(x91911,x91915)))+~P22(f312(f312(f227(a852),f312(x91914,x91912)),f312(x91914,x91913)))+P22(f312(f312(f314(f859(x91911,x91911)),f312(f312(f239(x91911,x91911),x91912),x91913)),f149(x91911,f312(f312(f147(f860(x91911,a852)),x91914),x91915))))
% 173.53/173.43 [9252]P22(f312(f312(f314(f859(x92524,x92524)),f312(f312(f239(x92524,x92524),x92522),x92523)),f149(x92524,x92525)))+P22(f312(f312(f228(a852),f312(x92521,x92522)),f312(x92521,x92523)))+~P22(f312(f312(f314(f859(x92524,x92524)),f312(f312(f239(x92524,x92524),x92522),x92523)),f149(x92524,f312(f312(f147(f860(x92524,a852)),x92521),x92525))))
% 173.53/173.43 [9396]~P22(f312(f312(f314(f859(f853(x93961),f853(x93961))),f312(f312(f239(f853(x93961),f853(x93961)),x93962),x93964)),f154(x93961,x93965)))+~P22(f312(f312(f228(a852),x93963),f312(f190(f853(x93961)),x93962)))+P22(f312(f312(f314(f859(x93961,x93961)),f312(f312(f239(x93961,x93961),f312(f312(f161(x93961),x93962),x93963)),f312(f312(f161(x93961),x93964),x93963))),x93965))
% 173.53/173.43 [9624]E(x96241,f2(a1))+~P22(f312(f57(x96243,x96241),f312(f312(f239(a1,a1),x96244),x96245)))+P22(f312(f57(f312(f312(f90(a1),x96242),x96243),x96241),f312(f312(f239(a1,a1),f312(f312(f89(a1),f312(f312(f90(a1),x96242),x96244)),f312(f47(a1,f312(f312(f90(a1),x96242),x96245)),x96241))),f54(a1,f312(f312(f90(a1),x96242),x96245),x96241))))
% 173.53/173.43 [9626]~P22(f312(f312(f228(a852),f2(a852)),x96263))+~P22(f312(f56(x96262,x96263),f312(f312(f239(a852,a852),x96264),x96265)))+P22(f312(f56(f312(f312(f90(a852),x96261),x96262),x96263),f312(f312(f239(a852,a852),f312(f312(f89(a852),f312(f312(f90(a852),x96261),x96264)),f312(f47(a852,f312(f312(f90(a852),x96261),x96265)),x96263))),f54(a852,f312(f312(f90(a852),x96261),x96265),x96263))))
% 173.53/173.43 [9950]~P26(x99502)+~P22(f312(f70(x99501),x99504))+E(f312(f312(f6(x99501,x99502),x99503),f312(f233(x99501),f312(f312(f18(x99501,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99501),a310),f312(f312(f7(x99501,f860(x99501,a845),a845),f314(x99501)),x99504))),f312(f312(f7(x99501,f860(x99501,a845),a845),f314(x99501)),x99505)))),f312(f312(f6(x99501,x99502),f312(f312(f7(x99501,x99502,x99502),f312(f312(f18(x99501,x99502,f860(x99502,x99502)),f312(f312(f8(a845,f860(x99502,f860(x99502,x99502)),x99501),f108(x99502)),f312(f312(f7(x99501,f860(x99501,a845),a845),f314(x99501)),x99505))),x99503)),f2(x99502))),x99504))
% 173.53/173.43 [8138]~E(f312(f312(f129(x81381),x81382),x81385),f312(f312(f129(x81381),x81383),x81384))+E(f312(f312(f129(x81381),f312(f312(f134(x81381),f312(f190(f853(x81381)),x81382)),x81383)),x81384),x81385)+P22(f312(f312(f227(a852),f312(f190(f853(x81381)),x81383)),f312(f190(f853(x81381)),x81382)))
% 173.53/173.43 [8343]~E(f312(f312(f129(x83432),x83433),x83431),f312(f312(f129(x83432),x83434),x83435))+E(x83431,f312(f312(f129(x83432),f312(f312(f134(x83432),f312(f190(f853(x83432)),x83433)),x83434)),x83435))+~P22(f312(f312(f227(a852),f312(f190(f853(x83432)),x83433)),f312(f190(f853(x83432)),x83434)))
% 173.53/173.43 [8434]~E(f312(f312(f89(a852),f312(f312(f90(a852),x84343),x84344)),x84341),f312(f312(f89(a852),f312(f312(f90(a852),x84342),x84344)),x84345))+~P22(f312(f312(f227(a852),x84343),x84342))+E(x84341,f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x84342),x84343)),x84344)),x84345))
% 173.53/173.43 [8435]~E(f312(f312(f89(a852),f312(f312(f90(a852),x84351),x84353)),x84354),f312(f312(f89(a852),f312(f312(f90(a852),x84352),x84353)),x84355))+~P22(f312(f312(f227(a852),x84352),x84351))+E(f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x84351),x84352)),x84353)),x84354),x84355)
% 173.53/173.43 [8590]E(f312(f312(f89(a852),f312(f312(f90(a852),x85901),x85902)),x85903),f312(f312(f89(a852),f312(f312(f90(a852),x85904),x85902)),x85905))+~P22(f312(f312(f227(a852),x85904),x85901))+~E(x85905,f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x85901),x85904)),x85902)),x85903))
% 173.53/173.43 [8591]E(f312(f312(f89(a852),f312(f312(f90(a852),x85911),x85912)),x85913),f312(f312(f89(a852),f312(f312(f90(a852),x85914),x85912)),x85915))+~P22(f312(f312(f227(a852),x85914),x85911))+~E(f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x85911),x85914)),x85912)),x85913),x85915)
% 173.53/173.43 [9446]~P64(x94462)+~P22(f312(f70(x94461),x94465))+E(f312(f312(f9(x94461,x94462),f312(f312(f18(x94461,x94462,x94462),f312(f312(f8(x94462,f860(x94462,x94462),x94461),f268(x94462)),x94463)),x94464)),x94465),f312(f312(f268(x94462),f312(f312(f9(x94461,x94462),x94463),x94465)),f312(f312(f9(x94461,x94462),x94464),x94465)))
% 173.53/173.43 [9566]~E(f769(x95665,x95664,x95663,x95662,x95661),f770(x95665,x95664,x95663,x95662,x95661))+P22(f312(f312(f314(f859(x95661,x95661)),f312(f312(f239(x95661,x95661),x95662),x95663)),f287(x95661,x95664)))+~P22(f312(f312(f314(f859(x95661,x95661)),f312(f312(f239(x95661,x95661),x95662),x95663)),f287(x95661,f312(f312(f124(f860(f859(x95661,x95661),a845)),x95664),x95665))))
% 173.53/173.43 [9567]~E(f771(x95675,x95674,x95673,x95672,x95671),f772(x95675,x95674,x95673,x95672,x95671))+P22(f312(f312(f314(f859(x95671,x95671)),f312(f312(f239(x95671,x95671),x95672),x95673)),f287(x95671,x95674)))+~P22(f312(f312(f314(f859(x95671,x95671)),f312(f312(f239(x95671,x95671),x95672),x95673)),f287(x95671,f312(f312(f124(f860(f859(x95671,x95671),a845)),x95674),x95675))))
% 173.53/173.43 [9775]P22(f312(f312(f314(f859(x97751,x97751)),f312(f312(f239(x97751,x97751),x97752),f772(x97755,x97754,x97753,x97752,x97751))),f287(x97751,x97754)))+P22(f312(f312(f314(f859(x97751,x97751)),f312(f312(f239(x97751,x97751),x97752),x97753)),f287(x97751,x97754)))+~P22(f312(f312(f314(f859(x97751,x97751)),f312(f312(f239(x97751,x97751),x97752),x97753)),f287(x97751,f312(f312(f124(f860(f859(x97751,x97751),a845)),x97754),x97755))))
% 173.53/173.43 [9859]P22(f312(f312(f314(f859(x98591,x98591)),f312(f312(f239(x98591,x98591),f770(x98595,x98594,x98593,x98592,x98591)),x98593)),f287(x98591,x98594)))+P22(f312(f312(f314(f859(x98591,x98591)),f312(f312(f239(x98591,x98591),x98592),x98593)),f287(x98591,x98594)))+~P22(f312(f312(f314(f859(x98591,x98591)),f312(f312(f239(x98591,x98591),x98592),x98593)),f287(x98591,f312(f312(f124(f860(f859(x98591,x98591),a845)),x98594),x98595))))
% 173.53/173.43 [9901]P22(f312(f312(f314(f859(x99011,x99011)),f312(f312(f239(x99011,x99011),x99012),x99013)),f287(x99011,x99014)))+P22(f312(f312(f314(f859(x99011,x99011)),f312(f312(f239(x99011,x99011),f769(x99015,x99014,x99013,x99012,x99011)),f770(x99015,x99014,x99013,x99012,x99011))),x99015))+~P22(f312(f312(f314(f859(x99011,x99011)),f312(f312(f239(x99011,x99011),x99012),x99013)),f287(x99011,f312(f312(f124(f860(f859(x99011,x99011),a845)),x99014),x99015))))
% 173.53/173.43 [9902]P22(f312(f312(f314(f859(x99021,x99021)),f312(f312(f239(x99021,x99021),x99022),x99023)),f287(x99021,x99024)))+P22(f312(f312(f314(f859(x99021,x99021)),f312(f312(f239(x99021,x99021),f772(x99025,x99024,x99023,x99022,x99021)),f771(x99025,x99024,x99023,x99022,x99021))),x99025))+~P22(f312(f312(f314(f859(x99021,x99021)),f312(f312(f239(x99021,x99021),x99022),x99023)),f287(x99021,f312(f312(f124(f860(f859(x99021,x99021),a845)),x99024),x99025))))
% 173.53/173.43 [10023]~P22(f312(f312(f314(f859(f853(x100231),f853(x100231))),f312(f312(f239(f853(x100231),f853(x100231)),x100234),x100235)),f154(x100231,x100232)))+~P22(f312(f312(f314(f859(x100231,x100231)),x100233),f312(f168(f859(x100231,x100231)),f312(f312(f177(x100231,x100231),x100234),x100235))))+P22(f312(f312(f249(x100231,x100231,a845),f312(f312(f7(x100231,f860(f859(x100231,x100231),a845),f860(x100231,a845)),f312(f312(f8(f860(x100231,f860(f860(f859(x100231,x100231),a845),a845)),f860(f860(f859(x100231,x100231),a845),f860(x100231,a845)),x100231),f7(x100231,f860(f859(x100231,x100231),a845),a845)),f312(f312(f8(f860(x100231,f859(x100231,x100231)),f860(x100231,f860(f860(f859(x100231,x100231),a845),a845)),x100231),f312(f8(f859(x100231,x100231),f860(f860(f859(x100231,x100231),a845),a845),x100231),f314(f859(x100231,x100231)))),f239(x100231,x100231)))),x100232)),x100233))
% 173.53/173.43 [9474]~P22(f312(f312(f227(a852),x94743),x94742))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),x94743),x94744)),x94741)),f312(f312(f89(a852),f312(f312(f90(a852),x94742),x94744)),x94745)))+P22(f312(f312(f228(a852),x94741),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x94742),x94743)),x94744)),x94745)))
% 173.53/173.43 [9475]~P22(f312(f312(f227(a852),x94753),x94752))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),x94753),x94754)),x94751)),f312(f312(f89(a852),f312(f312(f90(a852),x94752),x94754)),x94755)))+P22(f312(f312(f227(a852),x94751),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x94752),x94753)),x94754)),x94755)))
% 173.53/173.43 [9495]~P22(f312(f312(f227(a852),x94951),x94954))+P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),x94951),x94952)),x94953)),f312(f312(f89(a852),f312(f312(f90(a852),x94954),x94952)),x94955)))+~P22(f312(f312(f228(a852),x94953),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x94954),x94951)),x94952)),x94955)))
% 173.53/173.43 [9496]~P22(f312(f312(f227(a852),x94961),x94964))+P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),x94961),x94962)),x94963)),f312(f312(f89(a852),f312(f312(f90(a852),x94964),x94962)),x94965)))+~P22(f312(f312(f227(a852),x94963),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x94964),x94961)),x94962)),x94965)))
% 173.53/173.43 [9600]~P22(f312(f312(f227(a852),x96002),x96001))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),x96001),x96003)),x96004)),f312(f312(f89(a852),f312(f312(f90(a852),x96002),x96003)),x96005)))+P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x96001),x96002)),x96003)),x96004)),x96005))
% 173.53/173.43 [9601]~P22(f312(f312(f227(a852),x96012),x96011))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),x96011),x96013)),x96014)),f312(f312(f89(a852),f312(f312(f90(a852),x96012),x96013)),x96015)))+P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x96011),x96012)),x96013)),x96014)),x96015))
% 173.53/173.43 [9654]~P22(f312(f312(f227(a852),x96544),x96541))+P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),x96541),x96542)),x96543)),f312(f312(f89(a852),f312(f312(f90(a852),x96544),x96542)),x96545)))+~P22(f312(f312(f228(a852),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x96541),x96544)),x96542)),x96543)),x96545))
% 173.53/173.43 [9655]~P22(f312(f312(f227(a852),x96554),x96551))+P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),x96551),x96552)),x96553)),f312(f312(f89(a852),f312(f312(f90(a852),x96554),x96552)),x96555)))+~P22(f312(f312(f227(a852),f312(f312(f89(a852),f312(f312(f90(a852),f312(f312(f21(a852),x96551),x96554)),x96552)),x96553)),x96555))
% 173.53/173.43 [9886]~P9(x98861,x98862,x98865,x98863)+~P22(f312(f312(f314(f859(x98861,x98861)),x98864),x98865))+P22(f312(f312(f249(x98861,x98861,a845),f312(f312(f7(x98861,f860(x98861,x98862),f860(x98861,a845)),f312(f312(f8(f860(x98862,a845),f860(f860(x98861,x98862),f860(x98861,a845)),x98861),f8(x98862,a845,x98861)),f312(f312(f8(x98862,f860(x98862,a845),x98861),a309),x98863))),x98863)),x98864))
% 173.53/173.43 [9908]~P105(x99081)+~P49(x99081,f860(x99082,a845),x99083)+P49(x99081,f860(x99082,a845),f312(f312(f7(x99081,f860(x99082,a845),f860(x99082,a845)),f312(f312(f8(f860(x99082,a845),f860(f860(x99082,a845),f860(x99082,a845)),x99081),f124(f860(x99082,a845))),f312(f312(f7(x99081,f860(x99082,a845),f860(x99082,a845)),f312(f312(f8(f860(x99082,a845),f860(f860(x99082,a845),f860(x99082,a845)),x99081),f124(f860(x99082,a845))),x99083)),x99084))),x99085))
% 173.53/173.43 [6697]~E(f312(x66974,x66975),f192(x66972))+E(f312(f180(x66971,x66972,x66973,x66974),x66975),f312(f219(x66972),x66976))+~E(f312(x66973,x66975),f312(f219(x66972),x66976))
% 173.53/173.43 [6789]~E(f312(x67893,x67896),f192(x67891))+E(f312(f221(f856(x67891),x67892,f192(x67891),x67893),f312(x67894,x67895)),f192(x67891))+~E(f312(x67894,x67895),f312(f219(x67892),x67896))
% 173.53/173.43 [7371]E(f312(x73711,x73712),f192(x73713))+~E(f312(f180(x73715,x73713,x73716,x73711),x73712),f312(f219(x73713),x73714))+E(f312(x73711,x73712),f312(f219(x73713),x73714))
% 173.53/173.43 [7404]~E(f312(f180(x74046,x74043,x74045,x74041),x74042),f312(f219(x74043),x74044))+E(f312(x74041,x74042),f312(f219(x74043),x74044))+E(f312(x74045,x74042),f312(f219(x74043),x74044))
% 173.53/173.43 [8299]~P14(x82996,x82991,x82992,x82994)+E(f312(f82(x82991,x82991,x82991,f312(x82992,x82993)),f312(x82994,x82995)),f312(f82(x82991,x82991,x82991,f312(x82994,x82995)),f312(x82992,x82993)))+~P22(f312(f70(x82996),x82995))
% 173.53/173.43 [8723]~P19(x87231,x87233,x87235,x87236)+~P19(x87233,x87232,x87234,f312(f290(x87231,x87233,x87235),x87236))+P19(x87231,x87232,f312(f82(x87233,x87232,x87231,x87234),x87235),x87236)
% 173.53/173.43 [9284]~P22(f312(f312(x92843,x92842),x92846))+~P22(f312(f312(x92844,x92845),x92842))+P22(f312(f312(f314(x92841),x92842),f278(x92841,x92843,x92844,x92845,x92846)))
% 173.53/173.43 [9285]~P22(f312(f312(x92854,x92852),x92856))+~P22(f312(f312(x92853,x92855),x92852))+P22(f312(f312(f314(x92851),x92852),f275(x92851,x92853,x92854,x92855,x92856)))
% 173.53/173.43 [9397]E(x93971,x93972)+E(x93973,x93974)+~P22(f312(f312(f314(f859(f853(x93975),f853(x93975))),f312(f312(f239(f853(x93975),f853(x93975)),f312(f312(f147(x93975),x93973),x93971)),f312(f312(f147(x93975),x93974),x93972))),f153(x93975,x93976)))
% 173.53/173.43 [9406]~E(x94062,x94064)+P22(f312(f312(f314(f859(f853(x94061),f853(x94061))),f312(f312(f239(f853(x94061),f853(x94061)),f312(f312(f147(x94061),x94062),x94063)),f312(f312(f147(x94061),x94064),x94065))),f141(x94061,x94066)))+~P22(f312(f312(f314(f859(f853(x94061),f853(x94061))),f312(f312(f239(f853(x94061),f853(x94061)),x94063),x94065)),f141(x94061,x94066)))
% 173.53/173.43 [9407]~E(x94072,x94074)+P22(f312(f312(f314(f859(f853(x94071),f853(x94071))),f312(f312(f239(f853(x94071),f853(x94071)),f312(f312(f147(x94071),x94072),x94073)),f312(f312(f147(x94071),x94074),x94075))),f143(x94071,x94076)))+~P22(f312(f312(f314(f859(f853(x94071),f853(x94071))),f312(f312(f239(f853(x94071),f853(x94071)),x94073),x94075)),f143(x94071,x94076)))
% 173.53/173.43 [9408]~E(x94082,x94084)+P22(f312(f312(f314(f859(f853(x94081),f853(x94081))),f312(f312(f239(f853(x94081),f853(x94081)),f312(f312(f147(x94081),x94082),x94083)),f312(f312(f147(x94081),x94084),x94085))),f153(x94081,x94086)))+~P22(f312(f312(f314(f859(f853(x94081),f853(x94081))),f312(f312(f239(f853(x94081),f853(x94081)),x94083),x94085)),f153(x94081,x94086)))
% 173.53/173.43 [9409]~E(x94092,x94094)+P22(f312(f312(f314(f859(f853(x94091),f853(x94091))),f312(f312(f239(f853(x94091),f853(x94091)),f312(f312(f129(x94091),x94092),x94093)),f312(f312(f129(x94091),x94094),x94095))),f153(x94091,x94096)))+~P22(f312(f312(f314(f859(f853(x94091),f853(x94091))),f312(f312(f239(f853(x94091),f853(x94091)),x94093),x94095)),f153(x94091,x94096)))
% 173.53/173.43 [9410]~E(x94103,x94105)+P22(f312(f312(f314(f859(f853(x94101),f853(x94101))),f312(f312(f239(f853(x94101),f853(x94101)),f312(f312(f129(x94101),x94102),x94103)),f312(f312(f129(x94101),x94104),x94105))),f153(x94101,x94106)))+~P22(f312(f312(f314(f859(f853(x94101),f853(x94101))),f312(f312(f239(f853(x94101),f853(x94101)),x94102),x94104)),f153(x94101,x94106)))
% 173.53/173.43 [9462]E(x94621,x94622)+P22(f312(f312(f314(f859(f853(x94623),f853(x94623))),f312(f312(f239(f853(x94623),f853(x94623)),x94621),x94622)),f153(x94623,x94624)))+~P22(f312(f312(f314(f859(f853(x94623),f853(x94623))),f312(f312(f239(f853(x94623),f853(x94623)),f312(f312(f147(x94623),x94625),x94621)),f312(f312(f147(x94623),x94626),x94622))),f153(x94623,x94624)))
% 173.53/173.43 [9604]~E(x96043,x96045)+P22(f312(f312(f314(f859(f853(x96041),f853(x96041))),f312(f312(f239(f853(x96041),f853(x96041)),f312(f312(f129(x96041),x96042),f312(f312(f147(x96041),x96043),f127(x96041)))),f312(f312(f129(x96041),x96044),f312(f312(f147(x96041),x96045),f127(x96041))))),f153(x96041,x96046)))+~P22(f312(f312(f314(f859(f853(x96041),f853(x96041))),f312(f312(f239(f853(x96041),f853(x96041)),x96042),x96044)),f153(x96041,x96046)))
% 173.53/173.43 [9621]E(f312(x96211,x96212),f192(x96213))+~E(f312(f221(f856(x96216),x96213,f192(x96216),x96214),f312(x96211,x96212)),f192(x96216))+E(f312(x96214,f551(x96212,x96211,x96214,x96215,x96216,x96213)),f192(x96216))
% 173.53/173.43 [9622]E(f312(x96221,x96222),f192(x96223))+~E(f312(f221(f856(x96226),x96223,f192(x96226),x96224),f312(x96221,x96222)),f192(x96226))+E(f312(f219(x96223),f551(x96222,x96221,x96224,x96225,x96226,x96223)),f312(x96221,x96222))
% 173.53/173.43 [9658]E(x96581,x96582)+E(x96583,x96584)+~P22(f312(f312(f314(f859(f853(x96585),f853(x96585))),f312(f312(f239(f853(x96585),f853(x96585)),f312(f312(f129(x96585),x96583),f312(f312(f147(x96585),x96581),f127(x96585)))),f312(f312(f129(x96585),x96584),f312(f312(f147(x96585),x96582),f127(x96585))))),f153(x96585,x96586)))
% 173.53/173.43 [9682]E(x96821,x96822)+~P22(f312(f312(f314(f859(f853(x96823),f853(x96823))),f312(f312(f239(f853(x96823),f853(x96823)),f312(f312(f129(x96823),x96821),f312(f312(f147(x96823),x96825),f127(x96823)))),f312(f312(f129(x96823),x96822),f312(f312(f147(x96823),x96826),f127(x96823))))),f153(x96823,x96824)))+P22(f312(f312(f314(f859(f853(x96823),f853(x96823))),f312(f312(f239(f853(x96823),f853(x96823)),x96821),x96822)),f153(x96823,x96824)))
% 173.53/173.43 [9716]~P22(f312(f312(f314(f859(f860(x97161,a845),f860(x97161,a845))),f312(f312(f239(f860(x97161,a845),f860(x97161,a845)),x97162),x97164)),f303(x97161,x97166)))+~P22(f312(f312(f314(f859(f860(x97161,a845),f860(x97161,a845))),f312(f312(f239(f860(x97161,a845),f860(x97161,a845)),x97163),x97165)),f303(x97161,x97166)))+P22(f312(f312(f314(f859(f860(x97161,a845),f860(x97161,a845))),f312(f312(f239(f860(x97161,a845),f860(x97161,a845)),f312(f312(f124(f860(x97161,a845)),x97162),x97163)),f312(f312(f124(f860(x97161,a845)),x97164),x97165))),f303(x97161,x97166)))
% 173.53/173.43 [5178]~E(f312(x51783,x51786),x51785)+~E(x51784,f312(f219(x51781),x51786))+E(f312(f312(f193(x51781,x51782),x51783),x51784),f312(f219(x51782),x51785))
% 173.53/173.43 [5588]~E(f312(f312(f129(x55881),x55886),x55883),x55885)+E(f312(f312(f129(x55881),x55882),x55883),f312(f312(f147(x55881),x55884),x55885))+~E(x55882,f312(f312(f147(x55881),x55884),x55886))
% 173.53/173.43 [5589]~E(f312(f312(f129(x55891),x55896),x55893),x55895)+E(f312(f312(f129(x55891),x55892),x55893),f312(f312(f129(x55891),x55894),x55895))+~E(x55892,f312(f312(f129(x55891),x55894),x55896))
% 173.53/173.43 [5591]E(f312(f312(f129(x55911),x55912),x55913),f312(f312(f147(x55911),x55914),x55915))+~E(f312(f312(f147(x55911),x55914),x55916),x55912)+~E(x55915,f312(f312(f129(x55911),x55916),x55913))
% 173.53/173.43 [5593]~E(f312(f312(f129(x55931),x55932),x55936),x55934)+E(f312(f312(f129(x55931),x55932),x55933),f312(f312(f129(x55931),x55934),x55935))+~E(x55933,f312(f312(f129(x55931),x55936),x55935))
% 173.53/173.43 [6691]E(f312(x66911,x66912),f312(x66913,x66912))+~E(f312(f312(f150(x66914,x66915),x66911),x66916),f312(f312(f150(x66914,x66915),x66913),x66916))+~P22(f312(f312(f314(x66914),x66912),f312(f168(x66914),x66916)))
% 173.53/173.43 [7076]~P14(x70764,x70765,x70766,x70761)+E(f312(f312(x70761,x70762),x70763),f312(f312(f73(x70764,x70765,x70766),x70763),x70762))+~P22(f312(f70(x70764),x70762))
% 173.53/173.43 [7140]~E(x71402,f312(x71404,x71406))+~P22(f312(f312(f314(x71403),x71406),x71405))+P22(f312(f312(f314(x71401),x71402),f312(f290(x71403,x71401,x71404),x71405)))
% 173.53/173.43 [7141]~E(f312(x71414,x71412),x71416)+~P22(f312(f312(f314(x71413),x71416),x71415))+P22(f312(f312(f314(x71411),x71412),f312(f291(x71411,x71413,x71414),x71415)))
% 173.53/173.43 [7583]~P37(x75831,x75832,x75834,x75836)+P37(x75831,x75832,f312(f312(f147(x75831),x75833),x75834),f312(f312(f147(x75831),x75835),x75836))+~P22(f312(f312(x75832,x75833),x75835))
% 173.53/173.43 [8598]~P56(x85984,x85985,x85981,x85982,x85986)+E(f312(x85981,f312(x85982,x85983)),x85983)+~P22(f312(f312(f314(x85985),x85983),x85986))
% 173.53/173.43 [9399]E(x93991,x93992)+E(f312(f190(f853(x93993)),x93994),f312(f190(f853(x93993)),x93995))+~P22(f312(f312(f314(f859(f853(x93993),f853(x93993))),f312(f312(f239(f853(x93993),f853(x93993)),f312(f312(f147(x93993),x93991),x93994)),f312(f312(f147(x93993),x93992),x93995))),f141(x93993,x93996)))
% 173.53/173.43 [9465]E(f312(f190(f853(x94651)),x94652),f312(f190(f853(x94651)),x94653))+P22(f312(f312(f314(f859(f853(x94651),f853(x94651))),f312(f312(f239(f853(x94651),f853(x94651)),x94652),x94653)),f141(x94651,x94654)))+~P22(f312(f312(f314(f859(f853(x94651),f853(x94651))),f312(f312(f239(f853(x94651),f853(x94651)),f312(f312(f147(x94651),x94655),x94652)),f312(f312(f147(x94651),x94656),x94653))),f141(x94651,x94654)))
% 173.53/173.43 [9488]~P22(f312(f312(f314(f859(x94881,x94881)),f312(f312(f239(x94881,x94881),x94882),x94884)),f287(x94881,x94886)))+P22(f312(f312(f314(f859(f853(x94881),f853(x94881))),f312(f312(f239(f853(x94881),f853(x94881)),f312(f312(f147(x94881),x94882),x94883)),f312(f312(f147(x94881),x94884),x94885))),f287(f853(x94881),f153(x94881,x94886))))+~P22(f312(f312(f314(f859(f853(x94881),f853(x94881))),f312(f312(f239(f853(x94881),f853(x94881)),x94883),x94885)),f287(f853(x94881),f153(x94881,x94886))))
% 173.53/173.43 [9664]~P22(f312(x96642,x96646))+~E(f312(f132(x96641,x96642),x96643),f312(f312(f147(x96641),x96644),x96645))+~P22(f312(f312(f314(x96641),x96646),f312(f168(x96641),f727(x96645,x96644,x96643,x96642,x96641))))
% 173.53/173.43 [9665]~P22(f312(x96654,x96656))+~E(f312(f312(f147(x96651),x96652),x96653),f312(f132(x96651,x96654),x96655))+~P22(f312(f312(f314(x96651),x96656),f312(f168(x96651),f729(x96655,x96654,x96653,x96652,x96651))))
% 173.53/173.43 [9977]~P26(x99772)+E(f312(f312(f6(x99771,x99772),f312(f312(f8(f860(x99773,a845),x99772,x99771),f312(f6(x99773,x99772),x99774)),f312(f312(f8(f860(x99773,a845),f860(x99773,a845),x99771),f233(x99773)),f312(f312(f8(f860(x99773,a845),f860(x99773,a845),x99771),f312(f18(x99773,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99773),a310),f312(f312(f7(x99773,f860(x99773,a845),a845),f314(x99773)),x99775)))),f312(f7(x99773,x99771,a845),f312(f312(f8(x99771,f860(x99771,a845),x99773),a309),x99776)))))),f312(f290(x99773,x99771,x99776),x99775)),f312(f312(f6(x99773,x99772),x99774),x99775))+~P22(f312(f70(x99773),x99775))
% 173.53/173.43 [6744]~P103(x67443)+P22(f312(x67442,x67445))+E(f312(f132(x67441,x67442),f312(f312(f145(x67441,x67443,x67444),x67445),x67446)),f312(f132(x67441,x67442),x67446))
% 173.53/173.43 [6746]P22(f312(x67461,x67462))+~E(f163(x67463,x67461,x67464),f312(f312(f239(f853(x67463),f853(x67463)),x67465),x67466))+~P22(f312(f312(f314(x67463),x67462),f312(f168(x67463),x67465)))
% 173.53/173.43 [6787]~P22(f312(x67872,x67876))+~E(f163(x67871,x67872,x67873),f312(f312(f239(f853(x67871),f853(x67871)),x67874),x67875))+~P22(f312(f312(f314(x67871),x67876),f312(f168(x67871),x67875)))
% 173.53/173.43 [7448]~P11(x74481,x74482,x74483)+~P22(f312(f70(x74481),x74486))+E(f312(f312(f73(x74481,x74482,x74483),x74484),f312(f312(f289(x74481),x74485),x74486)),f312(f312(f73(x74481,x74482,x74483),f312(f312(x74483,x74485),x74484)),x74486))
% 173.53/173.43 [7499]~P103(x74992)+~P22(f312(f312(f227(x74992),f312(x74993,x74994)),f312(x74993,x74995)))+E(f312(f312(f145(x74991,x74992,x74993),x74994),f312(f312(f147(x74991),x74995),x74996)),f312(f312(f147(x74991),x74994),f312(f312(f147(x74991),x74995),x74996)))
% 173.53/173.43 [7612]E(x76121,x76122)+~E(f312(f312(f247(x76123,x76124),x76121),f312(f16(f860(x76124,a845),x76123),x76125)),f312(f312(f247(x76123,x76124),x76122),f312(f16(f860(x76124,a845),x76123),x76125)))+~P22(f312(f312(f314(x76124),x76126),x76125))
% 173.53/173.43 [7679]~P11(x76791,x76792,x76793)+~P22(f312(f70(x76791),x76796))+E(f312(f312(f73(x76791,x76792,x76793),x76794),f312(f312(f289(x76791),x76795),x76796)),f312(f312(x76793,x76795),f312(f312(f73(x76791,x76792,x76793),x76794),x76796)))
% 173.53/173.43 [7858]~P15(x78582,x78585,x78586,x78581)+~P22(f312(f70(x78582),x78584))+E(f312(x78581,f312(f312(f289(x78582),x78583),x78584)),f312(f82(x78585,x78585,x78585,f312(x78581,x78584)),f312(x78586,x78583)))
% 173.53/173.43 [7895]~P103(x78952)+P22(f312(f312(f227(x78952),f312(x78953,x78954)),f312(x78953,x78955)))+E(f312(f312(f145(x78951,x78952,x78953),x78954),f312(f312(f147(x78951),x78955),x78956)),f312(f312(f147(x78951),x78955),f312(f312(f145(x78951,x78952,x78953),x78954),x78956)))
% 173.53/173.43 [8038]~E(f312(f190(f853(x80381)),x80385),f312(f190(f853(x80382)),x80386))+~E(f312(f190(f853(x80381)),x80383),f312(f190(f853(x80382)),x80384))+E(f312(f312(f129(f859(x80381,x80382)),f312(f312(f177(x80381,x80382),x80383),x80384)),f312(f312(f177(x80381,x80382),x80385),x80386)),f312(f312(f177(x80381,x80382),f312(f312(f129(x80381),x80383),x80385)),f312(f312(f129(x80382),x80384),x80386)))
% 173.53/173.43 [8153]~E(x81532,f312(f290(x81533,x81531,x81534),x81536))+P22(f312(f312(f227(f860(x81531,a845)),x81532),f312(f290(x81533,x81531,x81534),x81535)))+~P22(f312(f312(f227(f860(x81533,a845)),x81536),x81535))
% 173.53/173.43 [8258]~P103(x82585)+E(f312(x82581,x82582),f312(x82581,x82583))+E(f312(f312(f145(x82584,x82585,x82581),x82582),f312(f312(f145(x82584,x82585,x82581),x82583),x82586)),f312(f312(f145(x82584,x82585,x82581),x82583),f312(f312(f145(x82584,x82585,x82581),x82582),x82586)))
% 173.53/173.43 [8292]~P19(x82923,x82921,x82924,x82925)+P19(x82923,x82921,f312(f312(f312(f81(x82923,x82921),x82924),x82926),x82922),x82925)+P22(f312(f312(f314(x82921),x82922),f312(f290(x82923,x82921,x82924),x82925)))
% 173.53/173.43 [8444]~P22(f312(f312(f314(x84442),x84444),f312(x84446,x84443)))+~P22(f312(f312(f314(x84441),x84443),x84445))+P22(f312(f312(f314(f859(x84441,x84442)),f312(f312(f239(x84441,x84442),x84443),x84444)),f312(f312(f247(x84441,x84442),x84445),x84446)))
% 173.53/173.43 [8902]~P72(x89022)+~P19(x89024,x89021,x89025,x89026)+E(f312(f312(f9(x89021,x89022),x89023),f312(f290(x89024,x89021,x89025),x89026)),f312(f312(f9(x89024,x89022),f312(f82(x89021,x89022,x89024,x89023),x89025)),x89026))
% 173.53/173.43 [8903]~P26(x89032)+~P19(x89034,x89031,x89035,x89036)+E(f312(f312(f6(x89031,x89032),x89033),f312(f290(x89034,x89031,x89035),x89036)),f312(f312(f6(x89034,x89032),f312(f82(x89031,x89032,x89034,x89033),x89035)),x89036))
% 173.53/173.43 [8950]~P39(x89502,x89505,x89501,x89503,x89506)+P22(f312(f312(x89501,f312(f312(f161(x89502),x89503),x89504)),f312(f312(f161(x89505),x89506),x89504)))+~P22(f312(f312(f228(a852),x89504),f312(f190(f853(x89505)),x89506)))
% 173.53/173.43 [8951]~P39(x89512,x89515,x89511,x89513,x89516)+P22(f312(f312(x89511,f312(f312(f161(x89512),x89513),x89514)),f312(f312(f161(x89515),x89516),x89514)))+~P22(f312(f312(f228(a852),x89514),f312(f190(f853(x89512)),x89513)))
% 173.53/173.43 [9150]~E(f312(f312(f312(a201,x91505),f40(x91501)),f312(f312(a202,x91504),x91501)),f312(f312(f312(a201,x91506),f40(x91501)),f312(f312(a202,x91504),x91501)))+~P22(f312(f312(f195(x91503),f312(f312(f312(a201,x91504),f40(x91501)),f312(x91502,x91504))),x91506))+P22(f312(f312(f195(f32(x91501,x91502,x91503)),x91504),f312(f312(f312(a201,x91505),f40(x91501)),f312(f312(a202,x91504),x91501))))
% 173.53/173.43 [9156]~P14(x91563,x91561,x91566,x91562)+~P22(f312(f70(x91563),x91564))+E(f312(f82(x91561,x91561,x91561,f312(x91562,f312(f312(f21(f860(x91563,a845)),x91564),f312(f312(f289(x91563),x91565),f189(f860(x91563,a845)))))),f312(x91566,x91565)),f312(x91562,f312(f312(f289(x91563),x91565),x91564)))
% 173.53/173.43 [9170]~P22(f312(f312(f314(x91705),x91703),x91706))+P22(f312(f312(f314(x91701),f312(x91702,x91703)),f110(f860(x91701,a845),x91704)))+~P22(f312(f312(f227(f860(x91701,a845)),f312(f290(x91705,x91701,x91702),x91706)),f312(x91704,f312(f290(x91705,x91701,x91702),x91706))))
% 173.53/173.43 [9561]~E(f312(f312(f312(a201,f312(f312(a203,x95615),f312(a202,x95614))),x95611),f312(f312(a202,x95615),a25)),f312(f312(f312(a201,f312(f312(a203,x95616),f312(a202,x95614))),x95611),f312(f312(a202,x95616),a25)))+~P22(f312(f312(f195(f312(a27,x95612)),f312(f312(f312(a201,f312(f312(a203,x95614),a204)),f40(a26)),f312(x95613,x95614))),x95616))+P22(f312(f312(f195(f31(x95611,x95612,x95613)),x95614),f312(f312(f312(a201,f312(f312(a203,x95615),f312(a202,x95614))),x95611),f312(f312(a202,x95615),a25))))
% 173.53/173.43 [9755]~E(f312(f290(x97552,x97554,x97556),f235(f860(x97552,a845))),f235(f860(x97554,a845)))+~E(f312(f290(x97551,x97553,x97555),f235(f860(x97551,a845))),f235(f860(x97553,a845)))+E(f312(f290(f859(x97551,x97552),f859(x97553,x97554),f250(x97551,x97553,x97552,x97554,x97555,x97556)),f235(f860(f859(x97551,x97552),a845))),f235(f860(f859(x97553,x97554),a845)))
% 173.53/173.43 [9808]~P19(x98083,x98084,x98085,f312(x98086,f707(x98086,x98085,x98084,x98083,x98082,x98081)))+P19(x98083,x98084,x98085,f312(f312(f51(x98082,f860(x98083,a845)),x98081),x98086))+E(x98081,f189(f860(x98082,a845)))
% 173.53/173.43 [9867]P19(x98676,x98675,x98674,f312(f312(f51(x98672,f860(x98676,a845)),x98671),x98673))+E(x98671,f189(f860(x98672,a845)))+P22(f312(f312(f314(x98672),f707(x98673,x98674,x98675,x98676,x98672,x98671)),x98671))
% 173.53/173.43 [9873]P22(f312(f312(f314(x98731),f732(x98732,x98733,x98734,x98735,x98736,x98731)),x98736))+P22(f312(f312(f227(f860(f859(x98731,x98734),a845)),f312(f312(f247(x98731,x98734),x98736),x98733)),f312(f312(f247(x98731,x98734),x98735),x98732)))+~P22(f312(f312(f227(f860(x98731,a845)),x98736),x98735))
% 173.53/173.43 [9914]P18(x99146,x99145,f312(f312(f289(f851(x99146)),f312(f312(f312(f100(x99146),x99141),x99143),x99142)),f189(f860(f851(x99146),a845))))+~P18(x99146,x99145,f312(f312(f289(f851(x99146)),f312(f312(f312(f100(x99146),x99144),x99143),x99142)),f189(f860(f851(x99146),a845))))+P22(f312(f312(x99141,f696(x99141,x99142,x99143,x99144,x99145,x99146)),f709(x99141,x99142,x99143,x99144,x99145,x99146)))
% 173.53/173.43 [9915]P18(x99156,x99155,f312(f312(f289(f851(x99156)),f312(f312(f312(f100(x99156),x99154),x99153),x99152)),f189(f860(f851(x99156),a845))))+~P18(x99156,x99155,f312(f312(f289(f851(x99156)),f312(f312(f312(f100(x99156),x99154),x99153),x99151)),f189(f860(f851(x99156),a845))))+P22(f312(f312(x99151,f717(x99152,x99151,x99153,x99154,x99155,x99156)),f730(x99152,x99151,x99153,x99154,x99155,x99156)))
% 173.53/173.43 [9954]~P18(x99541,x99542,f312(f312(f289(f851(x99541)),f312(f312(f312(f100(x99541),x99543),x99544),x99546)),f189(f860(f851(x99541),a845))))+P18(x99541,x99542,f312(f312(f289(f851(x99541)),f312(f312(f312(f100(x99541),x99543),x99544),x99545)),f189(f860(f851(x99541),a845))))+~P22(f312(f312(x99545,f717(x99545,x99546,x99544,x99543,x99542,x99541)),f730(x99545,x99546,x99544,x99543,x99542,x99541)))
% 173.53/173.43 [9955]~P18(x99551,x99552,f312(f312(f289(f851(x99551)),f312(f312(f312(f100(x99551),x99556),x99554),x99555)),f189(f860(f851(x99551),a845))))+P18(x99551,x99552,f312(f312(f289(f851(x99551)),f312(f312(f312(f100(x99551),x99553),x99554),x99555)),f189(f860(f851(x99551),a845))))+~P22(f312(f312(x99556,f696(x99553,x99555,x99554,x99556,x99552,x99551)),f709(x99553,x99555,x99554,x99556,x99552,x99551)))
% 173.53/173.43 [9989]~P22(f312(f312(f227(f860(x99892,a845)),f312(x99894,f732(x99896,x99894,x99892,x99895,x99893,x99891))),f312(x99896,f732(x99896,x99894,x99892,x99895,x99893,x99891))))+~P22(f312(f312(f227(f860(x99891,a845)),x99893),x99895))+P22(f312(f312(f227(f860(f859(x99891,x99892),a845)),f312(f312(f247(x99891,x99892),x99893),x99894)),f312(f312(f247(x99891,x99892),x99895),x99896)))
% 173.53/173.43 [7633]~P22(f312(x76331,x76335))+~P22(f312(x76336,x76334))+P22(f312(x76331,f312(f248(x76332,x76333),f312(f312(f239(x76332,x76333),x76334),x76335))))
% 173.53/173.43 [7634]~P22(f312(x76341,x76344))+~P22(f312(x76346,x76345))+P22(f312(x76341,f312(f246(x76342,x76343),f312(f312(f239(x76342,x76343),x76344),x76345))))
% 173.53/173.43 [7656]~E(f312(f190(f853(x76561)),x76563),f312(f190(f853(x76564)),x76565))+~E(f312(f312(f173(x76561,x76564),f312(f312(f177(x76561,x76564),x76563),x76565)),x76562),f312(f219(x76564),x76566))+P22(f312(f312(f314(x76561),x76562),f312(f168(x76561),x76563)))
% 173.53/173.43 [7684]~P22(f312(f312(x76844,x76846),x76845))+~P22(f312(f312(f314(x76841),x76846),x76843))+P22(f312(f312(f312(f50(x76841,f860(x76842,a845)),x76843),x76844),x76845))
% 173.53/173.43 [7984]~P22(f312(f312(f314(x79841),x79842),f312(x79845,x79846)))+~P22(f312(f312(f314(x79843),x79846),x79844))+P22(f312(f312(f314(x79841),x79842),f312(f312(f50(x79843,f860(x79841,a845)),x79844),x79845)))
% 173.53/173.43 [8030]P22(f312(f312(x80301,x80302),x80303))+~P22(f312(f312(x80304,x80302),x80303))+~P22(f312(f312(f227(f860(x80305,f860(x80306,a845))),x80304),x80301))
% 173.53/173.43 [8177]P22(f312(f312(x81771,x81772),x81773))+~P22(f312(f312(f314(x81774),x81772),x81775))+~P22(f312(f312(f312(f51(x81774,f860(x81776,a845)),x81775),x81771),x81773))
% 173.53/173.43 [8316]P22(f312(f312(f314(x83161),x83162),f312(x83163,x83164)))+~P22(f312(f312(f314(x83165),x83164),x83166))+~P22(f312(f312(f314(x83161),x83162),f312(f312(f51(x83165,f860(x83161,a845)),x83166),x83163)))
% 173.53/173.43 [8516]~P22(f312(f312(f312(f312(a198,x85161),x85163),x85164),x85166))+~P22(f312(f312(f312(f312(a198,x85162),x85166),x85164),x85165))+P22(f312(f312(f312(f312(a198,f36(x85161,x85162)),x85163),x85164),x85165))
% 173.53/173.43 [8580]~P9(x85804,x85805,x85806,x85801)+E(f312(x85801,x85802),f312(x85801,x85803))+~P22(f312(f312(f314(f859(x85804,x85804)),f312(f312(f239(x85804,x85804),x85802),x85803)),x85806))
% 173.53/173.43 [8611]P22(f312(f312(f227(f860(x86111,a845)),x86112),f312(x86113,x86114)))+~P22(f312(f312(f314(x86115),x86114),x86116))+~P22(f312(f312(f227(f860(x86111,a845)),x86112),f312(f312(f51(x86115,f860(x86111,a845)),x86116),x86113)))
% 173.53/173.43 [8641]~P54(x86413,x86414,f312(f265(x86414,x86413),x86415))+E(x86411,f189(f860(x86412,a845)))+E(f312(f312(f51(x86412,f860(x86413,a845)),x86411),f312(f312(f8(f860(x86414,a845),f860(x86413,a845),x86412),f264(x86414,x86413,x86415)),x86416)),f312(f264(x86414,x86413,x86415),f312(f312(f51(x86412,f860(x86414,a845)),x86411),x86416)))
% 173.53/173.43 [8714]P22(f312(f312(f314(x87141),x87142),f312(f264(x87143,x87141,x87144),x87145)))+~P22(f312(f312(f314(x87143),x87146),x87145))+~P22(f312(f312(f314(f859(x87143,x87141)),f312(f312(f239(x87143,x87141),x87146),x87142)),x87144))
% 173.53/173.43 [8829]P22(f312(x88291,x88292))+~P22(f312(f312(f312(f312(a198,x88294),x88292),x88295),x88296))+P22(f312(f312(f312(f312(a198,f33(x88291,x88293,x88294)),x88292),x88295),x88296))
% 173.53/173.43 [8846]~P22(f312(x88461,x88464))+~P22(f312(f312(f312(f312(a198,x88462),x88464),x88465),x88466))+P22(f312(f312(f312(f312(a198,f33(x88461,x88462,x88463)),x88464),x88465),x88466))
% 173.53/173.43 [9022]P22(f312(f312(f227(f860(x90221,a845)),f312(f264(x90222,x90221,x90223),x90224)),f312(f264(x90222,x90221,x90225),x90226)))+~P22(f312(f312(f227(f860(x90222,a845)),x90224),x90226))+~P22(f312(f312(f227(f860(f859(x90222,x90221),a845)),x90223),x90225))
% 173.53/173.43 [9107]P22(f312(x91071,x91072))+P22(f312(f312(f312(f312(a198,x91073),x91072),x91074),x91075))+~P22(f312(f312(f312(f312(a198,f33(x91071,x91076,x91073)),x91072),x91074),x91075))
% 173.53/173.43 [9112]~P22(f312(x91125,x91122))+P22(f312(f312(f312(f312(a198,x91121),x91122),x91123),x91124))+~P22(f312(f312(f312(f312(a198,f33(x91125,x91121,x91126)),x91122),x91123),x91124))
% 173.53/173.43 [9163]P22(f312(f312(f312(f312(a198,x91631),x91632),x91633),x91634))+P22(f312(f312(f312(f312(a198,x91635),x91632),x91633),x91634))+~P22(f312(f312(f312(f312(a198,f33(x91636,x91631,x91635)),x91632),x91633),x91634))
% 173.53/173.43 [9207]~P22(f312(f312(f314(x92072),x92076),x92074))+~P22(f312(f312(f227(f860(x92071,a845)),x92073),x92075))+P22(f312(f312(f227(f860(f859(x92071,x92072),a845)),f312(f312(f247(x92071,x92072),x92073),f312(f16(f860(x92072,a845),x92071),x92074))),f312(f312(f247(x92071,x92072),x92075),f312(f16(f860(x92072,a845),x92071),x92074))))
% 173.53/173.43 [9219]~P39(x92191,x92192,x92193,x92195,x92196)+P22(f312(f312(f249(x92191,x92192,a845),x92193),x92194))+~P22(f312(f312(f314(f859(x92191,x92192)),x92194),f312(f168(f859(x92191,x92192)),f312(f312(f177(x92191,x92192),x92195),x92196))))
% 173.53/173.43 [9352]~E(x93523,x93525)+P22(f312(f312(f314(f859(f853(x93521),f853(x93521))),f312(f312(f239(f853(x93521),f853(x93521)),f312(f312(f147(x93521),x93522),x93523)),f312(f312(f147(x93521),x93524),x93525))),f153(x93521,x93526)))+~P22(f312(f312(f314(f859(x93521,x93521)),f312(f312(f239(x93521,x93521),x93522),x93524)),x93526))
% 173.53/173.43 [9356]~E(f312(f190(f853(x93561)),x93565),f312(f190(f853(x93562)),x93566))+E(f182(x93561,x93562,f183(x93561,x93562,x93563,f312(f312(f21(f860(x93561,a845)),x93564),f312(f168(x93561),x93565))),x93565,x93566),f183(x93561,x93562,f182(x93561,x93562,x93563,x93565,x93566),x93564))+~P22(f312(f312(f227(f860(x93561,a845)),f312(f168(x93561),x93565)),x93564))
% 173.53/173.43 [9357]~E(f312(f190(f853(x93571)),x93573),f312(f190(f853(x93571)),x93575))+P22(f312(f312(f314(f859(f853(x93571),f853(x93571))),f312(f312(f239(f853(x93571),f853(x93571)),f312(f312(f147(x93571),x93572),x93573)),f312(f312(f147(x93571),x93574),x93575))),f141(x93571,x93576)))+~P22(f312(f312(f314(f859(x93571,x93571)),f312(f312(f239(x93571,x93571),x93572),x93574)),x93576))
% 173.53/173.43 [9389]P22(f312(f312(f314(f859(x93891,x93891)),f312(f312(f239(x93891,x93891),x93892),x93893)),f312(f312(f184(f859(x93891,x93891),a845),f312(a126,x93894)),x93895)))+~P22(f312(f312(f314(f859(x93891,x93891)),f312(f312(f239(x93891,x93891),x93896),x93893)),x93895))+~P22(f312(f312(f314(f859(x93891,x93891)),f312(f312(f239(x93891,x93891),x93892),x93896)),f312(f312(f184(f859(x93891,x93891),a845),x93894),x93895)))
% 173.53/173.43 [9390]P22(f312(f312(f314(f859(x93901,x93901)),f312(f312(f239(x93901,x93901),x93902),x93903)),f312(f312(f184(f859(x93901,x93901),a845),f312(a126,x93904)),x93905)))+~P22(f312(f312(f314(f859(x93901,x93901)),f312(f312(f239(x93901,x93901),x93902),x93906)),x93905))+~P22(f312(f312(f314(f859(x93901,x93901)),f312(f312(f239(x93901,x93901),x93906),x93903)),f312(f312(f184(f859(x93901,x93901),a845),x93904),x93905)))
% 173.53/173.43 [9395]~P22(f312(f312(f314(x93954),x93955),x93956))+P22(f312(f312(f227(f860(x93951,a845)),x93952),x93953))+~P22(f312(f312(f227(f860(f859(x93951,x93954),a845)),f312(f312(f247(x93951,x93954),x93952),f312(f16(f860(x93954,a845),x93951),x93956))),f312(f312(f247(x93951,x93954),x93953),f312(f16(f860(x93954,a845),x93951),x93956))))
% 173.53/173.43 [9438]E(x94381,x94382)+~P22(f312(f312(f314(f859(f853(x94383),f853(x94383))),f312(f312(f239(f853(x94383),f853(x94383)),f312(f312(f147(x94383),x94381),x94385)),f312(f312(f147(x94383),x94382),x94386))),f141(x94383,x94384)))+P22(f312(f312(f314(f859(x94383,x94383)),f312(f312(f239(x94383,x94383),x94381),x94382)),x94384))
% 173.53/173.43 [9439]E(x94391,x94392)+~P22(f312(f312(f314(f859(f853(x94393),f853(x94393))),f312(f312(f239(f853(x94393),f853(x94393)),f312(f312(f147(x94393),x94391),x94395)),f312(f312(f147(x94393),x94392),x94396))),f143(x94393,x94394)))+P22(f312(f312(f314(f859(x94393,x94393)),f312(f312(f239(x94393,x94393),x94391),x94392)),x94394))
% 173.53/173.43 [9440]E(x94401,x94402)+~P22(f312(f312(f314(f859(f853(x94403),f853(x94403))),f312(f312(f239(f853(x94403),f853(x94403)),f312(f312(f147(x94403),x94401),x94405)),f312(f312(f147(x94403),x94402),x94406))),f153(x94403,x94404)))+P22(f312(f312(f314(f859(x94403,x94403)),f312(f312(f239(x94403,x94403),x94401),x94402)),x94404))
% 173.53/173.43 [9473]P22(f312(f312(f314(f859(f853(x94731),f853(x94731))),f312(f312(f239(f853(x94731),f853(x94731)),f312(f312(f147(x94731),x94732),x94733)),f312(f312(f147(x94731),x94734),x94735))),f154(x94731,x94736)))+~P22(f312(f312(f314(f859(f853(x94731),f853(x94731))),f312(f312(f239(f853(x94731),f853(x94731)),x94733),x94735)),f154(x94731,x94736)))+~P22(f312(f312(f314(f859(x94731,x94731)),f312(f312(f239(x94731,x94731),x94732),x94734)),x94736))
% 173.53/173.43 [9493]P22(f312(x94931,x94932))+~P22(f312(x94931,f406(x94931,x94933,x94934,x94935,x94936)))+~P22(f312(f312(f314(x94936),x94932),f312(f312(f50(x94935,f860(x94936,a845)),x94934),x94933)))
% 173.53/173.43 [9498]~P22(f312(f312(f314(f859(f853(x94981),f853(x94981))),f312(f312(f239(f853(x94981),f853(x94981)),f312(f312(f147(x94981),x94982),x94985)),f312(f312(f147(x94981),x94983),x94986))),f141(x94981,x94984)))+P22(f312(f312(f314(f859(f853(x94981),f853(x94981))),f312(f312(f239(f853(x94981),f853(x94981)),x94985),x94986)),f141(x94981,x94984)))+P22(f312(f312(f314(f859(x94981,x94981)),f312(f312(f239(x94981,x94981),x94982),x94983)),x94984))
% 173.53/173.43 [9499]~P22(f312(f312(f314(f859(f853(x94991),f853(x94991))),f312(f312(f239(f853(x94991),f853(x94991)),f312(f312(f147(x94991),x94992),x94995)),f312(f312(f147(x94991),x94993),x94996))),f143(x94991,x94994)))+P22(f312(f312(f314(f859(f853(x94991),f853(x94991))),f312(f312(f239(f853(x94991),f853(x94991)),x94995),x94996)),f143(x94991,x94994)))+P22(f312(f312(f314(f859(x94991,x94991)),f312(f312(f239(x94991,x94991),x94992),x94993)),x94994))
% 173.53/173.43 [9500]~P22(f312(f312(f314(f859(f853(x95001),f853(x95001))),f312(f312(f239(f853(x95001),f853(x95001)),f312(f312(f147(x95001),x95002),x95005)),f312(f312(f147(x95001),x95003),x95006))),f153(x95001,x95004)))+P22(f312(f312(f314(f859(f853(x95001),f853(x95001))),f312(f312(f239(f853(x95001),f853(x95001)),x95005),x95006)),f153(x95001,x95004)))+P22(f312(f312(f314(f859(x95001,x95001)),f312(f312(f239(x95001,x95001),x95002),x95003)),x95004))
% 173.53/173.43 [9576]P22(f312(x95761,x95762))+P22(f312(f312(f314(x95763),f407(x95761,x95764,x95765,x95763,x95766)),x95765))+~P22(f312(f312(f314(x95766),x95762),f312(f312(f50(x95763,f860(x95766,a845)),x95765),x95764)))
% 173.53/173.43 [9585]~E(x95852,x95854)+P22(f312(f312(f314(f859(f853(x95851),f853(x95851))),f312(f312(f239(f853(x95851),f853(x95851)),f312(f312(f129(x95851),x95852),f312(f312(f147(x95851),x95853),f127(x95851)))),f312(f312(f129(x95851),x95854),f312(f312(f147(x95851),x95855),f127(x95851))))),f153(x95851,x95856)))+~P22(f312(f312(f314(f859(x95851,x95851)),f312(f312(f239(x95851,x95851),x95853),x95855)),x95856))
% 173.53/173.43 [9674]E(x96741,x96742)+~P22(f312(f312(f314(f859(f853(x96743),f853(x96743))),f312(f312(f239(f853(x96743),f853(x96743)),f312(f312(f129(x96743),x96745),f312(f312(f147(x96743),x96741),f127(x96743)))),f312(f312(f129(x96743),x96746),f312(f312(f147(x96743),x96742),f127(x96743))))),f153(x96743,x96744)))+P22(f312(f312(f314(f859(x96743,x96743)),f312(f312(f239(x96743,x96743),x96741),x96742)),x96744))
% 173.53/173.43 [9699]~P22(f312(f312(f314(f859(f853(x96991),f853(x96991))),f312(f312(f239(f853(x96991),f853(x96991)),f312(f312(f129(x96991),x96995),f312(f312(f147(x96991),x96992),f127(x96991)))),f312(f312(f129(x96991),x96996),f312(f312(f147(x96991),x96993),f127(x96991))))),f153(x96991,x96994)))+P22(f312(f312(f314(f859(f853(x96991),f853(x96991))),f312(f312(f239(f853(x96991),f853(x96991)),x96995),x96996)),f153(x96991,x96994)))+P22(f312(f312(f314(f859(x96991,x96991)),f312(f312(f239(x96991,x96991),x96992),x96993)),x96994))
% 173.53/173.43 [9717]P22(f312(x97171,x97172))+P22(f312(f312(f314(x97173),f406(x97171,x97174,x97175,x97176,x97173)),f312(x97174,f407(x97171,x97174,x97175,x97176,x97173))))+~P22(f312(f312(f314(x97173),x97172),f312(f312(f50(x97176,f860(x97173,a845)),x97175),x97174)))
% 173.53/173.43 [8811]~E(f312(f312(f173(x88111,x88112),x88114),x88115),f312(f219(x88112),x88116))+~P22(f312(f312(x88113,x88115),x88116))+E(f312(f312(f173(x88111,x88112),f312(f132(f859(x88111,x88112),f312(f249(x88111,x88112,a845),x88113)),x88114)),x88115),f312(f219(x88112),x88116))
% 173.53/173.43 [9029]~P22(f312(f312(f314(x90295),x90293),x90296))+P22(f312(f312(f227(f860(x90291,a845)),f312(x90292,x90293)),x90294))+~P22(f312(f312(f227(f860(x90291,a845)),f312(f312(f50(x90295,f860(x90291,a845)),x90296),x90292)),x90294))
% 173.53/173.43 [9649]~P3(x96491,x96495,x96494)+P22(f312(f312(f314(f859(x96491,x96491)),f312(f312(f239(x96491,x96491),x96492),x96493)),x96494))+~P22(f312(f312(f314(x96491),x96496),f312(f312(f115(f860(x96491,a845)),f312(f264(x96491,x96491,x96494),f312(f312(f289(x96491),x96492),f189(f860(x96491,a845))))),f312(f264(x96491,x96491,x96494),f312(f312(f289(x96491),x96493),f189(f860(x96491,a845)))))))
% 173.53/173.43 [8485]~P120(x84852)+~E(f312(f312(f89(x84852),f312(f312(f90(x84852),x84854),x84855)),x84851),f312(f312(f89(x84852),f312(f312(f90(x84852),x84853),x84855)),x84856))+E(x84851,f312(f312(f89(x84852),f312(f312(f90(x84852),f312(f312(f21(x84852),x84853),x84854)),x84855)),x84856))
% 173.53/173.43 [8486]~P120(x84861)+~E(f312(f312(f89(x84861),f312(f312(f90(x84861),x84862),x84864)),x84865),f312(f312(f89(x84861),f312(f312(f90(x84861),x84863),x84864)),x84866))+E(f312(f312(f89(x84861),f312(f312(f90(x84861),f312(f312(f21(x84861),x84862),x84863)),x84864)),x84865),x84866)
% 173.53/173.43 [8644]~P120(x86441)+E(f312(f312(f89(x86441),f312(f312(f90(x86441),x86442),x86443)),x86444),f312(f312(f89(x86441),f312(f312(f90(x86441),x86445),x86443)),x86446))+~E(x86446,f312(f312(f89(x86441),f312(f312(f90(x86441),f312(f312(f21(x86441),x86442),x86445)),x86443)),x86444))
% 173.53/173.43 [8645]~P120(x86451)+E(f312(f312(f89(x86451),f312(f312(f90(x86451),x86452),x86453)),x86454),f312(f312(f89(x86451),f312(f312(f90(x86451),x86455),x86453)),x86456))+~E(f312(f312(f89(x86451),f312(f312(f90(x86451),f312(f312(f21(x86451),x86452),x86455)),x86453)),x86454),x86456)
% 173.53/173.43 [8969]~P22(f312(f312(x89694,x89695),x89696))+~P22(f312(f312(x89693,x89695),x89696))+P22(f312(f312(f312(f312(f115(f860(x89691,f860(x89692,a845))),x89693),x89694),x89695),x89696))
% 173.53/173.43 [9227]P22(f312(f312(x92271,x92272),x92273))+P22(f312(f312(x92274,x92272),x92273))+~P22(f312(f312(f312(f312(f124(f860(x92275,f860(x92276,a845))),x92274),x92271),x92272),x92273))
% 173.53/173.43 [9513]~P128(x95131)+~P22(f312(f312(f228(x95131),f312(f312(f89(x95131),f312(f312(f90(x95131),x95134),x95135)),x95132)),f312(f312(f89(x95131),f312(f312(f90(x95131),x95133),x95135)),x95136)))+P22(f312(f312(f228(x95131),x95132),f312(f312(f89(x95131),f312(f312(f90(x95131),f312(f312(f21(x95131),x95133),x95134)),x95135)),x95136)))
% 173.53/173.43 [9514]~P128(x95141)+~P22(f312(f312(f227(x95141),f312(f312(f89(x95141),f312(f312(f90(x95141),x95144),x95145)),x95142)),f312(f312(f89(x95141),f312(f312(f90(x95141),x95143),x95145)),x95146)))+P22(f312(f312(f227(x95141),x95142),f312(f312(f89(x95141),f312(f312(f90(x95141),f312(f312(f21(x95141),x95143),x95144)),x95145)),x95146)))
% 173.53/173.43 [9531]~P128(x95311)+P22(f312(f312(f228(x95311),f312(f312(f89(x95311),f312(f312(f90(x95311),x95312),x95313)),x95314)),f312(f312(f89(x95311),f312(f312(f90(x95311),x95315),x95313)),x95316)))+~P22(f312(f312(f228(x95311),x95314),f312(f312(f89(x95311),f312(f312(f90(x95311),f312(f312(f21(x95311),x95315),x95312)),x95313)),x95316)))
% 173.53/173.43 [9532]~P128(x95321)+P22(f312(f312(f227(x95321),f312(f312(f89(x95321),f312(f312(f90(x95321),x95322),x95323)),x95324)),f312(f312(f89(x95321),f312(f312(f90(x95321),x95325),x95323)),x95326)))+~P22(f312(f312(f227(x95321),x95324),f312(f312(f89(x95321),f312(f312(f90(x95321),f312(f312(f21(x95321),x95325),x95322)),x95323)),x95326)))
% 173.53/173.43 [9638]~P128(x96381)+~P22(f312(f312(f228(x96381),f312(f312(f89(x96381),f312(f312(f90(x96381),x96382),x96384)),x96385)),f312(f312(f89(x96381),f312(f312(f90(x96381),x96383),x96384)),x96386)))+P22(f312(f312(f228(x96381),f312(f312(f89(x96381),f312(f312(f90(x96381),f312(f312(f21(x96381),x96382),x96383)),x96384)),x96385)),x96386))
% 173.53/173.43 [9639]~P128(x96391)+~P22(f312(f312(f227(x96391),f312(f312(f89(x96391),f312(f312(f90(x96391),x96392),x96394)),x96395)),f312(f312(f89(x96391),f312(f312(f90(x96391),x96393),x96394)),x96396)))+P22(f312(f312(f227(x96391),f312(f312(f89(x96391),f312(f312(f90(x96391),f312(f312(f21(x96391),x96392),x96393)),x96394)),x96395)),x96396))
% 173.53/173.43 [9684]~P128(x96841)+P22(f312(f312(f228(x96841),f312(f312(f89(x96841),f312(f312(f90(x96841),x96842),x96843)),x96844)),f312(f312(f89(x96841),f312(f312(f90(x96841),x96845),x96843)),x96846)))+~P22(f312(f312(f228(x96841),f312(f312(f89(x96841),f312(f312(f90(x96841),f312(f312(f21(x96841),x96842),x96845)),x96843)),x96844)),x96846))
% 173.53/173.43 [9685]~P128(x96851)+P22(f312(f312(f227(x96851),f312(f312(f89(x96851),f312(f312(f90(x96851),x96852),x96853)),x96854)),f312(f312(f89(x96851),f312(f312(f90(x96851),x96855),x96853)),x96856)))+~P22(f312(f312(f227(x96851),f312(f312(f89(x96851),f312(f312(f90(x96851),f312(f312(f21(x96851),x96852),x96855)),x96853)),x96854)),x96856))
% 173.53/173.43 [9860]~P26(x98602)+~P22(f312(f70(x98601),x98606))+E(f312(f312(f6(x98601,x98602),f312(f312(f18(x98601,x98602,x98602),f312(f312(f18(x98601,x98602,f860(x98602,x98602)),f312(f312(f8(a845,f860(x98602,f860(x98602,x98602)),x98601),f108(x98602)),x98603)),x98604)),x98605)),x98606),f312(f312(f89(x98602),f312(f312(f6(x98601,x98602),x98604),f312(f312(f115(f860(x98601,a845)),x98606),f312(f233(x98601),x98603)))),f312(f312(f6(x98601,x98602),x98605),f312(f312(f115(f860(x98601,a845)),x98606),f312(f88(f860(x98601,a845)),f312(f233(x98601),x98603))))))
% 173.53/173.43 [9923]P22(f312(f312(f314(x99232),x99234),x99236))+P22(f312(f312(f314(x99232),x99235),x99236))+E(f312(f291(x99231,x99232,f312(f312(f7(x99231,x99232,x99232),f312(f312(f7(x99231,x99232,f860(x99232,x99232)),f312(f312(f8(a845,f860(x99232,f860(x99232,x99232)),x99231),f108(x99232)),f312(f312(f7(x99231,f860(x99231,a845),a845),f314(x99231)),x99233))),x99234)),x99235)),x99236),f189(f860(x99231,a845)))
% 173.53/173.43 [9924]P22(f312(f312(f314(x99242),x99245),x99246))+~P22(f312(f312(f314(x99242),x99244),x99246))+E(f312(f291(x99241,x99242,f312(f312(f7(x99241,x99242,x99242),f312(f312(f7(x99241,x99242,f860(x99242,x99242)),f312(f312(f8(a845,f860(x99242,f860(x99242,x99242)),x99241),f108(x99242)),f312(f312(f7(x99241,f860(x99241,a845),a845),f314(x99241)),x99243))),x99244)),x99245)),x99246),x99243)
% 173.53/173.43 [9925]P22(f312(f312(f314(x99252),x99254),x99256))+~P22(f312(f312(f314(x99252),x99255),x99256))+E(f312(f291(x99251,x99252,f312(f312(f7(x99251,x99252,x99252),f312(f312(f7(x99251,x99252,f860(x99252,x99252)),f312(f312(f8(a845,f860(x99252,f860(x99252,x99252)),x99251),f108(x99252)),f312(f312(f7(x99251,f860(x99251,a845),a845),f314(x99251)),x99253))),x99254)),x99255)),x99256),f312(f88(f860(x99251,a845)),x99253))
% 173.53/173.43 [9926]~P22(f312(f312(f314(x99262),x99264),x99266))+~P22(f312(f312(f314(x99262),x99265),x99266))+E(f312(f291(x99261,x99262,f312(f312(f7(x99261,x99262,x99262),f312(f312(f7(x99261,x99262,f860(x99262,x99262)),f312(f312(f8(a845,f860(x99262,f860(x99262,x99262)),x99261),f108(x99262)),f312(f312(f7(x99261,f860(x99261,a845),a845),f314(x99261)),x99263))),x99264)),x99265)),x99266),f235(f860(x99261,a845)))
% 173.53/173.43 [10060]P18(x100601,x100602,f312(f312(f289(f851(x100601)),f312(f312(f312(f100(x100601),f312(x100603,x100604)),f312(a27,x100604)),f312(x100605,x100604))),f189(f860(f851(x100601),a845))))+~P22(f312(f312(f314(a848),x100604),x100606))+~P18(x100601,f312(f312(f124(f860(f851(x100601),a845)),x100602),f312(f290(a848,f851(x100601),f312(f312(f18(a848,f860(x100601,f860(a847,a845)),f851(x100601)),f312(f312(f18(a848,a846,f860(f860(x100601,f860(a847,a845)),f851(x100601))),f312(f312(f8(f860(x100601,f860(a847,a845)),f860(a846,f860(f860(x100601,f860(a847,a845)),f851(x100601))),a848),f100(x100601)),x100603)),a27)),x100605)),x100606)),f312(f290(a848,f851(x100601),f312(f312(f18(a848,f860(x100601,f860(a847,a845)),f851(x100601)),f312(f312(f18(a848,a846,f860(f860(x100601,f860(a847,a845)),f851(x100601))),f312(f312(f8(f860(x100601,f860(a847,a845)),f860(a846,f860(f860(x100601,f860(a847,a845)),f851(x100601))),a848),f100(x100601)),x100603)),f312(f312(f8(f856(a846),a846,a848),f223(a846)),a30))),x100605)),x100606))
% 173.53/173.43 [8513]E(x85131,x85132)+~P56(x85134,x85135,x85133,x85136,x85137)+~E(f312(x85133,x85131),f312(x85133,x85132))
% 173.53/173.43 [6900]E(f312(f221(f856(x69001),x69002,f192(x69001),x69003),f312(x69004,x69005)),f312(f219(x69001),x69006))+~E(f312(x69004,x69005),f312(f219(x69002),x69007))+~E(f312(x69003,x69007),f312(f219(x69001),x69006))
% 173.53/173.43 [8538]~P6(x85386,x85385,x85387,x85384,x85381)+E(f312(f312(x85381,x85382),x85383),x85384)+P22(f312(f70(x85385),x85383))
% 173.53/173.43 [9376]P45(x93761,x93762,x93763,x93764,x93765,f312(f312(x93763,x93766),x93767))+~E(f312(f312(x93763,x93766),x93767),x93764)+~E(x93765,f189(f860(x93761,a845)))
% 173.53/173.43 [9553]~P22(f312(x95536,x95533))+~P22(f312(f312(f314(f859(x95532,x95532)),f312(f312(f239(x95532,x95532),x95534),x95535)),f312(x95537,x95533)))+P22(f312(f312(f314(f859(f859(x95531,x95532),f859(x95531,x95532))),f312(f312(f239(f859(x95531,x95532),f859(x95531,x95532)),f312(f312(f239(x95531,x95532),x95533),x95534)),f312(f312(f239(x95531,x95532),x95533),x95535))),f262(x95531,x95532,x95536,x95537)))
% 173.53/173.43 [9979]~P45(x99792,x99797,x99793,x99796,x99791,f312(f312(x99793,x99795),x99794))+E(f312(f312(x99793,f800(x99794,x99795,x99791,x99796,x99793,x99797,x99792)),f801(x99794,x99795,x99791,x99796,x99793,x99797,x99792)),f312(f312(x99793,x99795),x99794))+E(x99791,f189(f860(x99792,a845)))
% 173.53/173.43 [9980]~P45(x99807,x99806,x99801,x99804,x99805,f312(f312(x99801,x99802),x99803))+E(f312(f312(x99801,f800(x99803,x99802,x99805,x99804,x99801,x99806,x99807)),f801(x99803,x99802,x99805,x99804,x99801,x99806,x99807)),f312(f312(x99801,x99802),x99803))+E(f312(f312(x99801,x99802),x99803),x99804)
% 173.53/173.43 [9064]~P39(x90641,x90642,x90643,x90645,x90647)+P39(x90641,x90642,x90643,f312(f312(f147(x90641),x90644),x90645),f312(f312(f147(x90642),x90646),x90647))+~P22(f312(f312(x90643,x90644),x90646))
% 173.53/173.43 [9082]P39(x90821,x90822,x90823,x90824,x90825)+~P39(x90821,x90822,x90823,f312(f312(f129(x90821),x90826),x90824),f312(f312(f129(x90822),x90827),x90825))+~E(f312(f190(f853(x90821)),x90826),f312(f190(f853(x90822)),x90827))
% 173.53/173.43 [9083]P39(x90831,x90832,x90833,x90834,x90835)+~P39(x90831,x90832,x90833,f312(f312(f129(x90831),x90834),x90836),f312(f312(f129(x90832),x90835),x90837))+~E(f312(f190(f853(x90831)),x90834),f312(f190(f853(x90832)),x90835))
% 173.53/173.43 [9287]~P39(x92871,x92872,x92873,x92875,x92877)+~P39(x92871,x92872,x92873,x92874,x92876)+P39(x92871,x92872,x92873,f312(f312(f129(x92871),x92874),x92875),f312(f312(f129(x92872),x92876),x92877))
% 173.53/173.43 [9625]~P22(f312(f75(x96251,x96254,x96255,x96256,x96253),x96257))+P22(f312(f75(x96251,x96254,x96255,x96256,f312(f312(f289(x96251),x96252),x96253)),f312(f312(x96255,x96252),x96257)))+P22(f312(f312(f314(x96251),x96252),x96253))
% 173.53/173.43 [9754]~P19(x97543,x97541,x97544,f235(f860(x97543,a845)))+E(f312(f312(f173(x97541,x97542),f312(f312(f150(f859(x97543,x97542),f859(x97541,x97542)),f312(f249(x97543,x97542,f859(x97541,x97542)),f312(f312(f8(x97541,f860(x97542,f859(x97541,x97542)),x97543),f239(x97541,x97542)),x97544))),x97545)),f312(x97544,x97546)),f312(f219(x97542),x97547))+~E(f312(f312(f173(x97543,x97542),x97545),x97546),f312(f219(x97542),x97547))
% 173.53/173.43 [10003]~P45(x100032,x100037,x100036,x100035,x100031,f312(f312(x100036,x100034),x100033))+E(x100031,f189(f860(x100032,a845)))+P22(f312(f312(f314(x100032),f800(x100033,x100034,x100031,x100035,x100036,x100037,x100032)),x100031))
% 173.53/173.43 [10004]~P45(x100045,x100047,x100041,x100044,x100046,f312(f312(x100041,x100042),x100043))+E(f312(f312(x100041,x100042),x100043),x100044)+P22(f312(f312(f314(x100045),f800(x100043,x100042,x100046,x100044,x100041,x100047,x100045)),x100046))
% 173.53/173.43 [6690]~E(x66905,x66907)+~E(x66906,x66904)+E(f312(f312(f312(f312(f81(x66901,f856(x66902)),x66903),x66904),f312(f219(x66902),x66905)),x66906),f312(f219(x66902),x66907))
% 173.53/173.43 [6810]E(x68101,x68102)+~E(f312(x68105,x68101),f312(f219(x68104),x68107))+E(f312(f312(f312(f312(f81(x68103,f856(x68104)),x68105),x68102),f312(f219(x68104),x68106)),x68101),f312(f219(x68104),x68107))
% 173.53/173.43 [7524]E(x75241,x75242)+~E(x75243,x75244)+~E(f312(f312(f312(f312(f81(x75245,f856(x75246)),x75247),x75244),f312(f219(x75246),x75241)),x75243),f312(f219(x75246),x75242))
% 173.53/173.43 [7589]E(x75891,x75892)+E(f312(x75893,x75894),f312(f219(x75895),x75891))+~E(f312(f312(f312(f312(f81(x75896,f856(x75895)),x75893),x75897),f312(f219(x75895),x75892)),x75894),f312(f219(x75895),x75891))
% 173.53/173.43 [7590]E(x75901,x75902)+E(f312(x75903,x75901),f312(f219(x75904),x75905))+~E(f312(f312(f312(f312(f81(x75906,f856(x75904)),x75903),x75902),f312(f219(x75904),x75907)),x75901),f312(f219(x75904),x75905))
% 173.53/173.43 [8754]~P16(x87544,x87545,x87546,x87547,x87541)+~P22(f312(f70(x87545),x87543))+E(f312(f312(x87541,x87542),x87543),f312(f312(f312(f74(x87544,x87545,x87546),x87542),x87547),x87543))
% 173.53/173.43 [8755]~P6(x87554,x87555,x87556,x87557,x87551)+~P22(f312(f70(x87555),x87553))+E(f312(f312(x87551,x87552),x87553),f312(f312(f312(f74(x87554,x87555,x87556),x87552),x87557),x87553))
% 173.53/173.43 [9345]~P18(x93451,x93452,f312(f312(f289(f851(x93451)),f312(f312(f312(f100(x93451),x93453),x93454),x93457)),f189(f860(f851(x93451),a845))))+P18(x93451,x93452,f312(f312(f289(f851(x93451)),f312(f312(f312(f100(x93451),x93453),f36(x93454,x93455)),x93456)),f189(f860(f851(x93451),a845))))+~P18(x93451,x93452,f312(f312(f289(f851(x93451)),f312(f312(f312(f100(x93451),x93457),x93455),x93456)),f189(f860(f851(x93451),a845))))
% 173.53/173.43 [9527]~P17(x95273,x95274,x95275,x95277,x95276,x95271)+~P22(f312(f70(x95274),x95272))+E(f312(x95271,x95272),f312(f312(f312(f74(x95273,x95274,x95275),x95276),x95277),x95272))
% 173.53/173.43 [9679]P45(x96791,x96792,x96793,x96794,x96795,f312(f312(x96793,x96796),x96797))+~P45(x96791,x96792,x96793,x96794,f312(f312(f21(f860(x96791,a845)),x96795),f312(f312(f289(x96791),x96796),f189(f860(x96791,a845)))),x96797)+~P22(f312(f312(f314(x96791),x96796),x96795))
% 173.53/173.43 [9956]~P18(x99561,x99562,f312(f312(f289(f851(x99561)),f312(f312(f312(f100(x99561),f103(x99561,x99563,x99564)),x99565),x99567)),f189(f860(f851(x99561),a845))))+P18(x99561,x99562,f312(f312(f289(f851(x99561)),f312(f312(f312(f100(x99561),x99563),f33(x99564,x99565,x99566)),x99567)),f189(f860(f851(x99561),a845))))+~P18(x99561,x99562,f312(f312(f289(f851(x99561)),f312(f312(f312(f100(x99561),f103(x99561,x99563,f312(f82(a845,a845,a847,a307),x99564))),x99566),x99567)),f189(f860(f851(x99561),a845))))
% 173.53/173.43 [10028]~P45(x100282,x100283,x100284,x100285,x100281,f312(f312(x100284,x100287),x100286))+P45(x100282,x100283,x100284,x100285,f312(f312(f21(f860(x100282,a845)),x100281),f312(f312(f289(x100282),f800(x100286,x100287,x100281,x100285,x100284,x100283,x100282)),f189(f860(x100282,a845)))),f801(x100286,x100287,x100281,x100285,x100284,x100283,x100282))+E(x100281,f189(f860(x100282,a845)))
% 173.53/173.43 [10029]~P45(x100295,x100296,x100291,x100294,x100297,f312(f312(x100291,x100292),x100293))+P45(x100295,x100296,x100291,x100294,f312(f312(f21(f860(x100295,a845)),x100297),f312(f312(f289(x100295),f800(x100293,x100292,x100297,x100294,x100291,x100296,x100295)),f189(f860(x100295,a845)))),f801(x100293,x100292,x100297,x100294,x100291,x100296,x100295))+E(f312(f312(x100291,x100292),x100293),x100294)
% 173.53/173.43 [9071]E(f182(x90711,x90712,x90713,x90714,f312(f312(f155(x90712,x90715),x90716),x90717)),f182(x90711,x90712,x90713,x90714,x90715))+~P22(f312(f312(f228(a852),x90716),f312(f190(f853(x90712)),x90715)))+~P22(f312(f312(f227(a852),f312(f190(f853(x90711)),x90714)),x90716))
% 173.53/173.43 [9365]P22(f312(f312(f227(f860(f859(x93651,x93652),a845)),f312(f312(f267(x93651,x93653,x93652),x93654),x93655)),f312(f312(f267(x93651,x93653,x93652),x93656),x93657)))+~P22(f312(f312(f227(f860(f859(x93653,x93652),a845)),x93655),x93657))+~P22(f312(f312(f227(f860(f859(x93651,x93653),a845)),x93654),x93656))
% 173.53/173.43 [9414]~E(f312(f312(f312(a201,x94146),f40(x94141)),f312(f312(a202,x94144),x94141)),f312(f312(f312(a201,x94147),f40(x94141)),f312(f312(a202,x94144),x94141)))+P22(f312(f312(f312(f312(a198,f32(x94141,x94142,x94143)),x94144),x94145),f312(f312(f312(a201,x94146),f40(x94141)),f312(f312(a202,x94144),x94141))))+~P22(f312(f312(f312(f312(a198,x94143),f312(f312(f312(a201,x94144),f40(x94141)),f312(x94142,x94144))),x94145),x94147))
% 173.53/173.43 [9694]~E(f312(f312(f312(a201,f312(f312(a203,x96946),f312(a202,x96944))),x96941),f312(f312(a202,x96946),a25)),f312(f312(f312(a201,f312(f312(a203,x96947),f312(a202,x96944))),x96941),f312(f312(a202,x96947),a25)))+P22(f312(f312(f312(f312(a198,f31(x96941,x96942,x96943)),x96944),x96945),f312(f312(f312(a201,f312(f312(a203,x96946),f312(a202,x96944))),x96941),f312(f312(a202,x96946),a25))))+~P22(f312(f312(f312(f312(a198,f312(a27,x96942)),f312(f312(f312(a201,f312(f312(a203,x96944),a204)),f40(a26)),f312(x96943,x96944))),x96945),x96947))
% 173.53/173.43 [9690]~P22(f312(f312(f314(x96901),x96906),x96905))+P22(f312(f75(x96901,x96902,x96903,x96904,x96905),f312(f312(x96903,x96906),x96907)))+~P22(f312(f75(x96901,x96902,x96903,x96904,f312(f312(f21(f860(x96901,a845)),x96905),f312(f312(f289(x96901),x96906),f189(f860(x96901,a845))))),x96907))
% 173.53/173.43 [10090]~P135(x100901)+~P19(f859(x100902,x100903),x100901,f312(f249(x100902,x100903,x100901),f312(f312(f7(x100902,f860(x100903,x100901),f860(x100903,x100901)),f312(f312(f8(f860(x100901,x100901),f860(f860(x100903,x100901),f860(x100903,x100901)),x100902),f8(x100901,x100901,x100903)),f312(f312(f8(x100901,f860(x100901,x100901),x100902),f90(x100901)),x100904))),x100905)),f312(f312(f247(x100902,x100903),x100906),f312(f16(f860(x100903,a845),x100902),x100907)))+E(f312(f312(f6(x100901,x100901),f39(x100901)),f312(f233(x100901),f312(f312(f8(f860(x100902,a845),a845,x100901),f96(x100902)),f312(f312(f8(f860(x100902,f860(x100903,a845)),f860(x100902,a845),x100901),f312(f8(f860(x100903,a845),a845,x100902),f96(x100903))),f312(f312(f7(x100901,f860(x100902,f860(x100903,a845)),f860(x100902,f860(x100903,a845))),f312(f312(f8(f860(x100902,f860(f860(x100903,a845),f860(x100903,a845))),f860(f860(x100902,f860(x100903,a845)),f860(x100902,f860(x100903,a845))),x100901),f18(x100902,f860(x100903,a845),f860(x100903,a845))),f312(f312(f8(f860(x100902,f860(x100903,f860(a845,a845))),f860(x100902,f860(f860(x100903,a845),f860(x100903,a845))),x100901),f312(f8(f860(x100903,f860(a845,a845)),f860(f860(x100903,a845),f860(x100903,a845)),x100902),f18(x100903,a845,a845))),f312(f312(f8(f860(x100902,f860(x100903,a845)),f860(x100902,f860(x100903,f860(a845,a845))),x100901),f312(f8(f860(x100903,a845),f860(x100903,f860(a845,a845)),x100902),f312(f8(a845,f860(a845,a845),x100903),a310))),f312(f312(f7(x100901,f860(x100902,f860(x100903,x100901)),f860(x100902,f860(x100903,a845))),f312(f312(f8(f860(f860(x100903,x100901),f860(x100903,a845)),f860(f860(x100902,f860(x100903,x100901)),f860(x100902,f860(x100903,a845))),x100901),f8(f860(x100903,x100901),f860(x100903,a845),x100902)),f312(f312(f8(f860(x100901,a845),f860(f860(x100903,x100901),f860(x100903,a845)),x100901),f8(x100901,a845,x100903)),a309))),f312(f312(f7(x100902,f860(x100903,x100901),f860(x100903,x100901)),f312(f312(f8(f860(x100901,x100901),f860(f860(x100903,x100901),f860(x100903,x100901)),x100902),f8(x100901,x100901,x100903)),f312(f312(f8(x100901,f860(x100901,x100901),x100902),f90(x100901)),x100904))),x100905)))))),f312(f312(f7(x100902,f860(x100903,a845),f860(x100903,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x100903,a845),f860(x100903,a845)),x100902),f8(a845,a845,x100903)),f312(f312(f8(a845,f860(a845,a845),x100902),a310),f312(f312(f7(x100902,f860(x100902,a845),a845),f314(x100902)),x100906)))),f312(f312(f7(x100903,f860(x100903,a845),a845),f314(x100903)),x100907))))))),f312(f312(f90(x100901),f312(f312(f6(x100902,x100901),x100904),x100906)),f312(f312(f6(x100903,x100901),x100905),x100907)))
% 173.53/173.43 [9785]P53(x97851,x97852,x97853,x97854,x97855,x97856,x97857)+~P22(f312(f312(x97854,x97856),x97858))+~P22(f312(f312(x97855,x97858),x97857))
% 173.53/173.43 [9133]~P14(x91338,x91331,x91333,x91335)+~P22(f312(f70(x91338),x91336))+E(f312(f82(x91331,x91331,x91332,f312(x91333,x91334)),f312(f82(x91331,x91331,x91332,f312(x91335,x91336)),x91337)),f312(f82(x91331,x91331,x91332,f312(x91335,x91336)),f312(f82(x91331,x91331,x91332,f312(x91333,x91334)),x91337)))
% 173.53/173.43 [9634]~P19(x96342,x96344,x96346,x96348)+~P19(x96341,x96343,x96345,x96347)+P19(f859(x96341,x96342),f859(x96343,x96344),f250(x96341,x96343,x96342,x96344,x96345,x96346),f312(f312(f247(x96341,x96342),x96347),f312(f16(f860(x96342,a845),x96341),x96348)))
% 173.53/173.43 [10054]P22(f312(f312(f312(f312(a198,x100541),x100542),f410(x100543,x100544,x100545,x100546,x100547,x100548,x100542,x100541)),x100547))+~P22(f312(f312(f312(f312(a198,x100541),x100542),x100548),x100547))+~P22(f312(f312(f312(f312(a198,x100546),x100545),x100544),x100543))
% 173.53/173.43 [10055]P22(f312(f312(f312(f312(a198,x100551),x100552),f410(x100553,x100554,x100552,x100551,x100555,x100556,x100557,x100558)),x100553))+~P22(f312(f312(f312(f312(a198,x100551),x100552),x100554),x100553))+~P22(f312(f312(f312(f312(a198,x100558),x100557),x100556),x100555))
% 173.53/173.43 [9312]P22(f312(f312(f314(f859(x93121,x93122)),f312(f312(f239(x93121,x93122),x93123),x93124)),f312(f312(f267(x93121,x93125,x93122),x93126),x93127)))+~P22(f312(f312(f314(f859(x93121,x93125)),f312(f312(f239(x93121,x93125),x93123),x93128)),x93126))+~P22(f312(f312(f314(f859(x93125,x93122)),f312(f312(f239(x93125,x93122),x93128),x93124)),x93127))
% 173.53/173.43 [9501]~P22(f312(f312(f227(f860(f859(x95013,x95012),a845)),x95015),f312(f312(f247(x95013,x95012),x95018),f312(f16(f860(x95012,a845),x95013),x95017))))+~P22(f312(f312(f227(f860(f859(x95011,x95013),a845)),x95014),f312(f312(f247(x95011,x95013),x95016),f312(f16(f860(x95013,a845),x95011),x95018))))+P22(f312(f312(f227(f860(f859(x95011,x95012),a845)),f312(f312(f267(x95011,x95013,x95012),x95014),x95015)),f312(f312(f247(x95011,x95012),x95016),f312(f16(f860(x95012,a845),x95011),x95017))))
% 173.53/173.43 [9548]~E(x95483,x95485)+P22(f312(f312(f314(f859(f859(x95481,x95482),f859(x95481,x95482))),f312(f312(f239(f859(x95481,x95482),f859(x95481,x95482)),f312(f312(f239(x95481,x95482),x95483),x95484)),f312(f312(f239(x95481,x95482),x95485),x95486))),f304(x95481,x95482,x95487,x95488)))+~P22(f312(f312(f314(f859(x95482,x95482)),f312(f312(f239(x95482,x95482),x95484),x95486)),x95488))
% 173.53/173.43 [9656]E(x96561,x96562)+~P22(f312(f312(f314(f859(f859(x96563,x96565),f859(x96563,x96565))),f312(f312(f239(f859(x96563,x96565),f859(x96563,x96565)),f312(f312(f239(x96563,x96565),x96561),x96566)),f312(f312(f239(x96563,x96565),x96562),x96567))),f304(x96563,x96565,x96564,x96568)))+P22(f312(f312(f314(f859(x96563,x96563)),f312(f312(f239(x96563,x96563),x96561),x96562)),x96564))
% 173.53/173.43 [9673]~P22(f312(f312(f314(f859(f859(x96731,x96735),f859(x96731,x96735))),f312(f312(f239(f859(x96731,x96735),f859(x96731,x96735)),f312(f312(f239(x96731,x96735),x96732),x96736)),f312(f312(f239(x96731,x96735),x96733),x96737))),f304(x96731,x96735,x96734,x96738)))+P22(f312(f312(f314(f859(x96731,x96731)),f312(f312(f239(x96731,x96731),x96732),x96733)),x96734))+P22(f312(f312(f314(f859(x96735,x96735)),f312(f312(f239(x96735,x96735),x96736),x96737)),x96738))
% 173.53/173.43 [9577]~P17(x95777,x95775,x95771,x95778,x95772,x95774)+~P22(f312(f70(x95775),x95776))+E(f312(f312(x95771,f312(x95772,x95773)),f312(x95774,f312(f312(f21(f860(x95775,a845)),x95776),f312(f312(f289(x95775),x95773),f189(f860(x95775,a845)))))),f312(x95774,f312(f312(f289(x95775),x95773),x95776)))
% 173.53/173.43 [9090]~P22(f312(f312(f312(x90905,x90908),x90906),x90907))+~P22(f312(f312(f314(x90901),x90908),x90904))+P22(f312(f312(f312(f312(f50(x90901,f860(x90902,f860(x90903,a845))),x90904),x90905),x90906),x90907))
% 173.53/173.43 [9298]P22(f312(f312(f312(x92981,x92982),x92983),x92984))+~P22(f312(f312(f314(x92985),x92982),x92986))+~P22(f312(f312(f312(f312(f51(x92985,f860(x92987,f860(x92988,a845))),x92986),x92981),x92983),x92984))
% 173.53/173.43 [9494]~P16(x94943,x94942,x94944,x94948,x94941)+~P22(f312(f70(x94942),x94947))+E(f312(f312(x94941,f312(f312(f18(x94942,x94943,x94943),f312(f312(f8(x94943,f860(x94943,x94943),x94942),x94944),x94945)),x94946)),x94947),f312(f312(x94944,f312(f312(x94941,x94945),x94947)),f312(f312(x94941,x94946),x94947)))
% 173.53/173.43 [9761]~E(f312(f290(x97612,x97614,x97616),x97618),x976110)+~E(f312(f290(x97611,x97613,x97615),x97617),x97619)+E(f312(f290(f859(x97611,x97612),f859(x97613,x97614),f250(x97611,x97613,x97612,x97614,x97615,x97616)),f312(f312(f247(x97611,x97612),x97617),f312(f16(f860(x97612,a845),x97611),x97618))),f312(f312(f247(x97613,x97614),x97619),f312(f16(f860(x97614,a845),x97613),x976110)))
% 173.53/173.43 [4774]~P103(x47742)+~P33(x47742,x47741)+P33(x47742,f128(x47742,x47741))+E(x47741,f127(x47742))
% 173.53/173.43 [4775]~P103(x47752)+~P33(x47752,x47751)+P33(x47752,f649(x47751,x47752))+E(x47751,f127(x47752))
% 173.53/173.43 [5001]~P31(x50012)+E(f10(x50012,x50011),f48(x50012,x50011))+E(x50011,f189(f860(x50012,a845)))+~P22(f312(f70(x50012),x50011))
% 173.53/173.43 [5002]~P31(x50022)+E(f11(x50022,x50021),f49(x50022,x50021))+E(x50021,f189(f860(x50022,a845)))+~P22(f312(f70(x50022),x50021))
% 173.53/173.43 [5166]~P103(x51662)+~P33(x51662,x51661)+E(x51661,f127(x51662))+E(f312(f312(f147(x51662),f688(x51661,x51662)),f649(x51661,x51662)),x51661)
% 173.53/173.43 [5948]~P87(x59482)+E(x59481,f189(f860(x59482,a845)))+P22(f312(f312(f227(x59482),f11(x59482,x59481)),f10(x59482,x59481)))+~P22(f312(f70(x59482),x59481))
% 173.53/173.43 [5957]~P43(x59572)+~P43(x59571)+E(x59571,x59572)+~E(f312(f290(a1,a852,a118),x59571),f312(f290(a1,a852,a118),x59572))
% 173.53/173.43 [8952]~P112(x89521)+~P22(f312(f312(f314(x89521),x89522),f123(x89521)))+P22(f312(f312(f228(x89521),f312(f312(f89(x89521),f312(f312(f89(x89521),f87(x89521)),x89522)),x89522)),f2(x89521)))+~P22(f312(f312(f228(x89521),x89522),f2(x89521)))
% 173.53/173.43 [9190]~P112(x91901)+~P22(f312(f312(f314(x91901),x91902),f123(x91901)))+~P22(f312(f312(f228(x91901),f312(f312(f89(x91901),f312(f312(f89(x91901),f87(x91901)),x91902)),x91902)),f2(x91901)))+P22(f312(f312(f228(x91901),x91902),f2(x91901)))
% 173.53/173.43 [4829]~P109(x48292)+~P135(x48292)+E(x48291,f2(a852))+E(f312(f312(f240(x48292),f2(x48292)),x48291),f2(x48292))
% 173.53/173.43 [4833]~P109(x48331)+~P135(x48331)+~E(x48332,f2(a852))+E(f312(f312(f240(x48331),f2(x48331)),x48332),f87(x48331))
% 173.53/173.43 [4988]~P134(x49882)+E(x49881,f87(x49882))+E(x49881,f312(f88(x49882),f87(x49882)))+~E(f312(f312(f90(x49882),x49881),x49881),f87(x49882))
% 173.53/173.43 [5244]~P85(x52442)+E(x52441,f2(x52442))+E(f91(x52442,x52441),f312(f88(x52442),f87(x52442)))+P22(f312(f312(f228(x52442),f2(x52442)),x52441))
% 173.53/173.43 [5472]~P85(x54722)+E(f91(x54722,x54721),f87(x54722))+E(x54721,f2(x54722))+~P22(f312(f312(f228(x54722),f2(x54722)),x54721))
% 173.53/173.43 [5483]E(x54831,x54832)+~E(f312(f117(a852),x54831),f312(f117(a852),x54832))+P22(f312(a194,f312(f117(a1),x54832)))+P22(f312(a194,f312(f117(a1),x54831)))
% 173.53/173.43 [5518]E(x55181,f2(a1))+~E(f312(f47(a1,x55182),x55181),f2(a1))+P22(f312(f312(f228(a1),x55181),x55182))+P22(f312(f312(f228(a1),x55182),x55181))
% 173.53/173.43 [5536]~P89(x55361)+~E(x55362,f2(x55361))+E(f312(f312(f89(x55361),x55362),x55362),f2(x55361))+~P22(f312(f312(f314(x55361),x55362),f123(x55361)))
% 173.53/173.43 [5547]E(x55471,f2(a1))+~E(f312(f47(a1,x55472),x55471),f2(a1))+P22(f312(f312(f227(a1),x55472),f2(a1)))+P22(f312(f312(f228(a1),x55472),x55471))
% 173.53/173.43 [5576]E(x55761,f2(a1))+~E(f312(f47(a1,x55762),x55761),f2(a1))+P22(f312(f312(f227(a1),f2(a1)),x55762))+P22(f312(f312(f228(a1),x55761),x55762))
% 173.53/173.43 [5670]~P89(x56702)+E(x56701,f2(x56702))+~E(f312(f312(f89(x56702),x56701),x56701),f2(x56702))+~P22(f312(f312(f314(x56702),x56701),f123(x56702)))
% 173.53/173.43 [5726]E(f312(f117(a852),x57261),f312(f117(a852),x57262))+~E(f312(f117(a1),x57262),f2(a1))+P22(f312(a194,f312(f117(a1),x57262)))+~P22(f312(a194,f312(f117(a1),x57261)))
% 173.53/173.43 [5749]~E(f312(f117(a852),x57492),f312(f117(a852),x57491))+E(f312(f117(a1),x57491),f2(a1))+P22(f312(a194,f312(f117(a1),x57491)))+~P22(f312(a194,f312(f117(a1),x57492)))
% 173.53/173.43 [5758]~P103(x57582)+E(x57581,f189(f860(x57582,a845)))+~P22(f312(f70(x57582),x57581))+P22(f312(f312(f314(x57582),f14(x57582,x57581)),x57581))
% 173.53/173.43 [5759]~P103(x57592)+E(x57591,f189(f860(x57592,a845)))+~P22(f312(f70(x57592),x57591))+P22(f312(f312(f314(x57592),f15(x57592,x57591)),x57591))
% 173.53/173.43 [5929]~P112(x59291)+~P90(x59291)+P22(f312(f312(f228(x59291),f2(x59291)),f312(f117(x59291),x59292)))+~P22(f312(f312(f228(a1),a92),x59292))
% 173.53/173.43 [5930]~P112(x59301)+~P90(x59301)+P22(f312(f312(f227(x59301),f2(x59301)),f312(f117(x59301),x59302)))+~P22(f312(f312(f227(a1),a92),x59302))
% 173.53/173.43 [5947]~P112(x59471)+~P90(x59471)+E(f312(f84(x59471),f312(f117(x59471),x59472)),f312(f117(x59471),x59472))+P22(f312(f312(f228(x59471),f312(f117(x59471),x59472)),f2(x59471)))
% 173.53/173.43 [5983]E(x59831,x59832)+~E(f312(a118,x59831),f312(a118,x59832))+~P22(f312(f312(f227(a1),f2(a1)),x59832))+~P22(f312(f312(f227(a1),f2(a1)),x59831))
% 173.53/173.43 [6173]~P90(x61732)+~P112(x61732)+~P22(f312(f312(f228(x61732),f2(x61732)),f312(f117(x61732),x61731)))+P22(f312(f312(f228(a1),a92),x61731))
% 173.53/173.43 [6174]~P90(x61742)+~P112(x61742)+~P22(f312(f312(f227(x61742),f2(x61742)),f312(f117(x61742),x61741)))+P22(f312(f312(f227(a1),a92),x61741))
% 173.53/173.43 [6179]~P112(x61791)+~P90(x61791)+P22(f312(f312(f228(x61791),f312(f117(x61791),x61792)),f2(x61791)))+~P22(f312(f312(f228(a1),x61792),a92))
% 173.53/173.43 [6180]~P112(x61801)+~P90(x61801)+P22(f312(f312(f227(x61801),f312(f117(x61801),x61802)),f2(x61801)))+~P22(f312(f312(f227(a1),x61802),a92))
% 173.53/173.43 [6480]~P90(x64802)+~P112(x64802)+~P22(f312(f312(f228(x64802),f312(f117(x64802),x64801)),f2(x64802)))+P22(f312(f312(f228(a1),x64801),a92))
% 173.53/173.43 [6481]~P90(x64812)+~P112(x64812)+~P22(f312(f312(f227(x64812),f312(f117(x64812),x64811)),f2(x64812)))+P22(f312(f312(f227(a1),x64811),a92))
% 173.53/173.43 [6571]~P112(x65711)+~P90(x65711)+E(f312(f84(x65711),f312(f117(x65711),x65712)),f312(f88(x65711),f312(f117(x65711),x65712)))+~P22(f312(f312(f228(x65711),f312(f117(x65711),x65712)),f2(x65711)))
% 173.53/173.43 [6594]E(f312(f117(a852),x65941),f312(f117(a852),x65942))+~E(f312(f117(a1),x65942),f2(a1))+~P22(f312(f312(f227(a1),f312(f117(a1),x65941)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x65941)))
% 173.53/173.43 [7455]~P103(x74552)+E(x74551,f189(f860(x74552,a845)))+~P22(f312(f70(x74552),x74551))+P22(f312(f312(f227(x74552),f13(x74552,f225(x74552),x74551)),f12(x74552,f226(x74552),x74551)))
% 173.53/173.43 [7771]~P43(x77712)+~P32(x77711)+P22(f312(f312(f314(a1),x77711),x77712))+~P22(f312(f312(f314(a852),f312(a118,x77711)),f312(f290(a1,a852,a118),x77712)))
% 173.53/173.43 [8041]~P63(x80412)+P22(f312(x80411,f192(x80412)))+~P22(f312(f66(f856(x80412)),x80411))+P22(f312(f66(x80412),f312(f312(f8(f856(x80412),a845,x80412),x80411),f219(x80412))))
% 173.53/173.43 [8519]~P63(x85191)+~P22(f312(x85192,f192(x85191)))+P22(f312(f67(f856(x85191)),x85192))+~P22(f312(f67(x85191),f312(f312(f8(f856(x85191),a845,x85191),x85192),f219(x85191))))
% 173.53/173.43 [9332]E(x93321,f2(a1))+E(x93322,f2(a1))+E(f312(f312(f95(a1,f859(a1,a1)),f312(f312(a200,x93322),x93321)),f312(f312(f18(a1,a1,f859(a1,a1)),f312(f312(f8(a1,f860(a1,f859(a1,a1)),a1),f239(a1,a1)),f47(a1,x93322))),f47(a1,x93321))),f210(x93322,x93321))+P22(f312(f312(f228(a1),x93321),f2(a1)))
% 173.53/173.43 [5755]~P111(x57552)+E(x57551,f2(a1))+E(f312(f88(x57552),f312(f116(x57552),f312(f88(a1),x57551))),f312(f116(x57552),x57551))+~P22(f312(f312(f228(a1),x57551),f2(a1)))
% 173.53/173.43 [5828]~P89(x58281)+~P90(x58281)+~P35(x58281,f312(f117(x58281),x58282))+P35(x58281,f312(f117(x58281),f312(f312(f89(a1),x58282),x58282)))
% 173.53/173.43 [6161]~P70(x61612)+E(x61611,f189(f860(x61612,a845)))+E(f15(x61612,f312(f290(x61612,x61612,f88(x61612)),x61611)),f312(f88(x61612),f14(x61612,x61611)))+~P22(f312(f70(x61612),x61611))
% 173.53/173.43 [6162]~P70(x61622)+E(x61621,f189(f860(x61622,a845)))+E(f14(x61622,f312(f290(x61622,x61622,f88(x61622)),x61621)),f312(f88(x61622),f15(x61622,x61621)))+~P22(f312(f70(x61622),x61621))
% 173.53/173.43 [6195]~P89(x61951)+~P90(x61951)+P35(x61951,f312(f117(x61951),x61952))+~P35(x61951,f312(f117(x61951),f312(f312(f89(a1),x61952),x61952)))
% 173.53/173.43 [7133]E(x71331,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x71331),x71332)),f54(a1,x71331,x71332)),f312(a59,f58(f312(f88(a1),x71331),f312(f88(a1),x71332))))+P22(f312(f312(f227(a1),f2(a1)),x71332))+~P22(f312(f312(f227(a1),f2(a1)),x71331))
% 173.53/173.43 [8560]~P43(x85602)+~P43(x85601)+P22(f312(f312(f228(f860(a852,a845)),f312(f290(a1,a852,a118),x85601)),f312(f290(a1,a852,a118),x85602)))+~P22(f312(f312(f228(f860(a1,a845)),x85601),x85602))
% 173.53/173.43 [8771]~E(f700(x87712,x87711),f701(x87712,x87711))+~P22(f312(f133(x87711),f702(x87712,x87711)))+~P22(f312(f133(f853(x87711)),x87712))+P22(f312(f133(x87711),f312(f138(f853(x87711),f853(x87711),f129(x87711),f127(x87711)),x87712)))
% 173.53/173.43 [8868]~P43(x88682)+~P43(x88681)+~P22(f312(f312(f228(f860(a852,a845)),f312(f290(a1,a852,a118),x88681)),f312(f290(a1,a852,a118),x88682)))+P22(f312(f312(f228(f860(a1,a845)),x88681),x88682))
% 173.53/173.43 [8869]~P43(x88692)+~P43(x88691)+~P22(f312(f312(f227(f860(a852,a845)),f312(f290(a1,a852,a118),x88691)),f312(f290(a1,a852,a118),x88692)))+P22(f312(f312(f227(f860(a1,a845)),x88691),x88692))
% 173.53/173.43 [8876]~E(f700(x88762,x88761),f701(x88762,x88761))+~P22(f312(f133(f853(x88761)),x88762))+P22(f312(f133(x88761),f312(f138(f853(x88761),f853(x88761),f129(x88761),f127(x88761)),x88762)))+P22(f312(f312(f314(f853(x88761)),f702(x88762,x88761)),f312(f168(f853(x88761)),x88762)))
% 173.53/173.43 [8920]~P22(f312(f133(x89201),f702(x89202,x89201)))+~P22(f312(f133(f853(x89201)),x89202))+P22(f312(f133(x89201),f312(f138(f853(x89201),f853(x89201),f129(x89201),f127(x89201)),x89202)))+P22(f312(f312(f314(f853(x89201)),f701(x89202,x89201)),f312(f168(f853(x89201)),x89202)))
% 173.53/173.43 [8921]~P22(f312(f133(x89211),f702(x89212,x89211)))+~P22(f312(f133(f853(x89211)),x89212))+P22(f312(f133(x89211),f312(f138(f853(x89211),f853(x89211),f129(x89211),f127(x89211)),x89212)))+P22(f312(f312(f314(f853(x89211)),f700(x89212,x89211)),f312(f168(f853(x89211)),x89212)))
% 173.53/173.43 [8993]~P22(f312(f133(f853(x89931)),x89932))+P22(f312(f133(x89931),f312(f138(f853(x89931),f853(x89931),f129(x89931),f127(x89931)),x89932)))+P22(f312(f312(f314(f853(x89931)),f701(x89932,x89931)),f312(f168(f853(x89931)),x89932)))+P22(f312(f312(f314(f853(x89931)),f702(x89932,x89931)),f312(f168(f853(x89931)),x89932)))
% 173.53/173.43 [8994]~P22(f312(f133(f853(x89941)),x89942))+P22(f312(f133(x89941),f312(f138(f853(x89941),f853(x89941),f129(x89941),f127(x89941)),x89942)))+P22(f312(f312(f314(f853(x89941)),f700(x89942,x89941)),f312(f168(f853(x89941)),x89942)))+P22(f312(f312(f314(f853(x89941)),f702(x89942,x89941)),f312(f168(f853(x89941)),x89942)))
% 173.53/173.43 [9006]~E(f312(f312(f115(f860(x90061,a845)),f312(f168(x90061),f701(x90062,x90061))),f312(f168(x90061),f700(x90062,x90061))),f189(f860(x90061,a845)))+~P22(f312(f133(x90061),f702(x90062,x90061)))+~P22(f312(f133(f853(x90061)),x90062))+P22(f312(f133(x90061),f312(f138(f853(x90061),f853(x90061),f129(x90061),f127(x90061)),x90062)))
% 173.53/173.43 [9067]~E(f312(f312(f115(f860(x90671,a845)),f312(f168(x90671),f701(x90672,x90671))),f312(f168(x90671),f700(x90672,x90671))),f189(f860(x90671,a845)))+~P22(f312(f133(f853(x90671)),x90672))+P22(f312(f133(x90671),f312(f138(f853(x90671),f853(x90671),f129(x90671),f127(x90671)),x90672)))+P22(f312(f312(f314(f853(x90671)),f702(x90672,x90671)),f312(f168(f853(x90671)),x90672)))
% 173.53/173.43 [8102]~P90(x81022)+~P112(x81022)+~P22(f312(f312(f228(x81022),f312(f117(x81022),x81021)),f87(x81022)))+P22(f312(f312(f228(a1),x81021),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 173.53/173.43 [8103]~P90(x81032)+~P112(x81032)+~P22(f312(f312(f227(x81032),f312(f117(x81032),x81031)),f87(x81032)))+P22(f312(f312(f227(a1),x81031),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 173.53/173.43 [8390]~P112(x83901)+~P90(x83901)+P22(f312(f312(f228(x83901),f312(f117(x83901),x83902)),f87(x83901)))+~P22(f312(f312(f228(a1),x83902),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 173.53/173.43 [8391]~P112(x83911)+~P90(x83911)+P22(f312(f312(f227(x83911),f312(f117(x83911),x83912)),f87(x83911)))+~P22(f312(f312(f227(a1),x83912),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 173.53/173.43 [8585]~P90(x85852)+~P112(x85852)+~P22(f312(f312(f228(x85852),f87(x85852)),f312(f117(x85852),x85851)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x85851))
% 173.53/173.43 [8586]~P90(x85862)+~P112(x85862)+~P22(f312(f312(f227(x85862),f87(x85862)),f312(f117(x85862),x85861)))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x85861))
% 173.53/173.43 [8958]~P112(x89581)+~P90(x89581)+P22(f312(f312(f228(x89581),f87(x89581)),f312(f117(x89581),x89582)))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x89582))
% 173.53/173.43 [8959]~P112(x89591)+~P90(x89591)+P22(f312(f312(f227(x89591),f87(x89591)),f312(f117(x89591),x89592)))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x89592))
% 173.53/173.43 [9464]~P134(x94642)+E(x94641,f87(x94642))+E(x94641,f312(f88(x94642),f87(x94642)))+~E(f312(f312(f240(x94642),x94641),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f87(x94642))
% 173.53/173.43 [9729]~P90(x97291)+~P66(x97291)+~P22(f312(f312(f228(x97291),f2(x97291)),x97292))+P22(f312(f312(f228(x97291),f2(x97291)),f312(f312(f268(x97291),x97292),f312(f117(x97291),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.43 [9795]~P90(x97951)+~P66(x97951)+P22(f312(f312(f228(x97951),f2(x97951)),x97952))+~P22(f312(f312(f228(x97951),f2(x97951)),f312(f312(f268(x97951),x97952),f312(f117(x97951),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.43 [10058]~P111(x100582)+E(x100581,f2(a1))+P22(f312(f312(f228(a1),x100581),f2(a1)))+E(f312(f312(f249(a1,a1,x100582),f312(f312(f7(a1,f860(a1,f860(x100582,x100582)),f860(a1,x100582)),f312(f312(f8(f860(f860(x100582,x100582),x100582),f860(f860(a1,f860(x100582,x100582)),f860(a1,x100582)),a1),f8(f860(x100582,x100582),x100582,a1)),f312(f312(f8(x100582,f860(f860(x100582,x100582),x100582),a1),f95(x100582,x100582)),f116(x100582)))),f312(f312(f7(a1,f860(x100582,x100582),f860(x100582,x100582)),f312(f312(f8(f860(x100582,f860(x100582,x100582)),f860(f860(x100582,x100582),f860(x100582,x100582)),a1),f18(x100582,x100582,x100582)),f312(f312(f7(a1,f860(x100582,x100582),f860(x100582,f860(x100582,x100582))),f312(f312(f8(f860(x100582,f860(x100582,x100582)),f860(f860(x100582,x100582),f860(x100582,f860(x100582,x100582))),a1),f8(x100582,f860(x100582,x100582),x100582)),f312(f312(f8(a845,f860(x100582,f860(x100582,x100582)),a1),f108(x100582)),f312(f312(f7(a1,a1,a845),a309),f2(a1))))),f312(f312(f18(x100582,x100582,x100582),f89(x100582)),f5(x100582))))),f312(f312(f7(x100582,x100582,x100582),f312(f312(f8(x100582,f860(x100582,x100582),x100582),f89(x100582)),f312(f312(f18(x100582,x100582,x100582),f89(x100582)),f5(x100582)))),f87(x100582))))),f312(f312(f239(a1,a1),f312(f47(a1,x100581),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f54(a1,x100581,f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f312(f116(x100582),x100581))
% 173.53/173.43 [5011]~P31(x50113)+~P49(x50113,x50113,x50111)+E(f312(x50111,x50112),x50112)+~E(x50112,f110(x50113,x50111))
% 173.53/173.43 [5012]~P31(x50123)+~P49(x50123,x50123,x50121)+E(f312(x50121,x50122),x50122)+~E(x50122,f109(x50123,x50121))
% 173.53/173.43 [4800]~P89(x48003)+~P90(x48003)+E(x48001,x48002)+~E(f312(f117(x48003),x48001),f312(f117(x48003),x48002))
% 173.53/173.43 [5938]~P22(f312(x59381,x59382))+~P22(f312(x59381,x59383))+~P22(f312(f312(f227(a852),x59383),f838(x59382,x59381)))+P22(f312(x59381,f2(a852)))
% 173.53/173.43 [6343]P139(x63432,x63431,x63433)+E(x63431,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f788(x63433,x63431,x63432)))+P22(f312(f312(f228(a1),x63431),f2(a1)))
% 173.53/173.43 [6344]P140(x63442,x63441,x63443)+E(x63441,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f791(x63443,x63441,x63442)))+P22(f312(f312(f228(a1),x63441),f2(a1)))
% 173.53/173.43 [6460]P139(x64601,x64602,x64603)+~P22(f312(x64601,x64603))+P22(f312(f312(f227(a1),f2(a1)),f788(x64603,x64602,x64601)))+P22(f312(f312(f228(a1),x64602),f2(a1)))
% 173.53/173.43 [6486]P140(x64861,x64862,x64863)+P22(f312(f312(f227(a1),f2(a1)),f791(x64863,x64862,x64861)))+~P22(f312(x64861,f2(a1)))+P22(f312(f312(f228(a1),x64862),f2(a1)))
% 173.53/173.43 [6514]P139(x65142,x65141,x65143)+E(x65141,f2(a1))+~P22(f312(x65142,f788(x65143,x65141,x65142)))+P22(f312(f312(f228(a1),x65141),f2(a1)))
% 173.53/173.43 [6515]P140(x65152,x65151,x65153)+E(x65151,f2(a1))+~P22(f312(x65152,f792(x65153,x65151,x65152)))+P22(f312(f312(f228(a1),x65151),f2(a1)))
% 173.53/173.43 [6614]~P103(x66141)+~P31(x66141)+~P22(f312(f312(f228(x66141),x66142),f48(x66141,x66143)))+P22(f312(f312(f228(x66141),x66142),f675(x66143,x66142,x66141)))
% 173.53/173.43 [6625]P139(x66251,x66252,x66253)+~P22(f312(x66251,x66253))+~P22(f312(x66251,f788(x66253,x66252,x66251)))+P22(f312(f312(f228(a1),x66252),f2(a1)))
% 173.53/173.43 [6657]P140(x66571,x66572,x66573)+~P22(f312(x66571,f792(x66573,x66572,x66571)))+~P22(f312(x66571,f2(a1)))+P22(f312(f312(f228(a1),x66572),f2(a1)))
% 173.53/173.43 [6905]P139(x69052,x69051,x69053)+E(x69051,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f788(x69053,x69051,x69052)))+P22(f312(f312(f228(a1),x69051),f787(x69053,x69051,x69052)))
% 173.53/173.43 [6906]P140(x69062,x69061,x69063)+E(x69061,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f791(x69063,x69061,x69062)))+P22(f312(f312(f228(a1),x69061),f796(x69063,x69061,x69062)))
% 173.53/173.43 [7023]P139(x70231,x70232,x70233)+~P22(f312(x70231,x70233))+P22(f312(f312(f227(a1),f2(a1)),f788(x70233,x70232,x70231)))+P22(f312(f312(f228(a1),x70232),f787(x70233,x70232,x70231)))
% 173.53/173.43 [7041]P140(x70411,x70412,x70413)+P22(f312(f312(f227(a1),f2(a1)),f791(x70413,x70412,x70411)))+P22(f312(f312(f228(a1),x70412),f796(x70413,x70412,x70411)))+~P22(f312(x70411,f2(a1)))
% 173.53/173.43 [7077]P139(x70772,x70771,x70773)+E(x70771,f2(a1))+~P22(f312(x70772,f788(x70773,x70771,x70772)))+P22(f312(f312(f228(a1),x70771),f787(x70773,x70771,x70772)))
% 173.53/173.43 [7078]P140(x70782,x70781,x70783)+E(x70781,f2(a1))+~P22(f312(x70782,f792(x70783,x70781,x70782)))+P22(f312(f312(f228(a1),x70781),f796(x70783,x70781,x70782)))
% 173.53/173.43 [7119]P139(x71192,x71191,x71193)+E(x71191,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f788(x71193,x71191,x71192)))+~P22(f312(x71192,f787(x71193,x71191,x71192)))
% 173.53/173.43 [7120]P140(x71202,x71201,x71203)+E(x71201,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f791(x71203,x71201,x71202)))+~P22(f312(x71202,f793(x71203,x71201,x71202)))
% 173.53/173.43 [7196]P139(x71961,x71962,x71963)+~P22(f312(x71961,x71963))+~P22(f312(x71961,f788(x71963,x71962,x71961)))+P22(f312(f312(f228(a1),x71962),f787(x71963,x71962,x71961)))
% 173.53/173.43 [7214]P140(x72141,x72142,x72143)+~P22(f312(x72141,f792(x72143,x72142,x72141)))+P22(f312(f312(f228(a1),x72142),f796(x72143,x72142,x72141)))+~P22(f312(x72141,f2(a1)))
% 173.53/173.43 [7218]P139(x72181,x72182,x72183)+~P22(f312(x72181,x72183))+P22(f312(f312(f227(a1),f2(a1)),f788(x72183,x72182,x72181)))+~P22(f312(x72181,f787(x72183,x72182,x72181)))
% 173.53/173.43 [7238]P140(x72381,x72382,x72383)+P22(f312(f312(f227(a1),f2(a1)),f791(x72383,x72382,x72381)))+~P22(f312(x72381,f793(x72383,x72382,x72381)))+~P22(f312(x72381,f2(a1)))
% 173.53/173.43 [7260]P139(x72602,x72601,x72603)+E(x72601,f2(a1))+~P22(f312(x72602,f788(x72603,x72601,x72602)))+~P22(f312(x72602,f787(x72603,x72601,x72602)))
% 173.53/173.43 [7261]P140(x72612,x72611,x72613)+E(x72611,f2(a1))+~P22(f312(x72612,f792(x72613,x72611,x72612)))+~P22(f312(x72612,f793(x72613,x72611,x72612)))
% 173.53/173.43 [7351]P139(x73511,x73512,x73513)+~P22(f312(x73511,x73513))+~P22(f312(x73511,f788(x73513,x73512,x73511)))+~P22(f312(x73511,f787(x73513,x73512,x73511)))
% 173.53/173.43 [7369]P140(x73691,x73692,x73693)+~P22(f312(x73691,f792(x73693,x73692,x73691)))+~P22(f312(x73691,f793(x73693,x73692,x73691)))+~P22(f312(x73691,f2(a1)))
% 173.53/173.43 [7414]P139(x74142,x74141,x74143)+E(x74141,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f788(x74143,x74141,x74142)))+P22(f312(f312(f227(a1),f787(x74143,x74141,x74142)),f2(a1)))
% 173.53/173.43 [7415]P140(x74152,x74151,x74153)+E(x74151,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f791(x74153,x74151,x74152)))+P22(f312(f312(f227(a1),f796(x74153,x74151,x74152)),f2(a1)))
% 173.53/173.43 [7416]~P111(x74161)+~P22(f312(f312(f314(x74161),x74163),f123(x74161)))+~P22(f312(f312(f314(x74161),x74162),f123(x74161)))+P22(f312(f312(f314(x74161),f312(f312(f89(x74161),x74162),x74163)),f123(x74161)))
% 173.53/173.43 [7417]~P23(x74171)+~P22(f312(f312(f314(x74171),x74173),f187(x74171)))+~P22(f312(f312(f314(x74171),x74172),f187(x74171)))+P22(f312(f312(f314(x74171),f312(f312(f89(x74171),x74172),x74173)),f187(x74171)))
% 173.53/173.43 [7418]~P111(x74181)+~P22(f312(f312(f314(x74181),x74183),f123(x74181)))+~P22(f312(f312(f314(x74181),x74182),f123(x74181)))+P22(f312(f312(f314(x74181),f312(f312(f21(x74181),x74182),x74183)),f123(x74181)))
% 173.53/173.43 [7419]~P111(x74191)+~P22(f312(f312(f314(x74191),x74193),f123(x74191)))+~P22(f312(f312(f314(x74191),x74192),f123(x74191)))+P22(f312(f312(f314(x74191),f312(f312(f90(x74191),x74192),x74193)),f123(x74191)))
% 173.53/173.43 [7420]~P23(x74201)+~P22(f312(f312(f314(x74201),x74203),f187(x74201)))+~P22(f312(f312(f314(x74201),x74202),f187(x74201)))+P22(f312(f312(f314(x74201),f312(f312(f90(x74201),x74202),x74203)),f187(x74201)))
% 173.53/173.43 [7421]~P84(x74211)+~P22(f312(f312(f228(x74211),x74213),f2(x74211)))+~P22(f312(f312(f228(x74211),x74212),f2(x74211)))+P22(f312(f312(f228(x74211),f312(f312(f89(x74211),x74212),x74213)),f2(x74211)))
% 173.53/173.43 [7422]~P84(x74221)+~P22(f312(f312(f227(x74221),x74222),f2(x74221)))+~P22(f312(f312(f228(x74221),x74223),f2(x74221)))+P22(f312(f312(f228(x74221),f312(f312(f89(x74221),x74222),x74223)),f2(x74221)))
% 173.53/173.43 [7423]~P84(x74231)+~P22(f312(f312(f227(x74231),x74233),f2(x74231)))+~P22(f312(f312(f228(x74231),x74232),f2(x74231)))+P22(f312(f312(f228(x74231),f312(f312(f89(x74231),x74232),x74233)),f2(x74231)))
% 173.53/173.43 [7424]~P84(x74241)+~P22(f312(f312(f227(x74241),x74243),f2(x74241)))+~P22(f312(f312(f227(x74241),x74242),f2(x74241)))+P22(f312(f312(f227(x74241),f312(f312(f89(x74241),x74242),x74243)),f2(x74241)))
% 173.53/173.43 [7450]P139(x74503,x74501,x74502)+E(x74501,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74501),f789(x74502,x74501,x74503))),f788(x74502,x74501,x74503)),x74502)+P22(f312(f312(f228(a1),x74501),f2(a1)))
% 173.53/173.43 [7451]P140(x74513,x74511,x74512)+E(x74511,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74511),f792(x74512,x74511,x74513))),f791(x74512,x74511,x74513)),x74512)+P22(f312(f312(f228(a1),x74511),f2(a1)))
% 173.53/173.43 [7535]P139(x75351,x75352,x75353)+~P22(f312(x75351,x75353))+P22(f312(f312(f227(a1),f2(a1)),f788(x75353,x75352,x75351)))+P22(f312(f312(f227(a1),f787(x75353,x75352,x75351)),f2(a1)))
% 173.53/173.43 [7562]P140(x75621,x75622,x75623)+P22(f312(f312(f227(a1),f2(a1)),f791(x75623,x75622,x75621)))+~P22(f312(x75621,f2(a1)))+P22(f312(f312(f227(a1),f796(x75623,x75622,x75621)),f2(a1)))
% 173.53/173.43 [7572]P139(x75723,x75721,x75722)+~P22(f312(x75723,x75722))+E(f312(f312(f89(a1),f312(f312(f90(a1),x75721),f789(x75722,x75721,x75723))),f788(x75722,x75721,x75723)),x75722)+P22(f312(f312(f228(a1),x75721),f2(a1)))
% 173.53/173.43 [7578]P139(x75782,x75781,x75783)+E(x75781,f2(a1))+~P22(f312(x75782,f788(x75783,x75781,x75782)))+P22(f312(f312(f227(a1),f787(x75783,x75781,x75782)),f2(a1)))
% 173.53/173.43 [7579]P140(x75792,x75791,x75793)+E(x75791,f2(a1))+~P22(f312(x75792,f792(x75793,x75791,x75792)))+P22(f312(f312(f227(a1),f796(x75793,x75791,x75792)),f2(a1)))
% 173.53/173.43 [7584]P140(x75843,x75841,x75842)+E(f312(f312(f89(a1),f312(f312(f90(a1),x75841),f792(x75842,x75841,x75843))),f791(x75842,x75841,x75843)),x75842)+~P22(f312(x75843,f2(a1)))+P22(f312(f312(f228(a1),x75841),f2(a1)))
% 173.53/173.43 [7640]P139(x76401,x76402,x76403)+~P22(f312(x76401,x76403))+~P22(f312(x76401,f788(x76403,x76402,x76401)))+P22(f312(f312(f227(a1),f787(x76403,x76402,x76401)),f2(a1)))
% 173.53/173.43 [7645]P140(x76451,x76452,x76453)+~P22(f312(x76451,f792(x76453,x76452,x76451)))+~P22(f312(x76451,f2(a1)))+P22(f312(f312(f227(a1),f796(x76453,x76452,x76451)),f2(a1)))
% 173.53/173.43 [7715]~P66(x77151)+~P22(f312(f312(f228(x77151),f312(f312(f268(x77151),x77153),x77152)),f2(x77151)))+P22(f312(f312(f228(x77151),x77152),f2(x77151)))+P22(f312(f312(f228(x77151),x77153),f2(x77151)))
% 173.53/173.43 [7716]~P118(x77161)+~P22(f312(f312(f227(x77161),f312(f312(f90(x77161),x77163),x77162)),f2(x77161)))+P22(f312(f312(f227(x77161),x77162),f2(x77161)))+P22(f312(f312(f227(x77161),x77163),f2(x77161)))
% 173.53/173.43 [7717]~P66(x77171)+~P22(f312(f312(f227(x77171),f312(f312(f268(x77171),x77173),x77172)),f2(x77171)))+P22(f312(f312(f227(x77171),x77172),f2(x77171)))+P22(f312(f312(f227(x77171),x77173),f2(x77171)))
% 173.53/173.43 [7824]P139(x78243,x78241,x78242)+E(x78241,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78241),f789(x78242,x78241,x78243))),f788(x78242,x78241,x78243)),x78242)+P22(f312(f312(f228(a1),x78241),f787(x78242,x78241,x78243)))
% 173.53/173.43 [7825]P140(x78253,x78251,x78252)+E(x78251,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78251),f792(x78252,x78251,x78253))),f791(x78252,x78251,x78253)),x78252)+P22(f312(f312(f228(a1),x78251),f796(x78252,x78251,x78253)))
% 173.53/173.43 [7836]P139(x78363,x78361,x78362)+E(x78361,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78361),f790(x78362,x78361,x78363))),f787(x78362,x78361,x78363)),x78362)+P22(f312(f312(f227(a1),f2(a1)),f788(x78362,x78361,x78363)))
% 173.53/173.43 [7837]P140(x78373,x78371,x78372)+E(x78371,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78371),f793(x78372,x78371,x78373))),f796(x78372,x78371,x78373)),x78372)+P22(f312(f312(f227(a1),f2(a1)),f791(x78372,x78371,x78373)))
% 173.53/173.43 [7880]P139(x78803,x78801,x78802)+~P22(f312(x78803,x78802))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78801),f789(x78802,x78801,x78803))),f788(x78802,x78801,x78803)),x78802)+P22(f312(f312(f228(a1),x78801),f787(x78802,x78801,x78803)))
% 173.53/173.43 [7892]P140(x78923,x78921,x78922)+E(f312(f312(f89(a1),f312(f312(f90(a1),x78921),f792(x78922,x78921,x78923))),f791(x78922,x78921,x78923)),x78922)+P22(f312(f312(f228(a1),x78921),f796(x78922,x78921,x78923)))+~P22(f312(x78923,f2(a1)))
% 173.53/173.43 [7898]P139(x78983,x78981,x78982)+~P22(f312(x78983,x78982))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78981),f790(x78982,x78981,x78983))),f787(x78982,x78981,x78983)),x78982)+P22(f312(f312(f227(a1),f2(a1)),f788(x78982,x78981,x78983)))
% 173.53/173.43 [7904]P140(x79043,x79041,x79042)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79041),f793(x79042,x79041,x79043))),f796(x79042,x79041,x79043)),x79042)+P22(f312(f312(f227(a1),f2(a1)),f791(x79042,x79041,x79043)))+~P22(f312(x79043,f2(a1)))
% 173.53/173.43 [7915]P139(x79153,x79151,x79152)+E(x79151,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79151),f789(x79152,x79151,x79153))),f788(x79152,x79151,x79153)),x79152)+~P22(f312(x79153,f787(x79152,x79151,x79153)))
% 173.53/173.43 [7916]P140(x79163,x79161,x79162)+E(x79161,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79161),f792(x79162,x79161,x79163))),f791(x79162,x79161,x79163)),x79162)+~P22(f312(x79163,f793(x79162,x79161,x79163)))
% 173.53/173.43 [7917]P139(x79173,x79171,x79172)+E(x79171,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79171),f790(x79172,x79171,x79173))),f787(x79172,x79171,x79173)),x79172)+~P22(f312(x79173,f788(x79172,x79171,x79173)))
% 173.53/173.43 [7918]P140(x79183,x79181,x79182)+E(x79181,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79181),f793(x79182,x79181,x79183))),f796(x79182,x79181,x79183)),x79182)+~P22(f312(x79183,f792(x79182,x79181,x79183)))
% 173.53/173.43 [7976]P139(x79763,x79761,x79762)+~P22(f312(x79763,x79762))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79761),f789(x79762,x79761,x79763))),f788(x79762,x79761,x79763)),x79762)+~P22(f312(x79763,f787(x79762,x79761,x79763)))
% 173.53/173.43 [7977]P139(x79773,x79771,x79772)+~P22(f312(x79773,x79772))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79771),f790(x79772,x79771,x79773))),f787(x79772,x79771,x79773)),x79772)+~P22(f312(x79773,f788(x79772,x79771,x79773)))
% 173.53/173.43 [7986]P140(x79863,x79861,x79862)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79861),f792(x79862,x79861,x79863))),f791(x79862,x79861,x79863)),x79862)+~P22(f312(x79863,f793(x79862,x79861,x79863)))+~P22(f312(x79863,f2(a1)))
% 173.53/173.43 [7987]P140(x79873,x79871,x79872)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79871),f793(x79872,x79871,x79873))),f796(x79872,x79871,x79873)),x79872)+~P22(f312(x79873,f792(x79872,x79871,x79873)))+~P22(f312(x79873,f2(a1)))
% 173.53/173.43 [8095]P139(x80953,x80951,x80952)+E(x80951,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80951),f789(x80952,x80951,x80953))),f788(x80952,x80951,x80953)),x80952)+P22(f312(f312(f227(a1),f787(x80952,x80951,x80953)),f2(a1)))
% 173.53/173.43 [8096]P140(x80963,x80961,x80962)+E(x80961,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80961),f792(x80962,x80961,x80963))),f791(x80962,x80961,x80963)),x80962)+P22(f312(f312(f227(a1),f796(x80962,x80961,x80963)),f2(a1)))
% 173.53/173.43 [8137]P139(x81373,x81371,x81372)+~P22(f312(x81373,x81372))+E(f312(f312(f89(a1),f312(f312(f90(a1),x81371),f789(x81372,x81371,x81373))),f788(x81372,x81371,x81373)),x81372)+P22(f312(f312(f227(a1),f787(x81372,x81371,x81373)),f2(a1)))
% 173.53/173.43 [8142]P140(x81423,x81421,x81422)+E(f312(f312(f89(a1),f312(f312(f90(a1),x81421),f792(x81422,x81421,x81423))),f791(x81422,x81421,x81423)),x81422)+~P22(f312(x81423,f2(a1)))+P22(f312(f312(f227(a1),f796(x81422,x81421,x81423)),f2(a1)))
% 173.53/173.43 [8272]P139(x82723,x82721,x82722)+E(x82721,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x82721),f790(x82722,x82721,x82723))),f787(x82722,x82721,x82723)),x82722)+E(f312(f312(f89(a1),f312(f312(f90(a1),x82721),f789(x82722,x82721,x82723))),f788(x82722,x82721,x82723)),x82722)
% 173.53/173.43 [8273]P140(x82733,x82731,x82732)+E(x82731,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x82731),f793(x82732,x82731,x82733))),f796(x82732,x82731,x82733)),x82732)+E(f312(f312(f89(a1),f312(f312(f90(a1),x82731),f792(x82732,x82731,x82733))),f791(x82732,x82731,x82733)),x82732)
% 173.53/173.43 [8298]P139(x82983,x82981,x82982)+~P22(f312(x82983,x82982))+E(f312(f312(f89(a1),f312(f312(f90(a1),x82981),f790(x82982,x82981,x82983))),f787(x82982,x82981,x82983)),x82982)+E(f312(f312(f89(a1),f312(f312(f90(a1),x82981),f789(x82982,x82981,x82983))),f788(x82982,x82981,x82983)),x82982)
% 173.53/173.43 [8311]P140(x83113,x83111,x83112)+E(f312(f312(f89(a1),f312(f312(f90(a1),x83111),f793(x83112,x83111,x83113))),f796(x83112,x83111,x83113)),x83112)+E(f312(f312(f89(a1),f312(f312(f90(a1),x83111),f792(x83112,x83111,x83113))),f791(x83112,x83111,x83113)),x83112)+~P22(f312(x83113,f2(a1)))
% 173.53/173.43 [8963]~P118(x89631)+~E(x89633,f2(x89631))+~E(x89632,f2(x89631))+P22(f312(f312(f227(x89631),f312(f312(f89(x89631),f312(f312(f90(x89631),x89632),x89632)),f312(f312(f90(x89631),x89633),x89633))),f2(x89631)))
% 173.53/173.43 [10006]~P112(x100061)+~E(x100063,f2(x100061))+~E(x100062,f2(x100061))+P22(f312(f312(f227(x100061),f312(f312(f89(x100061),f312(f312(f240(x100061),x100062),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x100061),x100063),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))),f2(x100061)))
% 173.53/173.43 [4749]~E(x47493,x47491)+~P114(x47492)+E(x47491,f2(x47492))+E(f312(f312(f268(x47492),x47493),x47491),f87(x47492))
% 173.53/173.43 [4801]~P94(x48011)+~E(x48013,f189(x48011))+~E(x48012,f189(x48011))+E(f312(f312(f124(x48011),x48012),x48013),f189(x48011))
% 173.53/173.43 [4802]~P97(x48021)+~E(x48023,f235(x48021))+~E(x48022,f235(x48021))+E(f312(f312(f115(x48021),x48022),x48023),f235(x48021))
% 173.53/173.43 [4891]~P114(x48913)+E(x48911,x48912)+E(x48912,f2(x48913))+~E(f312(f312(f268(x48913),x48911),x48912),f87(x48913))
% 173.53/173.43 [4909]~P133(x49092)+E(x49091,f2(x49092))+E(x49093,f2(x49092))+~E(f312(f312(f90(x49092),x49093),x49091),f2(x49092))
% 173.53/173.43 [4911]~P127(x49112)+E(x49111,f2(x49112))+E(x49113,f2(x49112))+~E(f312(f312(f90(x49112),x49113),x49111),f2(x49112))
% 173.53/173.43 [5280]~P113(x52803)+E(x52801,x52802)+E(x52801,f312(f88(x52803),x52802))+~E(f312(f312(f90(x52803),x52801),x52801),f312(f312(f90(x52803),x52802),x52802))
% 173.53/173.43 [5316]~P88(x53161)+E(f312(f88(x53161),x53162),x53163)+~E(f312(f312(f124(x53161),x53162),x53163),f235(x53161))+~E(f312(f312(f115(x53161),x53162),x53163),f189(x53161))
% 173.53/173.43 [5391]~P112(x53913)+E(x53911,x53912)+P22(f312(f312(f228(x53913),x53912),x53911))+P22(f312(f312(f228(x53913),x53911),x53912))
% 173.53/173.43 [5397]~P103(x53973)+E(x53971,x53972)+P22(f312(f312(f228(x53973),x53972),x53971))+P22(f312(f312(f228(x53973),x53971),x53972))
% 173.53/173.43 [5398]~E(x53982,x53983)+~P103(x53981)+P22(f312(f312(f227(x53981),x53982),x53983))+P22(f312(f312(f228(x53981),x53982),x53983))
% 173.53/173.43 [5652]~P105(x56523)+E(x56521,x56522)+~P22(f312(f312(f227(x56523),x56522),x56521))+P22(f312(f312(f228(x56523),x56522),x56521))
% 173.53/173.43 [5654]~P103(x56543)+E(x56541,x56542)+~P22(f312(f312(f227(x56543),x56541),x56542))+P22(f312(f312(f228(x56543),x56541),x56542))
% 173.53/173.43 [5660]~P105(x56603)+E(x56601,x56602)+~P22(f312(f312(f227(x56603),x56601),x56602))+P22(f312(f312(f228(x56603),x56601),x56602))
% 173.53/173.43 [5752]P139(x57521,x57522,x57523)+~P22(f312(x57521,x57523))+P22(f312(f312(f228(a1),x57522),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x57522))
% 173.53/173.43 [5801]P140(x58011,x58012,x58013)+~P22(f312(x58011,f2(a1)))+P22(f312(f312(f228(a1),x58012),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x58012))
% 173.53/173.43 [5805]~P87(x58051)+E(f312(f312(f124(x58051),x58052),f11(x58051,x58053)),x58052)+~P22(f312(f70(x58051),x58053))+~P22(f312(f312(f314(x58051),x58052),x58053))
% 173.53/173.43 [5806]~P87(x58061)+E(f312(f312(f115(x58061),x58062),f10(x58061,x58063)),x58062)+~P22(f312(f70(x58061),x58063))+~P22(f312(f312(f314(x58061),x58062),x58063))
% 173.53/173.43 [5838]~P87(x58381)+E(f312(f312(f124(x58381),x58382),f10(x58381,x58383)),f10(x58381,x58383))+~P22(f312(f70(x58381),x58383))+~P22(f312(f312(f314(x58381),x58382),x58383))
% 173.53/173.43 [5839]~P87(x58391)+E(f312(f312(f115(x58391),x58392),f11(x58391,x58393)),f11(x58391,x58393))+~P22(f312(f70(x58391),x58393))+~P22(f312(f312(f314(x58391),x58392),x58393))
% 173.53/173.43 [5840]~P103(x58401)+E(f312(f312(f225(x58401),x58402),f15(x58401,x58403)),f15(x58401,x58403))+~P22(f312(f70(x58401),x58403))+~P22(f312(f312(f314(x58401),x58402),x58403))
% 173.53/173.43 [5841]~P103(x58411)+E(f312(f312(f226(x58411),x58412),f14(x58411,x58413)),f14(x58411,x58413))+~P22(f312(f70(x58411),x58413))+~P22(f312(f312(f314(x58411),x58412),x58413))
% 173.53/173.43 [5886]E(x58861,x58862)+~P105(x58863)+~P22(f312(f312(f227(x58863),x58862),x58861))+~P22(f312(f312(f227(x58863),x58861),x58862))
% 173.53/173.43 [6024]~P102(x60241)+P22(f312(f312(f227(x60241),x60243),x60242))+~P22(f312(f312(f227(x60241),x60242),x60243))+P22(f312(f312(f228(x60241),x60242),x60243))
% 173.53/173.43 [6045]~P103(x60451)+~P22(f312(f70(x60451),x60453))+P22(f312(f312(f227(x60451),x60452),f14(x60451,x60453)))+~P22(f312(f312(f314(x60451),x60452),x60453))
% 173.53/173.43 [6094]~P103(x60941)+E(f312(f312(f225(x60941),x60942),f12(x60941,f226(x60941),x60943)),x60942)+~P22(f312(f70(x60941),x60943))+~P22(f312(f312(f314(x60941),x60942),x60943))
% 173.53/173.43 [6095]~P103(x60951)+E(f312(f312(f226(x60951),x60952),f13(x60951,f225(x60951),x60953)),x60952)+~P22(f312(f70(x60951),x60953))+~P22(f312(f312(f314(x60951),x60952),x60953))
% 173.53/173.43 [6231]E(x62311,x62312)+~E(f312(f312(f21(a852),x62311),x62313),f312(f312(f21(a852),x62312),x62313))+~P22(f312(f312(f227(a852),x62313),x62311))+~P22(f312(f312(f227(a852),x62313),x62312))
% 173.53/173.43 [6261]~P103(x62611)+~P22(f312(f70(x62611),x62612))+~P22(f312(f312(f314(x62611),x62613),x62612))+P22(f312(f312(f227(x62611),f15(x62611,x62612)),x62613))
% 173.53/173.43 [6321]P139(x63212,x63211,x63213)+E(x63211,f2(a1))+P22(f312(f312(f228(a1),x63211),f787(x63213,x63211,x63212)))+P22(f312(f312(f228(a1),f2(a1)),x63211))
% 173.53/173.43 [6322]P140(x63222,x63221,x63223)+E(x63221,f2(a1))+P22(f312(f312(f228(a1),x63221),f796(x63223,x63221,x63222)))+P22(f312(f312(f228(a1),f2(a1)),x63221))
% 173.53/173.43 [6324]~P103(x63241)+E(f312(f312(f225(x63241),x63242),f13(x63241,f225(x63241),x63243)),f13(x63241,f225(x63241),x63243))+~P22(f312(f70(x63241),x63243))+~P22(f312(f312(f314(x63241),x63242),x63243))
% 173.53/173.43 [6325]~P103(x63251)+E(f312(f312(f226(x63251),x63252),f12(x63251,f226(x63251),x63253)),f12(x63251,f226(x63251),x63253))+~P22(f312(f70(x63251),x63253))+~P22(f312(f312(f314(x63251),x63252),x63253))
% 173.53/173.43 [6332]~P22(f312(x63321,x63322))+P22(f312(x63321,f737(x63322,x63321,x63323)))+P22(f312(x63321,f2(a852)))+~P22(f312(f312(f228(a852),x63322),x63323))
% 173.53/173.43 [6385]~P22(f312(x63851,x63852))+~P22(f312(f70(x63853),x63852))+P22(f312(x63851,f431(x63851,x63852,x63853)))+P22(f312(x63851,f189(f860(x63853,a845))))
% 173.53/173.43 [6398]~P112(x63981)+~P90(x63981)+P22(f312(f312(f228(x63981),f312(f117(x63981),x63982)),f312(f117(x63981),x63983)))+~P22(f312(f312(f228(a1),x63982),x63983))
% 173.53/173.43 [6399]~P112(x63991)+~P90(x63991)+P22(f312(f312(f227(x63991),f312(f117(x63991),x63992)),f312(f117(x63991),x63993)))+~P22(f312(f312(f227(a1),x63992),x63993))
% 173.53/173.43 [6403]~P22(f312(x64031,x64033))+~P22(f312(f70(x64032),x64033))+P22(f312(f70(x64032),f431(x64031,x64033,x64032)))+P22(f312(x64031,f189(f860(x64032,a845))))
% 173.53/173.43 [6431]P139(x64311,x64312,x64313)+~P22(f312(x64311,x64313))+P22(f312(f312(f228(a1),x64312),f787(x64313,x64312,x64311)))+P22(f312(f312(f228(a1),f2(a1)),x64312))
% 173.53/173.43 [6469]P140(x64691,x64692,x64693)+P22(f312(f312(f228(a1),x64692),f796(x64693,x64692,x64691)))+~P22(f312(x64691,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x64692))
% 173.53/173.43 [6497]~P104(x64971)+~P91(x64971)+E(f312(f312(f225(x64971),f312(f117(x64971),x64972)),f312(f117(x64971),x64973)),f312(f117(x64971),x64973))+P22(f312(f312(f227(x64971),f312(f117(x64971),x64972)),f312(f117(x64971),x64973)))
% 173.53/173.43 [6498]~P104(x64981)+~P91(x64981)+E(f312(f312(f226(x64981),f312(f117(x64981),x64982)),f312(f117(x64981),x64983)),f312(f117(x64981),x64982))+P22(f312(f312(f227(x64981),f312(f117(x64981),x64982)),f312(f117(x64981),x64983)))
% 173.53/173.43 [6556]P139(x65562,x65561,x65563)+E(x65561,f2(a1))+~P22(f312(x65562,f787(x65563,x65561,x65562)))+P22(f312(f312(f228(a1),f2(a1)),x65561))
% 173.53/173.43 [6557]P140(x65572,x65571,x65573)+E(x65571,f2(a1))+~P22(f312(x65572,f793(x65573,x65571,x65572)))+P22(f312(f312(f228(a1),f2(a1)),x65571))
% 173.53/173.43 [6646]P139(x66461,x66462,x66463)+~P22(f312(x66461,x66463))+~P22(f312(x66461,f787(x66463,x66462,x66461)))+P22(f312(f312(f228(a1),f2(a1)),x66462))
% 173.53/173.43 [6675]P140(x66751,x66752,x66753)+~P22(f312(x66751,f793(x66753,x66752,x66751)))+~P22(f312(x66751,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x66752))
% 173.53/173.43 [6775]~P90(x67753)+~P112(x67753)+~P22(f312(f312(f228(x67753),f312(f117(x67753),x67751)),f312(f117(x67753),x67752)))+P22(f312(f312(f228(a1),x67751),x67752))
% 173.53/173.43 [6776]~P90(x67763)+~P112(x67763)+~P22(f312(f312(f227(x67763),f312(f117(x67763),x67761)),f312(f117(x67763),x67762)))+P22(f312(f312(f227(a1),x67761),x67762))
% 173.53/173.43 [6802]~P103(x68021)+~P33(x68021,x68023)+P33(x68021,f312(f312(f147(x68021),x68022),x68023))+~P22(f312(f312(f227(x68021),x68022),f645(x68023,x68022,x68021)))
% 173.53/173.43 [6803]~P103(x68031)+~P33(x68031,x68033)+P33(x68031,f312(f312(f147(x68031),x68032),x68033))+~P22(f312(f312(f227(x68031),x68032),f654(x68033,x68032,x68031)))
% 173.53/173.43 [6804]~P103(x68041)+~P33(x68041,x68043)+P33(x68041,f312(f312(f147(x68041),x68042),x68043))+~P22(f312(f312(f227(x68041),x68042),f742(x68042,x68043,x68041)))
% 173.53/173.43 [6892]P139(x68922,x68921,x68923)+E(x68921,f2(a1))+P22(f312(f312(f228(a1),x68921),f2(a1)))+P22(f312(f312(f228(a1),f788(x68923,x68921,x68922)),x68921))
% 173.53/173.43 [6893]P140(x68932,x68931,x68933)+E(x68931,f2(a1))+P22(f312(f312(f228(a1),x68931),f2(a1)))+P22(f312(f312(f228(a1),f791(x68933,x68931,x68932)),x68931))
% 173.53/173.43 [6937]P139(x69372,x69371,x69373)+E(x69371,f2(a1))+P22(f312(f312(f227(a1),f787(x69373,x69371,x69372)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x69371))
% 173.53/173.43 [6938]P140(x69382,x69381,x69383)+E(x69381,f2(a1))+P22(f312(f312(f227(a1),f796(x69383,x69381,x69382)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x69381))
% 173.53/173.43 [6958]~P103(x69581)+~P33(x69581,x69583)+E(f312(f312(f145(x69581,x69581,f5(x69581)),x69582),f166(x69581,x69582,x69583)),x69583)+~P22(f312(f312(f314(x69581),x69582),f312(f168(x69581),x69583)))
% 173.53/173.43 [7008]P139(x70081,x70082,x70083)+~P22(f312(x70081,x70083))+P22(f312(f312(f228(a1),x70082),f2(a1)))+P22(f312(f312(f228(a1),f788(x70083,x70082,x70081)),x70082))
% 173.53/173.43 [7012]~P104(x70121)+~P91(x70121)+E(f312(f312(f225(x70121),f312(f117(x70121),x70122)),f312(f117(x70121),x70123)),f312(f117(x70121),x70122))+~P22(f312(f312(f227(x70121),f312(f117(x70121),x70122)),f312(f117(x70121),x70123)))
% 173.53/173.43 [7013]~P104(x70131)+~P91(x70131)+E(f312(f312(f226(x70131),f312(f117(x70131),x70132)),f312(f117(x70131),x70133)),f312(f117(x70131),x70133))+~P22(f312(f312(f227(x70131),f312(f117(x70131),x70132)),f312(f117(x70131),x70133)))
% 173.53/173.43 [7028]P140(x70281,x70282,x70283)+~P22(f312(x70281,f2(a1)))+P22(f312(f312(f228(a1),x70282),f2(a1)))+P22(f312(f312(f228(a1),f791(x70283,x70282,x70281)),x70282))
% 173.53/173.43 [7034]P139(x70341,x70342,x70343)+~P22(f312(x70341,x70343))+P22(f312(f312(f227(a1),f787(x70343,x70342,x70341)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x70342))
% 173.53/173.43 [7061]P140(x70611,x70612,x70613)+~P22(f312(x70611,f2(a1)))+P22(f312(f312(f227(a1),f796(x70613,x70612,x70611)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x70612))
% 173.53/173.43 [7090]~P22(f312(x70901,x70902))+P22(f312(x70901,f2(a852)))+~P22(f312(f312(f228(a852),x70902),x70903))+P22(f312(f312(f228(a852),f737(x70902,x70901,x70903)),x70903))
% 173.53/173.43 [7106]~P103(x71061)+~P33(x71061,x71063)+P33(x71061,f312(f312(f147(x71061),x71062),x71063))+P22(f312(f312(f314(x71061),f645(x71063,x71062,x71061)),f312(f168(x71061),x71063)))
% 173.53/173.43 [7107]~P103(x71071)+~P33(x71071,x71073)+P33(x71071,f312(f312(f147(x71071),x71072),x71073))+P22(f312(f312(f314(x71071),f654(x71073,x71072,x71071)),f312(f168(x71071),x71073)))
% 173.53/173.43 [7108]~P103(x71081)+~P33(x71081,x71083)+P33(x71081,f312(f312(f147(x71081),x71082),x71083))+P22(f312(f312(f314(x71081),f742(x71082,x71083,x71081)),f312(f168(x71081),x71083)))
% 173.53/173.43 [7202]~P103(x72021)+~P31(x72021)+~P22(f312(f312(f228(x72021),x72023),f48(x72021,x72022)))+P22(f312(f312(f314(x72021),f675(x72022,x72023,x72021)),x72022))
% 173.53/173.43 [7367]~P103(x73671)+~P31(x73671)+~P22(f312(f312(f228(x73671),f49(x73671,x73673)),x73672))+P22(f312(f312(f314(x73671),f681(x73672,x73673,x73671)),x73673))
% 173.53/173.43 [7368]~P103(x73681)+~P31(x73681)+~P22(f312(f312(f228(x73681),f49(x73681,x73683)),x73682))+P22(f312(f312(f228(x73681),f681(x73682,x73683,x73681)),x73682))
% 173.53/173.43 [7381]P139(x73812,x73811,x73813)+E(x73811,f2(a1))+P22(f312(f312(f228(a1),x73811),f787(x73813,x73811,x73812)))+P22(f312(f312(f228(a1),f788(x73813,x73811,x73812)),x73811))
% 173.53/173.43 [7382]P140(x73822,x73821,x73823)+E(x73821,f2(a1))+P22(f312(f312(f228(a1),x73821),f796(x73823,x73821,x73822)))+P22(f312(f312(f228(a1),f791(x73823,x73821,x73822)),x73821))
% 173.53/173.43 [7472]P139(x74723,x74721,x74722)+E(x74721,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74721),f790(x74722,x74721,x74723))),f787(x74722,x74721,x74723)),x74722)+P22(f312(f312(f228(a1),f2(a1)),x74721))
% 173.53/173.43 [7473]P140(x74733,x74731,x74732)+E(x74731,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74731),f793(x74732,x74731,x74733))),f796(x74732,x74731,x74733)),x74732)+P22(f312(f312(f228(a1),f2(a1)),x74731))
% 173.53/173.43 [7475]~P122(x74751)+~P22(f312(f312(f228(x74751),x74753),f2(x74751)))+P22(f312(f312(f228(x74751),f312(f312(f90(x74751),x74752),x74753)),f2(x74751)))+~P22(f312(f312(f228(x74751),f2(x74751)),x74752))
% 173.53/173.43 [7476]~P122(x74761)+~P22(f312(f312(f228(x74761),x74762),f2(x74761)))+P22(f312(f312(f228(x74761),f312(f312(f90(x74761),x74762),x74763)),f2(x74761)))+~P22(f312(f312(f228(x74761),f2(x74761)),x74763))
% 173.53/173.43 [7477]~P67(x74771)+~P22(f312(f312(f228(x74771),x74773),f2(x74771)))+P22(f312(f312(f228(x74771),f312(f312(f268(x74771),x74772),x74773)),f2(x74771)))+~P22(f312(f312(f228(x74771),f2(x74771)),x74772))
% 173.53/173.43 [7478]~P67(x74781)+~P22(f312(f312(f228(x74781),x74782),f2(x74781)))+P22(f312(f312(f228(x74781),f312(f312(f268(x74781),x74782),x74783)),f2(x74781)))+~P22(f312(f312(f228(x74781),f2(x74781)),x74783))
% 173.53/173.43 [7479]~P66(x74791)+~P22(f312(f312(f228(x74791),x74793),f2(x74791)))+P22(f312(f312(f228(x74791),f312(f312(f268(x74791),x74792),x74793)),f2(x74791)))+~P22(f312(f312(f228(x74791),f2(x74791)),x74792))
% 173.53/173.43 [7480]~P66(x74801)+~P22(f312(f312(f228(x74801),x74802),f2(x74801)))+P22(f312(f312(f228(x74801),f312(f312(f268(x74801),x74802),x74803)),f2(x74801)))+~P22(f312(f312(f228(x74801),f2(x74801)),x74803))
% 173.53/173.43 [7483]~P121(x74831)+~P22(f312(f312(f227(x74831),x74833),f2(x74831)))+P22(f312(f312(f227(x74831),f312(f312(f90(x74831),x74832),x74833)),f2(x74831)))+~P22(f312(f312(f227(x74831),f2(x74831)),x74832))
% 173.53/173.43 [7485]~P121(x74851)+~P22(f312(f312(f227(x74851),x74852),f2(x74851)))+P22(f312(f312(f227(x74851),f312(f312(f90(x74851),x74852),x74853)),f2(x74851)))+~P22(f312(f312(f227(x74851),f2(x74851)),x74853))
% 173.53/173.43 [7486]~P118(x74861)+~P22(f312(f312(f227(x74861),x74863),f2(x74861)))+P22(f312(f312(f227(x74861),f312(f312(f90(x74861),x74862),x74863)),f2(x74861)))+~P22(f312(f312(f227(x74861),f2(x74861)),x74862))
% 173.53/173.43 [7487]~P118(x74871)+~P22(f312(f312(f227(x74871),x74872),f2(x74871)))+P22(f312(f312(f227(x74871),f312(f312(f90(x74871),x74872),x74873)),f2(x74871)))+~P22(f312(f312(f227(x74871),f2(x74871)),x74873))
% 173.53/173.43 [7488]~P67(x74881)+~P22(f312(f312(f228(x74881),x74883),f2(x74881)))+P22(f312(f312(f227(x74881),f312(f312(f268(x74881),x74882),x74883)),f2(x74881)))+~P22(f312(f312(f227(x74881),f2(x74881)),x74882))
% 173.53/173.43 [7489]~P67(x74891)+~P22(f312(f312(f227(x74891),x74892),f2(x74891)))+P22(f312(f312(f227(x74891),f312(f312(f268(x74891),x74892),x74893)),f2(x74891)))+~P22(f312(f312(f228(x74891),f2(x74891)),x74893))
% 173.53/173.43 [7490]~P66(x74901)+~P22(f312(f312(f227(x74901),x74903),f2(x74901)))+P22(f312(f312(f227(x74901),f312(f312(f268(x74901),x74902),x74903)),f2(x74901)))+~P22(f312(f312(f227(x74901),f2(x74901)),x74902))
% 173.53/173.43 [7491]~P66(x74911)+~P22(f312(f312(f227(x74911),x74912),f2(x74911)))+P22(f312(f312(f227(x74911),f312(f312(f268(x74911),x74912),x74913)),f2(x74911)))+~P22(f312(f312(f227(x74911),f2(x74911)),x74913))
% 173.53/173.43 [7506]P139(x75061,x75062,x75063)+~P22(f312(x75061,x75063))+P22(f312(f312(f228(a1),x75062),f787(x75063,x75062,x75061)))+P22(f312(f312(f228(a1),f788(x75063,x75062,x75061)),x75062))
% 173.53/173.43 [7519]P140(x75191,x75192,x75193)+P22(f312(f312(f228(a1),x75192),f796(x75193,x75192,x75191)))+~P22(f312(x75191,f2(a1)))+P22(f312(f312(f228(a1),f791(x75193,x75192,x75191)),x75192))
% 173.53/173.43 [7568]P139(x75682,x75681,x75683)+E(x75681,f2(a1))+~P22(f312(x75682,f787(x75683,x75681,x75682)))+P22(f312(f312(f228(a1),f788(x75683,x75681,x75682)),x75681))
% 173.53/173.43 [7569]P140(x75692,x75691,x75693)+E(x75691,f2(a1))+~P22(f312(x75692,f793(x75693,x75691,x75692)))+P22(f312(f312(f228(a1),f791(x75693,x75691,x75692)),x75691))
% 173.53/173.43 [7581]P139(x75813,x75811,x75812)+~P22(f312(x75813,x75812))+E(f312(f312(f89(a1),f312(f312(f90(a1),x75811),f790(x75812,x75811,x75813))),f787(x75812,x75811,x75813)),x75812)+P22(f312(f312(f228(a1),f2(a1)),x75811))
% 173.53/173.43 [7598]P140(x75983,x75981,x75982)+E(f312(f312(f89(a1),f312(f312(f90(a1),x75981),f793(x75982,x75981,x75983))),f796(x75982,x75981,x75983)),x75982)+~P22(f312(x75983,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x75981))
% 173.53/173.43 [7623]~P22(f312(x76231,x76233))+~P22(f312(f70(x76232),x76233))+P22(f312(f312(f314(x76232),f432(x76231,x76233,x76232)),f431(x76231,x76233,x76232)))+P22(f312(x76231,f189(f860(x76232,a845))))
% 173.53/173.43 [7626]~P22(f312(f312(f228(a1),x76261),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x76262))+~P22(f312(f312(f227(a1),x76262),x76263))+P22(f312(f312(f227(a1),f312(f47(a1,x76261),x76262)),f312(f47(a1,x76261),x76263)))
% 173.53/173.43 [7635]P139(x76351,x76352,x76353)+~P22(f312(x76351,x76353))+~P22(f312(x76351,f787(x76353,x76352,x76351)))+P22(f312(f312(f228(a1),f788(x76353,x76352,x76351)),x76352))
% 173.53/173.43 [7637]~P22(f312(f312(f228(a1),f2(a1)),x76373))+~P22(f312(f312(f227(a1),f2(a1)),x76371))+~P22(f312(f312(f227(a1),x76373),x76372))+P22(f312(f312(f227(a1),f312(f47(a1,x76371),x76372)),f312(f47(a1,x76371),x76373)))
% 173.53/173.43 [7641]P140(x76411,x76412,x76413)+~P22(f312(x76411,f793(x76413,x76412,x76411)))+~P22(f312(x76411,f2(a1)))+P22(f312(f312(f228(a1),f791(x76413,x76412,x76411)),x76412))
% 173.53/173.43 [7747]~P66(x77471)+~P22(f312(f312(f228(x77471),f312(f312(f268(x77471),x77473),x77472)),f2(x77471)))+P22(f312(f312(f228(x77471),x77472),f2(x77471)))+P22(f312(f312(f228(x77471),f2(x77471)),x77472))
% 173.53/173.43 [7748]~P66(x77481)+~P22(f312(f312(f228(x77481),f312(f312(f268(x77481),x77482),x77483)),f2(x77481)))+P22(f312(f312(f228(x77481),x77482),f2(x77481)))+P22(f312(f312(f228(x77481),f2(x77481)),x77482))
% 173.53/173.43 [7749]~P118(x77491)+~P22(f312(f312(f227(x77491),f312(f312(f90(x77491),x77493),x77492)),f2(x77491)))+P22(f312(f312(f227(x77491),x77492),f2(x77491)))+P22(f312(f312(f227(x77491),f2(x77491)),x77492))
% 173.53/173.43 [7750]~P118(x77501)+~P22(f312(f312(f227(x77501),f312(f312(f90(x77501),x77502),x77503)),f2(x77501)))+P22(f312(f312(f227(x77501),x77502),f2(x77501)))+P22(f312(f312(f227(x77501),f2(x77501)),x77502))
% 173.53/173.43 [7751]~P66(x77511)+~P22(f312(f312(f227(x77511),f312(f312(f268(x77511),x77513),x77512)),f2(x77511)))+P22(f312(f312(f227(x77511),x77512),f2(x77511)))+P22(f312(f312(f227(x77511),f2(x77511)),x77512))
% 173.53/173.43 [7752]~P66(x77521)+~P22(f312(f312(f227(x77521),f312(f312(f268(x77521),x77522),x77523)),f2(x77521)))+P22(f312(f312(f227(x77521),x77522),f2(x77521)))+P22(f312(f312(f227(x77521),f2(x77521)),x77522))
% 173.53/173.43 [7773]~P66(x77731)+~P22(f312(f312(f228(x77731),f312(f312(f268(x77731),x77732),x77733)),f2(x77731)))+P22(f312(f312(f228(x77731),f2(x77731)),x77732))+P22(f312(f312(f228(x77731),f2(x77731)),x77733))
% 173.53/173.43 [7774]~P118(x77741)+~P22(f312(f312(f227(x77741),f312(f312(f90(x77741),x77742),x77743)),f2(x77741)))+P22(f312(f312(f227(x77741),f2(x77741)),x77742))+P22(f312(f312(f227(x77741),f2(x77741)),x77743))
% 173.53/173.43 [7775]~P66(x77751)+~P22(f312(f312(f227(x77751),f312(f312(f268(x77751),x77752),x77753)),f2(x77751)))+P22(f312(f312(f227(x77751),f2(x77751)),x77752))+P22(f312(f312(f227(x77751),f2(x77751)),x77753))
% 173.53/173.43 [7795]P139(x77952,x77951,x77953)+E(x77951,f2(a1))+P22(f312(f312(f227(a1),f787(x77953,x77951,x77952)),f2(a1)))+P22(f312(f312(f228(a1),f788(x77953,x77951,x77952)),x77951))
% 173.53/173.43 [7796]P140(x77962,x77961,x77963)+E(x77961,f2(a1))+P22(f312(f312(f227(a1),f796(x77963,x77961,x77962)),f2(a1)))+P22(f312(f312(f228(a1),f791(x77963,x77961,x77962)),x77961))
% 173.53/173.43 [7801]~P117(x78011)+~P22(f312(f312(f228(x78011),x78012),f87(x78011)))+P22(f312(f312(f228(x78011),f312(f312(f240(x78011),x78012),f312(a126,x78013))),f87(x78011)))+~P22(f312(f312(f228(x78011),f2(x78011)),x78012))
% 173.53/173.43 [7853]~P103(x78531)+~E(x78533,f127(x78531))+~P33(x78531,f312(f165(x78531),x78533))+E(f312(f138(x78531,x78531,f312(f7(x78531,x78531,x78531),f226(x78531)),x78532),f312(f165(x78531),x78533)),x78532)
% 173.53/173.43 [7855]P139(x78551,x78552,x78553)+~P22(f312(x78551,x78553))+P22(f312(f312(f227(a1),f787(x78553,x78552,x78551)),f2(a1)))+P22(f312(f312(f228(a1),f788(x78553,x78552,x78551)),x78552))
% 173.53/173.43 [7864]P140(x78641,x78642,x78643)+~P22(f312(x78641,f2(a1)))+P22(f312(f312(f227(a1),f796(x78643,x78642,x78641)),f2(a1)))+P22(f312(f312(f228(a1),f791(x78643,x78642,x78641)),x78642))
% 173.53/173.43 [8089]P139(x80893,x80891,x80892)+E(x80891,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80891),f790(x80892,x80891,x80893))),f787(x80892,x80891,x80893)),x80892)+P22(f312(f312(f228(a1),f788(x80892,x80891,x80893)),x80891))
% 173.53/173.43 [8090]P140(x80903,x80901,x80902)+E(x80901,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80901),f793(x80902,x80901,x80903))),f796(x80902,x80901,x80903)),x80902)+P22(f312(f312(f228(a1),f791(x80902,x80901,x80903)),x80901))
% 173.53/173.43 [8127]P139(x81273,x81271,x81272)+~P22(f312(x81273,x81272))+E(f312(f312(f89(a1),f312(f312(f90(a1),x81271),f790(x81272,x81271,x81273))),f787(x81272,x81271,x81273)),x81272)+P22(f312(f312(f228(a1),f788(x81272,x81271,x81273)),x81271))
% 173.53/173.43 [8128]~P26(x81281)+~P72(x81281)+~P43(x81283)+E(f312(f312(f9(a852,x81281),f312(f312(f8(a1,x81281,a852),x81282),f114(a1))),f312(f290(a1,a852,a118),x81283)),f312(f312(f9(a1,x81281),x81282),x81283))
% 173.53/173.43 [8129]~P26(x81291)+~P72(x81291)+~P43(x81293)+E(f312(f312(f6(a852,x81291),f312(f312(f8(a1,x81291,a852),x81292),f114(a1))),f312(f290(a1,a852,a118),x81293)),f312(f312(f6(a1,x81291),x81292),x81293))
% 173.53/173.43 [8139]P140(x81393,x81391,x81392)+E(f312(f312(f89(a1),f312(f312(f90(a1),x81391),f793(x81392,x81391,x81393))),f796(x81392,x81391,x81393)),x81392)+~P22(f312(x81393,f2(a1)))+P22(f312(f312(f228(a1),f791(x81392,x81391,x81393)),x81391))
% 173.53/173.43 [8158]~E(x81582,f2(a852))+~E(f312(f246(a852,a852),x81583),f2(a852))+~E(x81581,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x81583)),x81582)),f312(f248(a852,a852),x81583)))+P22(f312(f56(x81581,x81582),x81583))
% 173.53/173.43 [9063]P22(f312(f312(f227(a1),x90631),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x90632),x90631)),x90633)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x90632))+~P22(f312(f312(f227(a1),f2(a1)),x90633))
% 173.53/173.43 [5717]~P87(x57172)+E(x57171,f189(f860(x57172,a845)))+~P22(f312(f70(x57172),x57171))+E(f11(x57172,f312(f312(f289(x57172),x57173),x57171)),f312(f312(f115(x57172),x57173),f11(x57172,x57171)))
% 173.53/173.43 [5718]~P87(x57182)+E(x57181,f189(f860(x57182,a845)))+~P22(f312(f70(x57182),x57181))+E(f10(x57182,f312(f312(f289(x57182),x57183),x57181)),f312(f312(f124(x57182),x57183),f10(x57182,x57181)))
% 173.53/173.43 [5719]~P103(x57192)+E(x57191,f189(f860(x57192,a845)))+~P22(f312(f70(x57192),x57191))+E(f14(x57192,f312(f312(f289(x57192),x57193),x57191)),f312(f312(f226(x57192),x57193),f14(x57192,x57191)))
% 173.53/173.43 [5720]~P103(x57202)+E(x57201,f189(f860(x57202,a845)))+~P22(f312(f70(x57202),x57201))+E(f15(x57202,f312(f312(f289(x57202),x57203),x57201)),f312(f312(f225(x57202),x57203),f15(x57202,x57201)))
% 173.53/173.43 [6022]~P118(x60221)+~E(x60223,f2(x60221))+~E(x60222,f2(x60221))+E(f312(f312(f89(x60221),f312(f312(f90(x60221),x60222),x60222)),f312(f312(f90(x60221),x60223),x60223)),f2(x60221))
% 173.53/173.43 [6088]~P93(x60882)+E(x60881,f189(f860(x60882,a845)))+~P22(f312(f70(x60882),x60881))+E(f312(f72(x60882,f90(x60882)),f312(f312(f289(x60882),x60883),x60881)),f312(f312(f90(x60882),x60883),f312(f72(x60882,f90(x60882)),x60881)))
% 173.53/173.43 [6214]~P103(x62142)+E(x62141,f189(f860(x62142,a845)))+~P22(f312(f70(x62142),x62141))+E(f12(x62142,f226(x62142),f312(f312(f289(x62142),x62143),x62141)),f312(f312(f226(x62142),x62143),f12(x62142,f226(x62142),x62141)))
% 173.53/173.43 [6215]~P103(x62152)+E(x62151,f189(f860(x62152,a845)))+~P22(f312(f70(x62152),x62151))+E(f13(x62152,f225(x62152),f312(f312(f289(x62152),x62153),x62151)),f312(f312(f225(x62152),x62153),f13(x62152,f225(x62152),x62151)))
% 173.53/173.43 [6723]~P103(x67231)+~P22(f312(f70(x67231),x67233))+E(f12(x67231,f226(x67231),f312(f312(f289(x67231),x67232),x67233)),f312(f312(f73(x67231,x67231,f226(x67231)),x67232),x67233))+P22(f312(f312(f314(x67231),x67232),x67233))
% 173.53/173.43 [6780]~E(f312(f312(f89(a1),x67802),f312(f312(f90(a1),x67803),x67801)),x67803)+~P22(f312(f312(f228(a1),f2(a1)),x67803))+P22(f312(f312(f227(a1),f87(a1)),x67801))+~P22(f312(f312(f228(a1),x67802),x67803))
% 173.53/173.43 [6809]~E(f312(f312(f89(a1),x68092),f312(f312(f90(a1),x68093),x68091)),x68093)+P22(f312(f312(f227(a1),x68091),f87(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x68093))+~P22(f312(f312(f227(a1),f2(a1)),x68092))
% 173.53/173.43 [6827]E(x68271,f2(a852))+~P22(f312(f56(x68273,x68271),x68272))+~P22(f312(f312(f228(a852),f2(a852)),x68271))+P22(f312(f312(f228(a852),f312(f248(a852,a852),x68272)),x68271))
% 173.53/173.43 [6858]~P131(x68581)+~P22(f312(f312(f227(x68581),x68582),f2(x68581)))+~P22(f312(f312(f227(x68581),x68583),f2(x68581)))+E(f312(f312(f90(x68581),f312(f84(x68581),x68582)),f312(f84(x68581),x68583)),f312(f84(x68581),f312(f312(f90(x68581),x68582),x68583)))
% 173.53/173.43 [6914]~P131(x69141)+~P22(f312(f312(f227(x69141),x69142),f2(x69141)))+E(f312(f312(f90(x69141),f312(f84(x69141),x69142)),f312(f84(x69141),x69143)),f312(f84(x69141),f312(f312(f90(x69141),x69142),x69143)))+~P22(f312(f312(f227(x69141),f2(x69141)),x69143))
% 173.53/173.43 [6915]~P131(x69151)+~P22(f312(f312(f227(x69151),x69153),f2(x69151)))+E(f312(f312(f90(x69151),f312(f84(x69151),x69152)),f312(f84(x69151),x69153)),f312(f84(x69151),f312(f312(f90(x69151),x69152),x69153)))+~P22(f312(f312(f227(x69151),f2(x69151)),x69152))
% 173.53/173.43 [6968]~P131(x69681)+E(f312(f312(f90(x69681),f312(f84(x69681),x69682)),f312(f84(x69681),x69683)),f312(f84(x69681),f312(f312(f90(x69681),x69682),x69683)))+~P22(f312(f312(f227(x69681),f2(x69681)),x69682))+~P22(f312(f312(f227(x69681),f2(x69681)),x69683))
% 173.53/173.43 [6984]~P118(x69841)+~P22(f312(f312(f228(x69841),x69843),f2(x69841)))+~P22(f312(f312(f228(x69841),x69842),f2(x69841)))+P22(f312(f312(f228(x69841),f2(x69841)),f312(f312(f90(x69841),x69842),x69843)))
% 173.53/173.43 [6985]~P67(x69851)+~P22(f312(f312(f228(x69851),x69853),f2(x69851)))+~P22(f312(f312(f228(x69851),x69852),f2(x69851)))+P22(f312(f312(f228(x69851),f2(x69851)),f312(f312(f268(x69851),x69852),x69853)))
% 173.53/173.43 [6986]~P66(x69861)+~P22(f312(f312(f228(x69861),x69863),f2(x69861)))+~P22(f312(f312(f228(x69861),x69862),f2(x69861)))+P22(f312(f312(f228(x69861),f2(x69861)),f312(f312(f268(x69861),x69862),x69863)))
% 173.53/173.43 [6988]~P128(x69881)+~P22(f312(f312(f227(x69881),x69883),f2(x69881)))+~P22(f312(f312(f227(x69881),x69882),f2(x69881)))+P22(f312(f312(f227(x69881),f2(x69881)),f312(f312(f90(x69881),x69882),x69883)))
% 173.53/173.43 [6989]~P118(x69891)+~P22(f312(f312(f227(x69891),x69893),f2(x69891)))+~P22(f312(f312(f227(x69891),x69892),f2(x69891)))+P22(f312(f312(f227(x69891),f2(x69891)),f312(f312(f90(x69891),x69892),x69893)))
% 173.53/173.43 [6990]~P67(x69901)+~P22(f312(f312(f228(x69901),x69903),f2(x69901)))+~P22(f312(f312(f227(x69901),x69902),f2(x69901)))+P22(f312(f312(f227(x69901),f2(x69901)),f312(f312(f268(x69901),x69902),x69903)))
% 173.53/173.43 [6991]~P66(x69911)+~P22(f312(f312(f227(x69911),x69913),f2(x69911)))+~P22(f312(f312(f227(x69911),x69912),f2(x69911)))+P22(f312(f312(f227(x69911),f2(x69911)),f312(f312(f268(x69911),x69912),x69913)))
% 173.53/173.43 [6992]~P117(x69921)+~P22(f312(f312(f228(a852),f2(a852)),x69923))+~P22(f312(f312(f228(x69921),f87(x69921)),x69922))+P22(f312(f312(f228(x69921),f87(x69921)),f312(f312(f240(x69921),x69922),x69923)))
% 173.53/173.43 [7091]~P84(x70911)+~P22(f312(f312(f228(x70911),f2(x70911)),x70913))+~P22(f312(f312(f228(x70911),f2(x70911)),x70912))+P22(f312(f312(f228(x70911),f2(x70911)),f312(f312(f89(x70911),x70912),x70913)))
% 173.53/173.43 [7094]~P122(x70941)+~P22(f312(f312(f228(x70941),f2(x70941)),x70943))+~P22(f312(f312(f228(x70941),f2(x70941)),x70942))+P22(f312(f312(f228(x70941),f2(x70941)),f312(f312(f90(x70941),x70942),x70943)))
% 173.53/173.43 [7095]~P67(x70951)+~P22(f312(f312(f228(x70951),f2(x70951)),x70953))+~P22(f312(f312(f228(x70951),f2(x70951)),x70952))+P22(f312(f312(f228(x70951),f2(x70951)),f312(f312(f268(x70951),x70952),x70953)))
% 173.53/173.43 [7096]~P66(x70961)+~P22(f312(f312(f228(x70961),f2(x70961)),x70963))+~P22(f312(f312(f228(x70961),f2(x70961)),x70962))+P22(f312(f312(f228(x70961),f2(x70961)),f312(f312(f268(x70961),x70962),x70963)))
% 173.53/173.43 [7097]~P117(x70971)+~P22(f312(f312(f228(x70971),f87(x70971)),x70973))+~P22(f312(f312(f228(x70971),f87(x70971)),x70972))+P22(f312(f312(f228(x70971),f87(x70971)),f312(f312(f90(x70971),x70972),x70973)))
% 173.53/173.43 [7099]~P121(x70991)+~P22(f312(f312(f227(x70991),f2(x70991)),x70993))+~P22(f312(f312(f227(x70991),f2(x70991)),x70992))+P22(f312(f312(f227(x70991),f2(x70991)),f312(f312(f90(x70991),x70992),x70993)))
% 173.53/173.43 [7100]~P128(x71001)+~P22(f312(f312(f227(x71001),f2(x71001)),x71003))+~P22(f312(f312(f227(x71001),f2(x71001)),x71002))+P22(f312(f312(f227(x71001),f2(x71001)),f312(f312(f90(x71001),x71002),x71003)))
% 173.53/173.43 [7101]~P118(x71011)+~P22(f312(f312(f227(x71011),f2(x71011)),x71013))+~P22(f312(f312(f227(x71011),f2(x71011)),x71012))+P22(f312(f312(f227(x71011),f2(x71011)),f312(f312(f90(x71011),x71012),x71013)))
% 173.53/173.43 [7102]~P67(x71021)+~P22(f312(f312(f228(x71021),f2(x71021)),x71023))+~P22(f312(f312(f227(x71021),f2(x71021)),x71022))+P22(f312(f312(f227(x71021),f2(x71021)),f312(f312(f268(x71021),x71022),x71023)))
% 173.53/173.43 [7103]~P66(x71031)+~P22(f312(f312(f227(x71031),f2(x71031)),x71033))+~P22(f312(f312(f227(x71031),f2(x71031)),x71032))+P22(f312(f312(f227(x71031),f2(x71031)),f312(f312(f268(x71031),x71032),x71033)))
% 173.53/173.43 [7170]~P87(x71701)+~P22(f312(f70(x71701),x71703))+E(f11(x71701,f312(f312(f289(x71701),x71702),x71703)),x71702)+~E(f312(f312(f21(f860(x71701,a845)),x71703),f312(f312(f289(x71701),x71702),f189(f860(x71701,a845)))),f189(f860(x71701,a845)))
% 173.53/173.43 [7171]~P87(x71711)+~P22(f312(f70(x71711),x71713))+E(f10(x71711,f312(f312(f289(x71711),x71712),x71713)),x71712)+~E(f312(f312(f21(f860(x71711,a845)),x71713),f312(f312(f289(x71711),x71712),f189(f860(x71711,a845)))),f189(f860(x71711,a845)))
% 173.53/173.43 [7172]~P103(x71721)+~P22(f312(f70(x71721),x71723))+E(f14(x71721,f312(f312(f289(x71721),x71722),x71723)),x71722)+~E(f312(f312(f21(f860(x71721,a845)),x71723),f312(f312(f289(x71721),x71722),f189(f860(x71721,a845)))),f189(f860(x71721,a845)))
% 173.53/173.43 [7173]~P103(x71731)+~P22(f312(f70(x71731),x71733))+E(f15(x71731,f312(f312(f289(x71731),x71732),x71733)),x71732)+~E(f312(f312(f21(f860(x71731,a845)),x71733),f312(f312(f289(x71731),x71732),f189(f860(x71731,a845)))),f189(f860(x71731,a845)))
% 173.53/173.43 [7174]~P66(x71741)+P22(f312(f312(f228(x71741),x71742),f2(x71741)))+P22(f312(f312(f228(x71741),f2(x71741)),x71743))+~P22(f312(f312(f228(x71741),f2(x71741)),f312(f312(f268(x71741),x71743),x71742)))
% 173.53/173.43 [7175]~P66(x71751)+P22(f312(f312(f228(x71751),x71752),f2(x71751)))+P22(f312(f312(f228(x71751),f2(x71751)),x71753))+~P22(f312(f312(f228(x71751),f2(x71751)),f312(f312(f268(x71751),x71752),x71753)))
% 173.53/173.43 [7176]~P66(x71761)+P22(f312(f312(f228(x71761),x71762),f2(x71761)))+P22(f312(f312(f228(x71761),f2(x71761)),x71762))+~P22(f312(f312(f228(x71761),f2(x71761)),f312(f312(f268(x71761),x71763),x71762)))
% 173.53/173.43 [7177]~P66(x71771)+P22(f312(f312(f228(x71771),x71772),f2(x71771)))+P22(f312(f312(f228(x71771),f2(x71771)),x71772))+~P22(f312(f312(f228(x71771),f2(x71771)),f312(f312(f268(x71771),x71772),x71773)))
% 173.53/173.43 [7178]~P118(x71781)+P22(f312(f312(f227(x71781),x71782),f2(x71781)))+P22(f312(f312(f227(x71781),f2(x71781)),x71783))+~P22(f312(f312(f227(x71781),f2(x71781)),f312(f312(f90(x71781),x71783),x71782)))
% 173.53/173.43 [7179]~P118(x71791)+P22(f312(f312(f227(x71791),x71792),f2(x71791)))+P22(f312(f312(f227(x71791),f2(x71791)),x71793))+~P22(f312(f312(f227(x71791),f2(x71791)),f312(f312(f90(x71791),x71792),x71793)))
% 173.53/173.43 [7180]~P66(x71801)+P22(f312(f312(f227(x71801),x71802),f2(x71801)))+P22(f312(f312(f227(x71801),f2(x71801)),x71803))+~P22(f312(f312(f227(x71801),f2(x71801)),f312(f312(f268(x71801),x71803),x71802)))
% 173.53/173.43 [7181]~P66(x71811)+P22(f312(f312(f227(x71811),x71812),f2(x71811)))+P22(f312(f312(f227(x71811),f2(x71811)),x71813))+~P22(f312(f312(f227(x71811),f2(x71811)),f312(f312(f268(x71811),x71812),x71813)))
% 173.53/173.43 [7182]~P118(x71821)+P22(f312(f312(f227(x71821),x71822),f2(x71821)))+P22(f312(f312(f227(x71821),f2(x71821)),x71822))+~P22(f312(f312(f227(x71821),f2(x71821)),f312(f312(f90(x71821),x71823),x71822)))
% 173.53/173.43 [7183]~P118(x71831)+P22(f312(f312(f227(x71831),x71832),f2(x71831)))+P22(f312(f312(f227(x71831),f2(x71831)),x71832))+~P22(f312(f312(f227(x71831),f2(x71831)),f312(f312(f90(x71831),x71832),x71833)))
% 173.53/173.43 [7184]~P66(x71841)+P22(f312(f312(f227(x71841),x71842),f2(x71841)))+P22(f312(f312(f227(x71841),f2(x71841)),x71842))+~P22(f312(f312(f227(x71841),f2(x71841)),f312(f312(f268(x71841),x71843),x71842)))
% 173.53/173.43 [7185]~P66(x71851)+P22(f312(f312(f227(x71851),x71852),f2(x71851)))+P22(f312(f312(f227(x71851),f2(x71851)),x71852))+~P22(f312(f312(f227(x71851),f2(x71851)),f312(f312(f268(x71851),x71852),x71853)))
% 173.53/173.43 [7268]~E(f312(f312(f115(f860(x72681,a845)),f312(f168(x72681),x72682)),f312(f168(x72681),x72683)),f189(f860(x72681,a845)))+~P22(f312(f133(x72681),x72683))+~P22(f312(f133(x72681),x72682))+P22(f312(f133(x72681),f312(f312(f129(x72681),x72682),x72683)))
% 173.53/173.43 [7269]~P103(x72691)+~P22(f312(f70(x72691),x72693))+E(f12(x72691,f226(x72691),f312(f312(f289(x72691),x72692),x72693)),x72692)+~E(f312(f312(f21(f860(x72691,a845)),x72693),f312(f312(f289(x72691),x72692),f189(f860(x72691,a845)))),f189(f860(x72691,a845)))
% 173.53/173.43 [7270]~P103(x72701)+~P22(f312(f70(x72701),x72703))+E(f13(x72701,f225(x72701),f312(f312(f289(x72701),x72702),x72703)),x72702)+~E(f312(f312(f21(f860(x72701,a845)),x72703),f312(f312(f289(x72701),x72702),f189(f860(x72701,a845)))),f189(f860(x72701,a845)))
% 173.53/173.43 [7286]~P112(x72861)+~P22(f312(f312(f228(x72861),x72862),x72863))+~P22(f312(f312(f228(x72861),f312(f88(x72861),x72862)),x72863))+P22(f312(f312(f228(x72861),f312(f84(x72861),x72862)),x72863))
% 173.53/173.43 [7288]~P83(x72881)+~P22(f312(f312(f227(x72881),x72882),x72883))+~P22(f312(f312(f227(x72881),f312(f88(x72881),x72882)),x72883))+P22(f312(f312(f227(x72881),f312(f84(x72881),x72882)),x72883))
% 173.53/173.43 [7355]~P122(x73551)+P22(f312(f312(f228(x73551),f2(x73551)),x73552))+~P22(f312(f312(f228(x73551),f2(x73551)),x73553))+~P22(f312(f312(f228(x73551),f2(x73551)),f312(f312(f90(x73551),x73553),x73552)))
% 173.53/173.43 [7356]~P122(x73561)+P22(f312(f312(f228(x73561),f2(x73561)),x73562))+~P22(f312(f312(f228(x73561),f2(x73561)),x73563))+~P22(f312(f312(f228(x73561),f2(x73561)),f312(f312(f90(x73561),x73562),x73563)))
% 173.53/173.43 [7658]E(x76581,x76582)+~P22(f312(f70(x76583),x76581))+~P22(f312(f312(f227(a852),f312(f53(x76583),x76581)),f312(f53(x76583),x76582)))+~P22(f312(f312(f227(f860(x76583,a845)),x76582),x76581))
% 173.53/173.43 [7943]E(f312(x79431,f841(x79432,x79431,x79433)),x79432)+~P22(f312(f312(f227(a1),x79432),f312(x79431,x79433)))+P22(f312(f312(f228(a852),f842(x79432,x79431,x79433)),x79433))+~P22(f312(f312(f227(a1),f312(x79431,f2(a852))),x79432))
% 173.53/173.43 [7944]E(f312(x79441,f322(x79442,x79441,x79443)),x79442)+~P22(f312(f312(f227(a1),x79442),f312(x79441,x79443)))+P22(f312(f312(f228(a852),f843(x79442,x79441,x79443)),x79443))+~P22(f312(f312(f227(a1),f312(x79441,f2(a852))),x79442))
% 173.53/173.43 [8051]~P22(f312(f70(x80511),x80513))+~P22(f312(f312(f228(a852),f312(f53(x80511),x80512)),f312(f53(x80511),x80513)))+~P22(f312(f312(f227(f860(x80511,a845)),x80512),x80513))+P22(f312(f312(f228(f860(x80511,a845)),x80512),x80513))
% 173.53/173.43 [8080]E(f312(f312(f21(a1),f465(x80803,x80801,x80802)),f466(x80803,x80801,x80802)),x80801)+E(f312(f312(f89(a1),x80801),x80802),x80801)+~P22(f312(f312(f228(a1),f2(a1)),x80802))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x80801),f87(a1))),x80803))
% 173.53/173.43 [8081]E(f312(f312(f89(a1),f457(x80813,x80811,x80812)),f458(x80813,x80811,x80812)),x80811)+E(f312(f312(f21(a1),x80811),x80812),x80811)+~P22(f312(f312(f228(a1),f2(a1)),x80812))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x80811),f87(a1))),x80813))
% 173.53/173.43 [8135]~P22(f312(f312(f227(a852),x81353),x81351))+P22(f312(f312(f228(a852),x81351),x81352))+~P22(f312(f312(f227(a852),x81353),x81352))+~P22(f312(f312(f228(a852),f312(f312(f21(a852),x81351),x81353)),f312(f312(f21(a852),x81352),x81353)))
% 173.53/173.43 [8136]~P22(f312(f312(f227(a852),x81363),x81361))+P22(f312(f312(f227(a852),x81361),x81362))+~P22(f312(f312(f227(a852),x81363),x81362))+~P22(f312(f312(f227(a852),f312(f312(f21(a852),x81361),x81363)),f312(f312(f21(a852),x81362),x81363)))
% 173.53/173.43 [8151]~P103(x81512)+E(x81511,f127(x81512))+~P33(x81512,f312(f165(x81512),x81511))+E(f312(f138(x81512,x81512,f312(f7(x81512,x81512,x81512),f226(x81512)),x81513),f312(f165(x81512),x81511)),f312(f312(f226(x81512),f312(f312(f161(x81512),x81511),f2(a852))),x81513))
% 173.53/173.43 [8197]~P31(x81971)+~P49(x81971,x81971,x81973)+P22(f312(f312(f227(x81971),x81972),f110(x81971,x81973)))+~P22(f312(f312(f227(x81971),x81972),f312(x81973,f312(f312(f124(x81971),x81972),f110(x81971,x81973)))))
% 173.53/173.43 [8217]E(f312(f312(f89(a1),x82171),x82172),x82171)+~P22(f312(f312(f228(a1),f2(a1)),x82172))+P22(f312(f312(f314(a1),f465(x82173,x82171,x82172)),x82173))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x82171),f87(a1))),x82173))
% 173.53/173.43 [8218]E(f312(f312(f21(a1),x82181),x82182),x82181)+~P22(f312(f312(f228(a1),f2(a1)),x82182))+P22(f312(f312(f314(a1),f457(x82183,x82181,x82182)),x82183))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x82181),f87(a1))),x82183))
% 173.53/173.43 [8296]~P22(f312(f312(f227(a1),x82961),f312(x82962,x82963)))+P22(f312(f312(f227(a852),f841(x82961,x82962,x82963)),x82963))+P22(f312(f312(f228(a852),f842(x82961,x82962,x82963)),x82963))+~P22(f312(f312(f227(a1),f312(x82962,f2(a852))),x82961))
% 173.53/173.43 [8297]~P22(f312(f312(f227(a1),x82971),f312(x82972,x82973)))+P22(f312(f312(f227(a852),f322(x82971,x82972,x82973)),x82973))+P22(f312(f312(f228(a852),f843(x82971,x82972,x82973)),x82973))+~P22(f312(f312(f227(a1),f312(x82972,f2(a852))),x82971))
% 173.53/173.43 [8381]E(f312(f312(f89(a1),x83811),x83812),x83811)+~P22(f312(f312(f228(a1),f2(a1)),x83812))+P22(f312(f312(f314(a1),f466(x83813,x83811,x83812)),f283(a1,f87(a1),x83812)))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x83811),f87(a1))),x83813))
% 173.53/173.43 [8382]E(f312(f312(f21(a1),x83821),x83822),x83821)+~P22(f312(f312(f228(a1),f2(a1)),x83822))+P22(f312(f312(f314(a1),f458(x83823,x83821,x83822)),f283(a1,f87(a1),x83822)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x83821),f87(a1))),x83823))
% 173.53/173.43 [8514]~P117(x85141)+~P22(f312(f312(f228(x85141),x85142),f87(x85141)))+~P22(f312(f312(f228(x85141),f2(x85141)),x85142))+P22(f312(f312(f228(x85141),f312(f312(f90(x85141),x85142),f312(f312(f240(x85141),x85142),x85143))),f312(f312(f240(x85141),x85142),x85143)))
% 173.53/173.43 [8592]~P22(f312(x85921,x85922))+P22(f312(x85921,f2(a852)))+~P22(f312(f312(f228(a852),x85922),x85923))+~P22(f312(x85921,f54(a852,f312(a126,f737(x85922,x85921,x85923)),x85923)))
% 173.53/173.43 [8730]E(f358(x87301,x87302,x87303),f2(a852))+P22(f312(f312(x87301,x87303),x87302))+P22(f312(f312(x87301,f358(x87301,x87302,x87303)),f54(a852,f357(x87301,x87302,x87303),f358(x87301,x87302,x87303))))+~P22(f312(f300(f859(a852,a852),a211),f312(f312(f239(a852,a852),x87303),x87302)))
% 173.53/173.43 [8768]~P19(x87681,x87681,x87682,x87683)+E(f312(f290(x87681,x87681,x87682),x87683),x87683)+~P22(f312(f70(x87681),x87683))+~P22(f312(f312(f227(f860(x87681,a845)),f312(f290(x87681,x87681,x87682),x87683)),x87683))
% 173.53/173.43 [8841]~P31(x88411)+~P49(x88411,x88411,x88413)+P22(f312(f312(f227(x88411),f312(f312(f124(x88411),x88412),f110(x88411,x88413))),f312(x88413,f312(f312(f124(x88411),x88412),f110(x88411,x88413)))))+~P22(f312(f312(f227(x88411),x88412),f312(x88413,f312(f312(f124(x88411),x88412),f110(x88411,x88413)))))
% 173.53/173.43 [9005]P22(f312(f312(x90051,x90052),x90053))+~P22(f312(f312(f228(a1),f356(x90051,x90053,x90052)),f2(a1)))+P22(f312(f312(x90051,f312(f88(a1),f355(x90051,x90053,x90052))),f312(f88(a1),f356(x90051,x90053,x90052))))+~P22(f312(f300(f859(a1,a1),a212),f312(f312(f239(a1,a1),x90052),x90053)))
% 173.53/173.43 [9194]P22(f312(f312(x91941,x91942),x91943))+P22(f312(f312(x91941,f312(f312(f89(a1),f616(x91941,x91943,x91942)),f87(a1))),f618(x91941,x91943,x91942)))+~P22(f312(f312(f227(a1),f616(x91941,x91943,x91942)),f618(x91941,x91943,x91942)))+~P22(f312(f300(f859(a1,a1),a178),f312(f312(f239(a1,a1),x91942),x91943)))
% 173.53/173.43 [9610]~P63(x96102)+~P63(x96101)+~P22(f312(f67(f859(x96101,x96102)),x96103))+P22(f312(f67(x96101),f312(f312(f8(f860(x96102,a845),a845,x96101),f67(x96102)),f312(f312(f8(f860(x96102,f859(x96101,x96102)),f860(x96102,a845),x96101),f312(f8(f859(x96101,x96102),a845,x96102),x96103)),f239(x96101,x96102)))))
% 173.53/173.43 [9611]~P63(x96112)+~P63(x96111)+~P22(f312(f66(f859(x96111,x96112)),x96113))+P22(f312(f66(x96111),f312(f312(f8(f860(x96112,a845),a845,x96111),f66(x96112)),f312(f312(f8(f860(x96112,f859(x96111,x96112)),f860(x96112,a845),x96111),f312(f8(f859(x96111,x96112),a845,x96112),x96113)),f239(x96111,x96112)))))
% 173.53/173.43 [9709]~P63(x97092)+~P63(x97091)+P22(f312(f67(f859(x97091,x97092)),x97093))+~P22(f312(f67(x97091),f312(f312(f8(f860(x97092,a845),a845,x97091),f67(x97092)),f312(f312(f8(f860(x97092,f859(x97091,x97092)),f860(x97092,a845),x97091),f312(f8(f859(x97091,x97092),a845,x97092),x97093)),f239(x97091,x97092)))))
% 173.53/173.43 [9710]~P63(x97102)+~P63(x97101)+P22(f312(f66(f859(x97101,x97102)),x97103))+~P22(f312(f66(x97101),f312(f312(f8(f860(x97102,a845),a845,x97101),f66(x97102)),f312(f312(f8(f860(x97102,f859(x97101,x97102)),f860(x97102,a845),x97101),f312(f8(f859(x97101,x97102),a845,x97102),x97103)),f239(x97101,x97102)))))
% 173.53/173.43 [9891]E(f312(x98911,f841(x98912,x98911,x98913)),x98912)+~P22(f312(f312(f227(a1),x98912),f312(x98911,x98913)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98911,f312(f312(f89(a852),f842(x98912,x98911,x98913)),f87(a852)))),f312(x98911,f842(x98912,x98911,x98913))))),f87(a1)))+~P22(f312(f312(f227(a1),f312(x98911,f2(a852))),x98912))
% 173.53/173.43 [9892]E(f312(x98921,f322(x98922,x98921,x98923)),x98922)+~P22(f312(f312(f227(a1),x98922),f312(x98921,x98923)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98921,f312(f312(f89(a852),f843(x98922,x98921,x98923)),f87(a852)))),f312(x98921,f843(x98922,x98921,x98923))))),f87(a1)))+~P22(f312(f312(f227(a1),f312(x98921,f2(a852))),x98922))
% 173.53/173.43 [9896]~P22(f312(f312(f227(a1),x98961),f312(x98962,x98963)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98962,f312(f312(f89(a852),f842(x98961,x98962,x98963)),f87(a852)))),f312(x98962,f842(x98961,x98962,x98963))))),f87(a1)))+P22(f312(f312(f227(a852),f841(x98961,x98962,x98963)),x98963))+~P22(f312(f312(f227(a1),f312(x98962,f2(a852))),x98961))
% 173.53/173.43 [9897]~P22(f312(f312(f227(a1),x98971),f312(x98972,x98973)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98972,f312(f312(f89(a852),f843(x98971,x98972,x98973)),f87(a852)))),f312(x98972,f843(x98971,x98972,x98973))))),f87(a1)))+P22(f312(f312(f227(a852),f322(x98971,x98972,x98973)),x98973))+~P22(f312(f312(f227(a1),f312(x98972,f2(a852))),x98971))
% 173.53/173.43 [9951]E(x99511,x99512)+~E(f312(f138(f853(x99513),f853(x99513),f129(x99513),f127(x99513)),x99511),f312(f138(f853(x99513),f853(x99513),f129(x99513),f127(x99513)),x99512))+~E(f312(f190(f853(f853(x99513))),x99511),f312(f190(f853(f853(x99513))),x99512))+~P22(f312(f312(f249(f853(x99513),f853(x99513),a845),f312(f312(f7(f853(x99513),f860(f853(x99513),a852),f860(f853(x99513),a845)),f312(f312(f8(f860(a852,a845),f860(f860(f853(x99513),a852),f860(f853(x99513),a845)),f853(x99513)),f8(a852,a845,f853(x99513))),f312(f312(f8(a852,f860(a852,a845),f853(x99513)),a309),f190(f853(x99513))))),f190(f853(x99513)))),f660(x99511,x99512,x99513)))
% 173.53/173.43 [9952]E(x99521,x99522)+~E(f312(f138(f853(x99523),f853(x99523),f129(x99523),f127(x99523)),x99521),f312(f138(f853(x99523),f853(x99523),f129(x99523),f127(x99523)),x99522))+~E(f312(f190(f853(f853(x99523))),x99521),f312(f190(f853(f853(x99523))),x99522))+~P22(f312(f312(f249(f853(x99523),f853(x99523),a845),f312(f312(f7(f853(x99523),f860(f853(x99523),a852),f860(f853(x99523),a845)),f312(f312(f8(f860(a852,a845),f860(f860(f853(x99523),a852),f860(f853(x99523),a845)),f853(x99523)),f8(a852,a845,f853(x99523))),f312(f312(f8(a852,f860(a852,a845),f853(x99523)),a309),f190(f853(x99523))))),f190(f853(x99523)))),f661(x99522,x99521,x99523)))
% 173.53/173.43 [6695]~E(f87(a852),f2(a852))+~P22(f312(f70(x66951),x66953))+~P22(f312(f70(x66951),x66952))+E(f312(f312(f89(a852),f312(f53(x66951),x66952)),f312(f53(x66951),x66953)),f312(f53(x66951),f312(f312(f124(f860(x66951,a845)),x66952),x66953)))
% 173.53/173.43 [7109]~P99(x71091)+~P22(f312(f70(x71091),x71092))+~P22(f312(f312(f314(x71091),x71093),x71092))+P22(f312(f312(f227(x71091),f312(f72(x71091,f115(x71091)),x71092)),x71093))
% 173.53/173.43 [7110]~P103(x71101)+~P22(f312(f70(x71101),x71102))+~P22(f312(f312(f314(x71101),x71103),x71102))+P22(f312(f312(f227(x71101),f312(f72(x71101,f225(x71101)),x71102)),x71103))
% 173.53/173.43 [7350]~P22(f312(f70(x73501),x73503))+~P22(f312(f70(x73501),x73502))+~E(f312(f312(f115(f860(x73501,a845)),x73502),x73503),f189(f860(x73501,a845)))+E(f312(f312(f89(a852),f312(f53(x73501),x73502)),f312(f53(x73501),x73503)),f312(f53(x73501),f312(f312(f124(f860(x73501,a845)),x73502),x73503)))
% 173.53/173.43 [8140]~P41(x81401,x81403)+~P41(x81401,x81402)+~E(f312(f312(f115(f860(x81401,a845)),f312(f238(x81401,x81401),x81402)),f312(f236(x81401,x81401),x81403)),f189(f860(x81401,a845)))+P41(x81401,f312(f312(f124(f860(f859(x81401,x81401),a845)),x81402),x81403))
% 173.53/173.43 [8222]E(x82221,f312(f47(a852,x82222),x82223))+~P22(f312(f312(f228(a852),f2(a852)),x82223))+~P22(f312(f312(f228(a852),x82222),f312(f312(f90(a852),x82223),f312(a126,x82221))))+~P22(f312(f312(f227(a852),f312(f312(f90(a852),x82223),x82221)),x82222))
% 173.53/173.43 [8379]~P22(f312(f70(x83791),x83792))+~P22(f312(f70(x83791),x83793))+E(f312(f312(f89(a852),f312(f53(x83791),x83792)),f312(f53(x83791),x83793)),f312(f53(x83791),f312(f312(f124(f860(x83791,a845)),x83792),x83793)))+P22(f312(f312(f314(x83791),f393(x83793,x83792,x83791)),f312(f312(f115(f860(x83791,a845)),x83792),x83793)))
% 173.53/173.43 [8742]~P118(x87422)+~E(x87421,f2(x87422))+~E(x87423,f2(x87422))+~P22(f312(f312(f228(x87422),f2(x87422)),f312(f312(f89(x87422),f312(f312(f90(x87422),x87423),x87423)),f312(f312(f90(x87422),x87421),x87421))))
% 173.53/173.43 [9270]~P41(x92701,x92703)+~P41(x92701,x92702)+P41(x92701,f312(f312(f124(f860(f859(x92701,x92701),a845)),x92702),x92703))+~P22(f312(f312(f227(f860(f859(x92701,x92701),a845)),f312(f312(f267(x92701,x92701,x92701),x92702),x92703)),x92702))
% 173.53/173.43 [9398]~P22(f312(x93981,x93983))+~P22(f312(f70(x93982),x93983))+P22(f312(x93981,f189(f860(x93982,a845))))+~P22(f312(x93981,f312(f312(f21(f860(x93982,a845)),f431(x93981,x93983,x93982)),f312(f312(f289(x93982),f432(x93981,x93983,x93982)),f189(f860(x93982,a845))))))
% 173.53/173.43 [9643]~P63(x96431)+~P63(x96432)+P8(x96431,f312(f312(f8(f860(x96432,x96431),a845,f853(x96431)),x96433),f312(f312(f8(f860(x96432,f856(x96431)),f860(x96432,x96431),f853(x96431)),f82(f856(x96431),x96431,x96432,f223(x96431))),f312(f312(f8(f853(f859(x96432,x96431)),f860(x96432,f856(x96431)),f853(x96431)),f173(x96432,x96431)),f312(f177(x96432,x96431),f64(x96432))))),f312(f190(f853(x96432)),f64(x96432)))+~P22(f312(f67(f860(x96432,x96431)),x96433))
% 173.53/173.43 [9644]~P63(x96441)+~P63(x96442)+P7(x96441,f312(f312(f8(f860(x96442,x96441),a845,f853(x96441)),x96443),f312(f312(f8(f860(x96442,f856(x96441)),f860(x96442,x96441),f853(x96441)),f82(f856(x96441),x96441,x96442,f223(x96441))),f312(f312(f8(f853(f859(x96442,x96441)),f860(x96442,f856(x96441)),f853(x96441)),f173(x96442,x96441)),f312(f177(x96442,x96441),f64(x96442))))),f312(f190(f853(x96442)),f64(x96442)))+~P22(f312(f66(f860(x96442,x96441)),x96443))
% 173.53/173.43 [9736]~P63(x97361)+~P63(x97362)+~P8(x97362,f312(f312(f8(f860(x97361,x97362),a845,f853(x97362)),x97363),f312(f312(f8(f860(x97361,f856(x97362)),f860(x97361,x97362),f853(x97362)),f82(f856(x97362),x97362,x97361,f223(x97362))),f312(f312(f8(f853(f859(x97361,x97362)),f860(x97361,f856(x97362)),f853(x97362)),f173(x97361,x97362)),f312(f177(x97361,x97362),f64(x97361))))),f312(f190(f853(x97361)),f64(x97361)))+P22(f312(f67(f860(x97361,x97362)),x97363))
% 173.53/173.43 [9737]~P63(x97371)+~P63(x97372)+~P7(x97372,f312(f312(f8(f860(x97371,x97372),a845,f853(x97372)),x97373),f312(f312(f8(f860(x97371,f856(x97372)),f860(x97371,x97372),f853(x97372)),f82(f856(x97372),x97372,x97371,f223(x97372))),f312(f312(f8(f853(f859(x97371,x97372)),f860(x97371,f856(x97372)),f853(x97372)),f173(x97371,x97372)),f312(f177(x97371,x97372),f64(x97371))))),f312(f190(f853(x97371)),f64(x97371)))+P22(f312(f66(f860(x97371,x97372)),x97373))
% 173.53/173.43 [8546]~P22(f312(f312(f228(a1),f2(a1)),x85463))+P22(f312(f312(f227(a1),f2(a1)),x85461))+~P22(f312(f312(f228(a1),x85462),x85463))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x85463),x85461)),x85462)))
% 173.53/173.43 [8566]~P87(x85661)+~P22(f312(f70(x85661),x85662))+E(f312(f312(f21(f860(x85661,a845)),x85662),f312(f312(f289(x85661),x85663),f189(f860(x85661,a845)))),f189(f860(x85661,a845)))+E(f312(f312(f115(x85661),x85663),f11(x85661,f312(f312(f21(f860(x85661,a845)),x85662),f312(f312(f289(x85661),x85663),f189(f860(x85661,a845)))))),f11(x85661,f312(f312(f289(x85661),x85663),x85662)))
% 173.53/173.43 [8567]~P87(x85671)+~P22(f312(f70(x85671),x85672))+E(f312(f312(f21(f860(x85671,a845)),x85672),f312(f312(f289(x85671),x85673),f189(f860(x85671,a845)))),f189(f860(x85671,a845)))+E(f312(f312(f124(x85671),x85673),f10(x85671,f312(f312(f21(f860(x85671,a845)),x85672),f312(f312(f289(x85671),x85673),f189(f860(x85671,a845)))))),f10(x85671,f312(f312(f289(x85671),x85673),x85672)))
% 173.53/173.43 [8568]~P103(x85681)+~P22(f312(f70(x85681),x85682))+E(f312(f312(f21(f860(x85681,a845)),x85682),f312(f312(f289(x85681),x85683),f189(f860(x85681,a845)))),f189(f860(x85681,a845)))+E(f312(f312(f226(x85681),x85683),f14(x85681,f312(f312(f21(f860(x85681,a845)),x85682),f312(f312(f289(x85681),x85683),f189(f860(x85681,a845)))))),f14(x85681,f312(f312(f289(x85681),x85683),x85682)))
% 173.53/173.43 [8569]~P103(x85691)+~P22(f312(f70(x85691),x85692))+E(f312(f312(f21(f860(x85691,a845)),x85692),f312(f312(f289(x85691),x85693),f189(f860(x85691,a845)))),f189(f860(x85691,a845)))+E(f312(f312(f225(x85691),x85693),f15(x85691,f312(f312(f21(f860(x85691,a845)),x85692),f312(f312(f289(x85691),x85693),f189(f860(x85691,a845)))))),f15(x85691,f312(f312(f289(x85691),x85693),x85692)))
% 173.53/173.43 [8634]~P103(x86341)+~P22(f312(f70(x86341),x86342))+E(f312(f312(f21(f860(x86341,a845)),x86342),f312(f312(f289(x86341),x86343),f189(f860(x86341,a845)))),f189(f860(x86341,a845)))+E(f312(f312(f226(x86341),x86343),f12(x86341,f226(x86341),f312(f312(f21(f860(x86341,a845)),x86342),f312(f312(f289(x86341),x86343),f189(f860(x86341,a845)))))),f12(x86341,f226(x86341),f312(f312(f289(x86341),x86343),x86342)))
% 173.53/173.43 [8635]~P103(x86351)+~P22(f312(f70(x86351),x86352))+E(f312(f312(f21(f860(x86351,a845)),x86352),f312(f312(f289(x86351),x86353),f189(f860(x86351,a845)))),f189(f860(x86351,a845)))+E(f312(f312(f225(x86351),x86353),f13(x86351,f225(x86351),f312(f312(f21(f860(x86351,a845)),x86352),f312(f312(f289(x86351),x86353),f189(f860(x86351,a845)))))),f13(x86351,f225(x86351),f312(f312(f289(x86351),x86353),x86352)))
% 173.53/173.43 [9009]~P31(x90091)+~P49(x90091,x90091,x90092)+P22(f312(f312(f227(x90091),f109(x90091,x90092)),x90093))+~P22(f312(f312(f227(x90091),f312(x90092,f312(f312(f115(x90091),f109(x90091,x90092)),x90093))),x90093))
% 173.53/173.43 [9213]E(x92131,x92132)+~E(f312(f138(f853(x92133),f853(x92133),f129(x92133),f127(x92133)),x92131),f312(f138(f853(x92133),f853(x92133),f129(x92133),f127(x92133)),x92132))+~E(f312(f190(f853(f853(x92133))),x92131),f312(f190(f853(f853(x92133))),x92132))+P22(f312(f312(f314(f859(f853(x92133),f853(x92133))),f660(x92131,x92132,x92133)),f312(f168(f859(f853(x92133),f853(x92133))),f312(f312(f177(f853(x92133),f853(x92133)),x92132),x92131))))
% 173.53/173.43 [9214]E(x92141,x92142)+~E(f312(f138(f853(x92143),f853(x92143),f129(x92143),f127(x92143)),x92141),f312(f138(f853(x92143),f853(x92143),f129(x92143),f127(x92143)),x92142))+~E(f312(f190(f853(f853(x92143))),x92141),f312(f190(f853(f853(x92143))),x92142))+P22(f312(f312(f314(f859(f853(x92143),f853(x92143))),f661(x92142,x92141,x92143)),f312(f168(f859(f853(x92143),f853(x92143))),f312(f312(f177(f853(x92143),f853(x92143)),x92141),x92142))))
% 173.53/173.43 [10038]~P74(x100382)+E(x100381,f189(f860(x100382,a845)))+~P22(f312(f70(x100382),x100381))+E(f14(x100382,f312(f233(x100382),f312(f312(f8(f860(x100382,a845),a845,x100382),f96(x100382)),f312(f312(f7(x100382,f860(x100382,a845),f860(x100382,a845)),f312(f312(f8(f860(x100382,f860(a845,a845)),f860(f860(x100382,a845),f860(x100382,a845)),x100382),f18(x100382,a845,a845)),f312(f312(f8(f860(x100382,a845),f860(x100382,f860(a845,a845)),x100382),f312(f8(a845,f860(a845,a845),x100382),a310)),f312(f312(f7(x100382,f860(x100382,x100382),f860(x100382,a845)),f312(f312(f8(f860(x100382,a845),f860(f860(x100382,x100382),f860(x100382,a845)),x100382),f8(x100382,a845,x100382)),a309)),f312(f89(x100382),x100383))))),f312(f312(f7(x100382,f860(x100382,a845),a845),f314(x100382)),x100381))))),f312(f312(f89(x100382),x100383),f14(x100382,x100381)))
% 173.53/173.43 [10039]~P74(x100392)+E(x100391,f189(f860(x100392,a845)))+~P22(f312(f70(x100392),x100391))+E(f15(x100392,f312(f233(x100392),f312(f312(f8(f860(x100392,a845),a845,x100392),f96(x100392)),f312(f312(f7(x100392,f860(x100392,a845),f860(x100392,a845)),f312(f312(f8(f860(x100392,f860(a845,a845)),f860(f860(x100392,a845),f860(x100392,a845)),x100392),f18(x100392,a845,a845)),f312(f312(f8(f860(x100392,a845),f860(x100392,f860(a845,a845)),x100392),f312(f8(a845,f860(a845,a845),x100392),a310)),f312(f312(f7(x100392,f860(x100392,x100392),f860(x100392,a845)),f312(f312(f8(f860(x100392,a845),f860(f860(x100392,x100392),f860(x100392,a845)),x100392),f8(x100392,a845,x100392)),a309)),f312(f89(x100392),x100393))))),f312(f312(f7(x100392,f860(x100392,a845),a845),f314(x100392)),x100391))))),f312(f312(f89(x100392),x100393),f15(x100392,x100391)))
% 173.53/173.43 [10040]~P96(x100402)+E(x100401,f189(f860(x100402,a845)))+~P22(f312(f70(x100402),x100401))+E(f11(x100402,f312(f233(x100402),f312(f312(f8(f860(x100402,a845),a845,x100402),f96(x100402)),f312(f312(f7(x100402,f860(x100402,a845),f860(x100402,a845)),f312(f312(f8(f860(x100402,f860(a845,a845)),f860(f860(x100402,a845),f860(x100402,a845)),x100402),f18(x100402,a845,a845)),f312(f312(f8(f860(x100402,a845),f860(x100402,f860(a845,a845)),x100402),f312(f8(a845,f860(a845,a845),x100402),a310)),f312(f312(f7(x100402,f860(x100402,x100402),f860(x100402,a845)),f312(f312(f8(f860(x100402,a845),f860(f860(x100402,x100402),f860(x100402,a845)),x100402),f8(x100402,a845,x100402)),a309)),f312(f124(x100402),x100403))))),f312(f312(f7(x100402,f860(x100402,a845),a845),f314(x100402)),x100401))))),f312(f312(f124(x100402),x100403),f11(x100402,x100401)))
% 173.53/173.43 [10041]~P96(x100412)+E(x100411,f189(f860(x100412,a845)))+~P22(f312(f70(x100412),x100411))+E(f10(x100412,f312(f233(x100412),f312(f312(f8(f860(x100412,a845),a845,x100412),f96(x100412)),f312(f312(f7(x100412,f860(x100412,a845),f860(x100412,a845)),f312(f312(f8(f860(x100412,f860(a845,a845)),f860(f860(x100412,a845),f860(x100412,a845)),x100412),f18(x100412,a845,a845)),f312(f312(f8(f860(x100412,a845),f860(x100412,f860(a845,a845)),x100412),f312(f8(a845,f860(a845,a845),x100412),a310)),f312(f312(f7(x100412,f860(x100412,x100412),f860(x100412,a845)),f312(f312(f8(f860(x100412,a845),f860(f860(x100412,x100412),f860(x100412,a845)),x100412),f8(x100412,a845,x100412)),a309)),f312(f115(x100412),x100413))))),f312(f312(f7(x100412,f860(x100412,a845),a845),f314(x100412)),x100411))))),f312(f312(f115(x100412),x100413),f10(x100412,x100411)))
% 173.53/173.43 [10042]~P103(x100422)+E(x100421,f189(f860(x100422,a845)))+~P22(f312(f70(x100422),x100421))+E(f12(x100422,f226(x100422),f312(f233(x100422),f312(f312(f8(f860(x100422,a845),a845,x100422),f96(x100422)),f312(f312(f7(x100422,f860(x100422,a845),f860(x100422,a845)),f312(f312(f8(f860(x100422,f860(a845,a845)),f860(f860(x100422,a845),f860(x100422,a845)),x100422),f18(x100422,a845,a845)),f312(f312(f8(f860(x100422,a845),f860(x100422,f860(a845,a845)),x100422),f312(f8(a845,f860(a845,a845),x100422),a310)),f312(f312(f7(x100422,f860(x100422,x100422),f860(x100422,a845)),f312(f312(f8(f860(x100422,a845),f860(f860(x100422,x100422),f860(x100422,a845)),x100422),f8(x100422,a845,x100422)),a309)),f312(f225(x100422),x100423))))),f312(f312(f7(x100422,f860(x100422,a845),a845),f314(x100422)),x100421))))),f312(f312(f225(x100422),x100423),f12(x100422,f226(x100422),x100421)))
% 173.53/173.43 [10043]~P103(x100432)+E(x100431,f189(f860(x100432,a845)))+~P22(f312(f70(x100432),x100431))+E(f13(x100432,f225(x100432),f312(f233(x100432),f312(f312(f8(f860(x100432,a845),a845,x100432),f96(x100432)),f312(f312(f7(x100432,f860(x100432,a845),f860(x100432,a845)),f312(f312(f8(f860(x100432,f860(a845,a845)),f860(f860(x100432,a845),f860(x100432,a845)),x100432),f18(x100432,a845,a845)),f312(f312(f8(f860(x100432,a845),f860(x100432,f860(a845,a845)),x100432),f312(f8(a845,f860(a845,a845),x100432),a310)),f312(f312(f7(x100432,f860(x100432,x100432),f860(x100432,a845)),f312(f312(f8(f860(x100432,a845),f860(f860(x100432,x100432),f860(x100432,a845)),x100432),f8(x100432,a845,x100432)),a309)),f312(f226(x100432),x100433))))),f312(f312(f7(x100432,f860(x100432,a845),a845),f314(x100432)),x100431))))),f312(f312(f226(x100432),x100433),f13(x100432,f225(x100432),x100431)))
% 173.53/173.43 [9788]~P112(x97881)+~E(x97883,f2(x97881))+~E(x97882,f2(x97881))+E(f312(f312(f89(x97881),f312(f312(f240(x97881),x97882),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x97881),x97883),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f2(x97881))
% 173.53/173.43 [9936]~P117(x99361)+~P22(f312(f312(f227(x99361),f2(x99361)),x99363))+P22(f312(f312(f227(x99361),x99362),x99363))+~P22(f312(f312(f227(x99361),f312(f312(f240(x99361),x99362),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99361),x99363),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))))
% 173.53/173.43 [9981]~P112(x99812)+~E(x99811,f2(x99812))+~E(x99813,f2(x99812))+~P22(f312(f312(f228(x99812),f2(x99812)),f312(f312(f89(x99812),f312(f312(f240(x99812),x99813),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))),f312(f312(f240(x99812),x99811),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))))
% 173.53/173.43 [9176]E(x91761,x91762)+~E(f604(x91761,x91762,x91764,x91763),f609(x91761,x91762,x91764,x91763))+P22(f312(f312(f314(f859(f853(x91763),f853(x91763))),f312(f312(f239(f853(x91763),f853(x91763)),x91762),x91761)),f143(x91763,x91764)))+P22(f312(f312(f314(f859(f853(x91763),f853(x91763))),f312(f312(f239(f853(x91763),f853(x91763)),x91761),x91762)),f143(x91763,x91764)))
% 173.53/173.43 [4787]~P64(x47872)+~E(x47874,f2(x47872))+~E(x47871,f2(x47872))+E(x47871,f312(f312(f268(x47872),x47873),x47874))
% 173.53/173.43 [4788]~P64(x47881)+~E(x47883,f2(x47881))+~E(x47884,f2(x47881))+E(f312(f312(f268(x47881),x47882),x47883),x47884)
% 173.53/173.43 [4900]~P64(x49002)+E(x49001,f2(x49002))+~E(x49003,f2(x49002))+~E(x49001,f312(f312(f268(x49002),x49004),x49003))
% 173.53/173.43 [4901]~P64(x49012)+E(x49011,f2(x49012))+~E(x49013,f2(x49012))+~E(f312(f312(f268(x49012),x49014),x49013),x49011)
% 173.53/173.43 [5074]~P114(x50742)+E(x50741,f2(x50742))+~E(f312(f312(f268(x50742),x50743),x50741),x50744)+E(x50743,f312(f312(f90(x50742),x50744),x50741))
% 173.53/173.43 [5076]~P114(x50762)+E(x50761,f2(x50762))+~E(f312(f312(f90(x50762),x50763),x50761),x50764)+E(x50763,f312(f312(f268(x50762),x50764),x50761))
% 173.53/173.43 [5077]~P64(x50772)+E(x50771,f2(x50772))+~E(f312(f312(f268(x50772),x50773),x50771),x50774)+E(x50773,f312(f312(f90(x50772),x50774),x50771))
% 173.53/173.43 [5078]~P64(x50782)+E(x50781,f2(x50782))+~E(f312(f312(f90(x50782),x50783),x50781),x50784)+E(x50783,f312(f312(f268(x50782),x50784),x50781))
% 173.53/173.43 [5079]~P114(x50792)+E(x50791,f2(x50792))+~E(x50793,f312(f312(f268(x50792),x50794),x50791))+E(f312(f312(f90(x50792),x50793),x50791),x50794)
% 173.53/173.43 [5081]~P114(x50812)+E(x50811,f2(x50812))+~E(x50813,f312(f312(f90(x50812),x50814),x50811))+E(f312(f312(f268(x50812),x50813),x50811),x50814)
% 173.53/173.43 [5082]~P64(x50822)+E(x50821,f2(x50822))+~E(x50823,f312(f312(f268(x50822),x50824),x50821))+E(f312(f312(f90(x50822),x50823),x50821),x50824)
% 173.53/173.43 [5083]~P64(x50832)+E(x50831,f2(x50832))+~E(x50833,f312(f312(f90(x50832),x50834),x50831))+E(f312(f312(f268(x50832),x50833),x50831),x50834)
% 173.53/173.43 [5116]~P64(x51162)+~E(x51161,f2(x51162))+~E(f312(f312(f90(x51162),x51161),x51164),x51163)+E(x51161,f312(f312(f268(x51162),x51163),x51164))
% 173.53/173.43 [5117]~P64(x51171)+~E(x51174,f2(x51171))+~E(x51172,f312(f312(f90(x51171),x51174),x51173))+E(f312(f312(f268(x51171),x51172),x51173),x51174)
% 173.53/173.43 [5188]~E(x51883,x51884)+~E(x51882,x51883)+~P105(x51881)+E(f283(x51881,x51882,x51883),f312(f312(f289(x51881),x51884),f189(f860(x51881,a845))))
% 173.53/173.43 [5386]~E(f128(x53862,x53861),x53863)+~E(f140(x53862,x53861),x53864)+E(x53861,f127(x53862))+E(f312(f312(f129(x53862),x53863),f312(f312(f147(x53862),x53864),f127(x53862))),x53861)
% 173.53/173.43 [5991]~P117(x59913)+E(x59911,x59912)+~E(f312(f312(f240(x59913),x59914),x59911),f312(f312(f240(x59913),x59914),x59912))+~P22(f312(f312(f228(x59913),f87(x59913)),x59914))
% 173.53/173.43 [5992]E(x59921,x59922)+~E(f312(f312(f289(x59923),x59924),x59921),f312(f312(f289(x59923),x59924),x59922))+P22(f312(f312(f314(x59923),x59924),x59922))+P22(f312(f312(f314(x59923),x59924),x59921))
% 173.53/173.43 [6028]E(f312(x60281,x60282),f2(a852))+~E(f312(f312(f6(x60283,a852),x60281),x60284),f2(a852))+~P22(f312(f70(x60283),x60284))+~P22(f312(f312(f314(x60283),x60282),x60284))
% 173.53/173.43 [6029]E(f312(x60291,x60292),f87(a852))+~E(f312(f312(f9(x60293,a852),x60291),x60294),f87(a852))+~P22(f312(f70(x60293),x60294))+~P22(f312(f312(f314(x60293),x60292),x60294))
% 173.53/173.43 [6244]~P105(x62441)+~P22(f312(f312(f228(x62441),x62444),x62443))+P22(f312(f312(f228(x62441),x62442),x62443))+~P22(f312(f312(f228(x62441),x62442),x62444))
% 173.53/173.43 [6245]~P105(x62451)+~P22(f312(f312(f227(x62451),x62454),x62453))+P22(f312(f312(f228(x62451),x62452),x62453))+~P22(f312(f312(f228(x62451),x62452),x62454))
% 173.53/173.43 [6246]~P105(x62461)+~P22(f312(f312(f227(x62461),x62462),x62464))+P22(f312(f312(f228(x62461),x62462),x62463))+~P22(f312(f312(f228(x62461),x62464),x62463))
% 173.53/173.43 [6247]~P102(x62471)+~P22(f312(f312(f228(x62471),x62472),x62474))+P22(f312(f312(f228(x62471),x62472),x62473))+~P22(f312(f312(f228(x62471),x62474),x62473))
% 173.53/173.43 [6248]~P102(x62481)+~P22(f312(f312(f227(x62481),x62482),x62484))+P22(f312(f312(f228(x62481),x62482),x62483))+~P22(f312(f312(f228(x62481),x62484),x62483))
% 173.53/173.43 [6249]~P102(x62491)+~P22(f312(f312(f227(x62491),x62494),x62493))+P22(f312(f312(f228(x62491),x62492),x62493))+~P22(f312(f312(f228(x62491),x62492),x62494))
% 173.53/173.43 [6250]~P105(x62501)+~P22(f312(f312(f227(x62501),x62504),x62503))+P22(f312(f312(f227(x62501),x62502),x62503))+~P22(f312(f312(f227(x62501),x62502),x62504))
% 173.53/173.43 [6251]~P102(x62511)+~P22(f312(f312(f227(x62511),x62512),x62514))+P22(f312(f312(f227(x62511),x62512),x62513))+~P22(f312(f312(f227(x62511),x62514),x62513))
% 173.53/173.43 [6474]~P31(x64741)+~P22(f312(f312(f227(x64741),x64742),f49(x64741,x64744)))+P22(f312(f312(f227(x64741),x64742),x64743))+~P22(f312(f312(f314(x64741),x64743),x64744))
% 173.53/173.43 [6617]~P103(x66171)+~P33(x66171,f312(f312(f147(x66171),x66172),x66174))+~P22(f312(f312(f314(x66171),x66173),f312(f168(x66171),x66174)))+P22(f312(f312(f227(x66171),x66172),x66173))
% 173.53/173.43 [6704]~P31(x67041)+~P22(f312(f312(f227(x67041),f48(x67041,x67044)),x67043))+P22(f312(f312(f227(x67041),x67042),x67043))+~P22(f312(f312(f314(x67041),x67042),x67044))
% 173.53/173.43 [7112]~P103(x71121)+E(f312(f312(f124(f860(x71121,a845)),f312(f282(x71121,x71122),x71123)),f312(f282(x71121,x71123),x71124)),f312(f282(x71121,x71122),x71124))+~P22(f312(f312(f227(x71121),x71123),x71124))+~P22(f312(f312(f227(x71121),x71122),x71123))
% 173.53/173.43 [7213]~P103(x72131)+E(f312(f312(f124(f860(x72131,a845)),f312(f282(x72131,x72132),x72133)),f283(x72131,x72133,x72134)),f283(x72131,x72132,x72134))+~P22(f312(f312(f227(x72131),x72133),x72134))+~P22(f312(f312(f227(x72131),x72132),x72133))
% 173.53/173.43 [7278]~P103(x72781)+E(f312(f312(f124(f860(x72781,a845)),f285(x72781,x72782,x72783)),f312(f282(x72781,x72783),x72784)),f285(x72781,x72782,x72784))+~P22(f312(f312(f228(x72781),x72782),x72783))+~P22(f312(f312(f227(x72781),x72783),x72784))
% 173.53/173.43 [7300]~P103(x73001)+E(f312(f312(f124(f860(x73001,a845)),f283(x73001,x73002,x73003)),f285(x73001,x73003,x73004)),f312(f282(x73001,x73002),x73004))+~P22(f312(f312(f228(x73001),x73003),x73004))+~P22(f312(f312(f227(x73001),x73002),x73003))
% 173.53/173.43 [7330]~P103(x73301)+E(f312(f312(f124(f860(x73301,a845)),f285(x73301,x73302,x73303)),f283(x73301,x73303,x73304)),f284(x73301,x73302,x73304))+~P22(f312(f312(f228(x73301),x73302),x73303))+~P22(f312(f312(f227(x73301),x73303),x73304))
% 173.53/173.43 [7331]~P103(x73311)+E(f312(f312(f124(f860(x73311,a845)),f284(x73311,x73312,x73313)),f285(x73311,x73313,x73314)),f285(x73311,x73312,x73314))+~P22(f312(f312(f228(x73311),x73313),x73314))+~P22(f312(f312(f227(x73311),x73312),x73313))
% 173.53/173.43 [7332]~P103(x73321)+E(f312(f312(f124(f860(x73321,a845)),f284(x73321,x73322,x73323)),f284(x73321,x73323,x73324)),f284(x73321,x73322,x73324))+~P22(f312(f312(f227(x73321),x73323),x73324))+~P22(f312(f312(f227(x73321),x73322),x73323))
% 173.53/173.43 [7333]~P103(x73331)+E(f312(f312(f124(f860(x73331,a845)),f283(x73331,x73332,x73333)),f284(x73331,x73333,x73334)),f283(x73331,x73332,x73334))+~P22(f312(f312(f227(x73331),x73333),x73334))+~P22(f312(f312(f227(x73331),x73332),x73333))
% 173.53/173.43 [8123]P19(x81231,x81232,f388(x81233,x81232,x81234,x81231),x81234)+~P22(f312(f70(x81232),x81233))+~P22(f312(f70(x81231),x81234))+~P22(f312(f312(f227(a852),f312(f53(x81231),x81234)),f312(f53(x81232),x81233)))
% 173.53/173.43 [8196]~P72(x81961)+~E(f312(x81963,f735(x81963,x81964,x81962,x81961)),f87(x81961))+E(f312(f312(f312(f74(x81961,x81962,f90(x81961)),x81963),f87(x81961)),x81964),f87(x81961))+~P22(f312(f70(x81962),x81964))
% 173.53/173.43 [8483]~P117(x84831)+~P22(f312(f312(f227(x84831),f2(x84831)),x84833))+P22(f312(f312(f227(x84831),x84832),x84833))+~P22(f312(f312(f227(x84831),f312(f312(f240(x84831),x84832),f312(a126,x84834))),f312(f312(f240(x84831),x84833),f312(a126,x84834))))
% 173.53/173.43 [8633]~P49(f860(x86334,a845),f860(x86334,a845),x86333)+P22(f312(x86331,x86332))+~P22(f312(x86331,f558(x86331,x86333,x86332,x86334)))+~P22(f312(f312(f314(x86334),x86332),f109(f860(x86334,a845),x86333)))
% 173.53/173.43 [8852]~P72(x88521)+E(f312(f312(f312(f74(x88521,x88522,f90(x88521)),x88523),f87(x88521)),x88524),f87(x88521))+~P22(f312(f70(x88522),x88524))+P22(f312(f312(f314(x88522),f735(x88523,x88524,x88522,x88521)),x88524))
% 173.53/173.43 [9338]~P22(f312(f312(f227(a1),x93384),f2(a1)))+P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x93381),f54(a1,x93382,x93383))),x93384)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x93383))+~P22(f312(f312(f228(a1),x93381),x93384))
% 173.53/173.43 [9777]~P22(f312(f70(x97771),x97772))+~P22(f312(f312(f314(x97771),x97774),x97772))+~P22(f312(f312(f314(x97771),x97773),x97772))+P22(f312(f312(f228(a852),f312(f53(x97771),f312(f312(f21(f860(x97771,a845)),f312(f312(f21(f860(x97771,a845)),x97772),f312(f312(f289(x97771),x97773),f189(f860(x97771,a845))))),f312(f312(f289(x97771),x97774),f189(f860(x97771,a845)))))),f312(f53(x97771),x97772)))
% 173.53/173.43 [6812]~P103(x68121)+~P22(f312(f312(f228(x68121),x68122),x68124))+~P22(f312(f312(f228(x68121),x68122),x68123))+P22(f312(f312(f228(x68121),x68122),f312(f312(f225(x68121),x68123),x68124)))
% 173.53/173.43 [6815]~P99(x68151)+~P22(f312(f312(f227(x68151),x68152),x68154))+~P22(f312(f312(f227(x68151),x68152),x68153))+P22(f312(f312(f227(x68151),x68152),f312(f312(f115(x68151),x68153),x68154)))
% 173.53/173.43 [6818]~P103(x68181)+~P22(f312(f312(f227(x68181),x68182),x68184))+~P22(f312(f312(f227(x68181),x68182),x68183))+P22(f312(f312(f227(x68181),x68182),f312(f312(f225(x68181),x68183),x68184)))
% 173.53/173.43 [6840]~P65(x68402)+E(x68401,f2(x68402))+E(f312(f312(f268(x68402),f312(f312(f240(x68402),x68401),x68403)),f312(f312(f240(x68402),x68401),x68404)),f312(f312(f240(x68402),x68401),f312(f312(f21(a852),x68403),x68404)))+~P22(f312(f312(f227(a852),x68404),x68403))
% 173.53/173.43 [6886]~P103(x68861)+~P33(x68861,f312(f312(f147(x68861),x68863),x68864))+P33(x68861,f312(f312(f147(x68861),x68862),f312(f312(f147(x68861),x68863),x68864)))+~P22(f312(f312(f227(x68861),x68862),x68863))
% 173.53/173.43 [6930]~P117(x69301)+~P22(f312(f312(f228(x69301),f2(x69301)),x69303))+~P22(f312(f312(f228(x69301),x69302),x69304))+P22(f312(f312(f228(x69301),x69302),f312(f312(f89(x69301),x69303),x69304)))
% 173.53/173.43 [6931]~P84(x69311)+~P22(f312(f312(f227(x69311),f2(x69311)),x69313))+~P22(f312(f312(f228(x69311),x69312),x69314))+P22(f312(f312(f228(x69311),x69312),f312(f312(f89(x69311),x69313),x69314)))
% 173.53/173.43 [6932]~P84(x69321)+~P22(f312(f312(f227(x69321),x69322),x69324))+~P22(f312(f312(f228(x69321),f2(x69321)),x69323))+P22(f312(f312(f228(x69321),x69322),f312(f312(f89(x69321),x69323),x69324)))
% 173.53/173.43 [6933]~P84(x69331)+~P22(f312(f312(f227(x69331),f2(x69331)),x69334))+~P22(f312(f312(f227(x69331),x69332),x69333))+P22(f312(f312(f227(x69331),x69332),f312(f312(f89(x69331),x69333),x69334)))
% 173.53/173.43 [6934]~P84(x69341)+~P22(f312(f312(f227(x69341),f2(x69341)),x69343))+~P22(f312(f312(f227(x69341),x69342),x69344))+P22(f312(f312(f227(x69341),x69342),f312(f312(f89(x69341),x69343),x69344)))
% 173.53/173.43 [6971]~P103(x69711)+P22(f312(f312(f228(x69711),x69712),x69713))+P22(f312(f312(f228(x69711),x69712),x69714))+~P22(f312(f312(f228(x69711),x69712),f312(f312(f226(x69711),x69714),x69713)))
% 173.53/173.43 [6972]~P103(x69721)+P22(f312(f312(f227(x69721),x69722),x69723))+P22(f312(f312(f227(x69721),x69722),x69724))+~P22(f312(f312(f227(x69721),x69722),f312(f312(f226(x69721),x69724),x69723)))
% 173.53/173.43 [7253]~P105(x72532)+~P63(x72531)+~P22(f312(f312(f228(f860(x72531,x72532)),x72533),x72534))+P22(f312(f312(f227(f860(x72531,x72532)),x72533),x72534))
% 173.53/173.43 [7617]~P67(x76171)+~P22(f312(f312(f228(x76171),x76174),f2(x76171)))+~P22(f312(f312(f228(x76171),x76173),f312(f312(f268(x76171),x76172),x76174)))+P22(f312(f312(f228(x76171),x76172),f312(f312(f90(x76171),x76173),x76174)))
% 173.53/173.43 [7618]~P67(x76181)+~P22(f312(f312(f228(x76181),x76184),f2(x76181)))+~P22(f312(f312(f228(x76181),x76183),f312(f312(f90(x76181),x76182),x76184)))+P22(f312(f312(f228(x76181),x76182),f312(f312(f268(x76181),x76183),x76184)))
% 173.53/173.43 [7619]~P67(x76191)+~P22(f312(f312(f228(x76191),x76194),f2(x76191)))+~P22(f312(f312(f227(x76191),x76193),f312(f312(f268(x76191),x76192),x76194)))+P22(f312(f312(f227(x76191),x76192),f312(f312(f90(x76191),x76193),x76194)))
% 173.53/173.43 [7620]~P67(x76201)+~P22(f312(f312(f228(x76201),x76204),f2(x76201)))+~P22(f312(f312(f227(x76201),x76203),f312(f312(f90(x76201),x76202),x76204)))+P22(f312(f312(f227(x76201),x76202),f312(f312(f268(x76201),x76203),x76204)))
% 173.53/173.43 [7733]~P118(x77331)+~P22(f312(f312(f228(x77331),x77333),f2(x77331)))+~P22(f312(f312(f228(x77331),x77334),x77332))+P22(f312(f312(f228(x77331),f312(f312(f90(x77331),x77332),x77333)),f312(f312(f90(x77331),x77334),x77333)))
% 173.53/173.43 [7734]~P118(x77341)+~P22(f312(f312(f228(x77341),x77342),f2(x77341)))+~P22(f312(f312(f228(x77341),x77344),x77343))+P22(f312(f312(f228(x77341),f312(f312(f90(x77341),x77342),x77343)),f312(f312(f90(x77341),x77342),x77344)))
% 173.53/173.43 [7735]~P67(x77351)+~P22(f312(f312(f228(x77351),x77353),f2(x77351)))+~P22(f312(f312(f228(x77351),x77354),x77352))+P22(f312(f312(f228(x77351),f312(f312(f268(x77351),x77352),x77353)),f312(f312(f268(x77351),x77354),x77353)))
% 173.53/173.43 [7736]~P128(x77361)+~P22(f312(f312(f227(x77361),x77362),f2(x77361)))+~P22(f312(f312(f227(x77361),x77364),x77363))+P22(f312(f312(f227(x77361),f312(f312(f90(x77361),x77362),x77363)),f312(f312(f90(x77361),x77362),x77364)))
% 173.53/173.43 [7737]~P118(x77371)+~P22(f312(f312(f228(x77371),x77372),f2(x77371)))+~P22(f312(f312(f227(x77371),x77374),x77373))+P22(f312(f312(f227(x77371),f312(f312(f90(x77371),x77372),x77373)),f312(f312(f90(x77371),x77372),x77374)))
% 173.53/173.43 [7738]~P128(x77381)+~P22(f312(f312(f227(x77381),x77383),f2(x77381)))+~P22(f312(f312(f227(x77381),x77384),x77382))+P22(f312(f312(f227(x77381),f312(f312(f90(x77381),x77382),x77383)),f312(f312(f90(x77381),x77384),x77383)))
% 173.53/173.43 [7739]~P66(x77391)+~P22(f312(f312(f227(x77391),x77393),f2(x77391)))+~P22(f312(f312(f227(x77391),x77394),x77392))+P22(f312(f312(f227(x77391),f312(f312(f268(x77391),x77392),x77393)),f312(f312(f268(x77391),x77394),x77393)))
% 173.53/173.43 [7741]~P117(x77411)+~P22(f312(f312(f228(x77411),f87(x77411)),x77412))+~P22(f312(f312(f228(a852),x77413),x77414))+P22(f312(f312(f228(x77411),f312(f312(f240(x77411),x77412),x77413)),f312(f312(f240(x77411),x77412),x77414)))
% 173.53/173.43 [7742]~P117(x77421)+~P22(f312(f312(f228(x77421),f87(x77421)),x77422))+~P22(f312(f312(f227(a852),x77423),x77424))+P22(f312(f312(f227(x77421),f312(f312(f240(x77421),x77422),x77423)),f312(f312(f240(x77421),x77422),x77424)))
% 173.53/173.43 [7743]~P117(x77431)+~P22(f312(f312(f227(x77431),f87(x77431)),x77432))+~P22(f312(f312(f227(a852),x77433),x77434))+P22(f312(f312(f227(x77431),f312(f312(f240(x77431),x77432),x77433)),f312(f312(f240(x77431),x77432),x77434)))
% 173.53/173.43 [7768]P22(f312(f312(f228(a852),f2(a852)),f312(x77681,x77682)))+~P22(f312(f70(x77683),x77684))+~P22(f312(f312(f314(x77683),x77682),x77684))+~P22(f312(f312(f228(a852),f2(a852)),f312(f312(f9(x77683,a852),x77681),x77684)))
% 173.53/173.43 [7776]~P122(x77761)+~P22(f312(f312(f228(x77761),x77763),x77764))+~P22(f312(f312(f228(x77761),f2(x77761)),x77762))+P22(f312(f312(f228(x77761),f312(f312(f90(x77761),x77762),x77763)),f312(f312(f90(x77761),x77762),x77764)))
% 173.53/173.43 [7778]~P116(x77781)+~P22(f312(f312(f228(x77781),x77783),x77784))+~P22(f312(f312(f228(x77781),f2(x77781)),x77782))+P22(f312(f312(f228(x77781),f312(f312(f90(x77781),x77782),x77783)),f312(f312(f90(x77781),x77782),x77784)))
% 173.53/173.43 [7779]~P118(x77791)+~P22(f312(f312(f228(x77791),x77792),x77794))+~P22(f312(f312(f228(x77791),f2(x77791)),x77793))+P22(f312(f312(f228(x77791),f312(f312(f90(x77791),x77792),x77793)),f312(f312(f90(x77791),x77794),x77793)))
% 173.53/173.43 [7780]~P122(x77801)+~P22(f312(f312(f228(x77801),x77802),x77804))+~P22(f312(f312(f228(x77801),f2(x77801)),x77803))+P22(f312(f312(f228(x77801),f312(f312(f90(x77801),x77802),x77803)),f312(f312(f90(x77801),x77804),x77803)))
% 173.53/173.43 [7781]~P118(x77811)+~P22(f312(f312(f228(x77811),x77813),x77814))+~P22(f312(f312(f228(x77811),f2(x77811)),x77812))+P22(f312(f312(f228(x77811),f312(f312(f90(x77811),x77812),x77813)),f312(f312(f90(x77811),x77812),x77814)))
% 173.53/173.43 [7782]~P67(x77821)+~P22(f312(f312(f228(x77821),x77822),x77824))+~P22(f312(f312(f228(x77821),f2(x77821)),x77823))+P22(f312(f312(f228(x77821),f312(f312(f268(x77821),x77822),x77823)),f312(f312(f268(x77821),x77824),x77823)))
% 173.53/173.43 [7783]~P130(x77831)+~P22(f312(f312(f227(x77831),x77833),x77834))+~P22(f312(f312(f227(x77831),f2(x77831)),x77832))+P22(f312(f312(f227(x77831),f312(f312(f90(x77831),x77832),x77833)),f312(f312(f90(x77831),x77832),x77834)))
% 173.53/173.43 [7784]~P118(x77841)+~P22(f312(f312(f228(x77841),f2(x77841)),x77842))+~P22(f312(f312(f227(x77841),x77843),x77844))+P22(f312(f312(f227(x77841),f312(f312(f90(x77841),x77842),x77843)),f312(f312(f90(x77841),x77842),x77844)))
% 173.53/173.43 [7785]~P129(x77851)+~P22(f312(f312(f227(x77851),x77853),x77854))+~P22(f312(f312(f227(x77851),f2(x77851)),x77852))+P22(f312(f312(f227(x77851),f312(f312(f90(x77851),x77852),x77853)),f312(f312(f90(x77851),x77852),x77854)))
% 173.53/173.43 [7786]~P130(x77861)+~P22(f312(f312(f227(x77861),x77862),x77864))+~P22(f312(f312(f227(x77861),f2(x77861)),x77863))+P22(f312(f312(f227(x77861),f312(f312(f90(x77861),x77862),x77863)),f312(f312(f90(x77861),x77864),x77863)))
% 173.53/173.43 [7787]~P117(x77871)+~P22(f312(f312(f227(x77871),x77872),x77874))+~P22(f312(f312(f227(x77871),f2(x77871)),x77872))+P22(f312(f312(f227(x77871),f312(f312(f240(x77871),x77872),x77873)),f312(f312(f240(x77871),x77874),x77873)))
% 173.53/173.43 [7788]~P66(x77881)+~P22(f312(f312(f227(x77881),x77882),x77884))+~P22(f312(f312(f227(x77881),f2(x77881)),x77883))+P22(f312(f312(f227(x77881),f312(f312(f268(x77881),x77882),x77883)),f312(f312(f268(x77881),x77884),x77883)))
% 173.53/173.43 [7826]~P104(x78262)+P22(f312(f312(f227(f860(x78261,x78262)),x78264),x78263))+~P22(f312(f312(f227(f860(x78261,x78262)),x78263),x78264))+P22(f312(f312(f228(f860(x78261,x78262)),x78263),x78264))
% 173.53/173.43 [7866]P22(f312(f312(f314(x78661),x78662),x78663))+P22(f312(f312(f314(x78661),x78662),x78664))+~P22(f312(f312(f227(f860(x78661,a845)),x78664),x78663))+P22(f312(f312(f228(f860(x78661,a845)),x78664),f312(f312(f289(x78661),x78662),x78663)))
% 173.53/173.43 [8028]P22(f312(f312(f314(x80281),x80282),x80283))+P22(f312(f312(f314(x80281),x80282),x80284))+~P22(f312(f312(f228(f860(x80281,a845)),x80284),f312(f312(f289(x80281),x80282),x80283)))+P22(f312(f312(f227(f860(x80281,a845)),x80284),x80283))
% 173.53/173.43 [8037]~P63(x80371)+P7(x80371,x80372,x80373)+~P22(f312(x80372,x80374))+~P22(f312(f312(f314(f853(x80371)),x80374),f312(f168(f853(x80371)),f63(x80371,x80373,f64(x80371)))))
% 173.53/173.43 [8047]~P8(x80473,x80471,x80474)+~P63(x80473)+P22(f312(x80471,x80472))+~P22(f312(f312(f314(f853(x80473)),x80472),f312(f168(f853(x80473)),f63(x80473,x80474,f64(x80473)))))
% 173.53/173.43 [8100]~P118(x81001)+P22(f312(f312(f228(x81001),x81003),x81002))+P22(f312(f312(f228(x81001),x81002),x81003))+~P22(f312(f312(f228(x81001),f312(f312(f90(x81001),x81004),x81002)),f312(f312(f90(x81001),x81004),x81003)))
% 173.53/173.43 [8101]~P118(x81011)+P22(f312(f312(f228(x81011),x81013),x81012))+P22(f312(f312(f228(x81011),x81012),x81013))+~P22(f312(f312(f228(x81011),f312(f312(f90(x81011),x81012),x81014)),f312(f312(f90(x81011),x81013),x81014)))
% 173.53/173.43 [8112]~P118(x81121)+P22(f312(f312(f228(x81121),x81124),f2(x81121)))+P22(f312(f312(f228(x81121),x81122),x81123))+~P22(f312(f312(f228(x81121),f312(f312(f90(x81121),x81122),x81124)),f312(f312(f90(x81121),x81123),x81124)))
% 173.53/173.43 [8113]~P118(x81131)+P22(f312(f312(f228(x81131),x81134),f2(x81131)))+P22(f312(f312(f228(x81131),x81132),x81133))+~P22(f312(f312(f228(x81131),f312(f312(f90(x81131),x81134),x81132)),f312(f312(f90(x81131),x81134),x81133)))
% 173.53/173.43 [8117]~P118(x81171)+P22(f312(f312(f228(x81171),x81172),x81173))+P22(f312(f312(f228(x81171),f2(x81171)),x81174))+~P22(f312(f312(f228(x81171),f312(f312(f90(x81171),x81174),x81173)),f312(f312(f90(x81171),x81174),x81172)))
% 173.53/173.43 [8118]~P118(x81181)+P22(f312(f312(f228(x81181),x81182),x81183))+P22(f312(f312(f228(x81181),f2(x81181)),x81184))+~P22(f312(f312(f228(x81181),f312(f312(f90(x81181),x81183),x81184)),f312(f312(f90(x81181),x81182),x81184)))
% 173.53/173.43 [8131]~P118(x81311)+P22(f312(f312(f228(x81311),x81312),f2(x81311)))+P22(f312(f312(f228(x81311),f2(x81311)),x81312))+~P22(f312(f312(f228(x81311),f312(f312(f90(x81311),x81313),x81312)),f312(f312(f90(x81311),x81314),x81312)))
% 173.53/173.43 [8132]~P118(x81321)+P22(f312(f312(f228(x81321),x81322),f2(x81321)))+P22(f312(f312(f228(x81321),f2(x81321)),x81322))+~P22(f312(f312(f228(x81321),f312(f312(f90(x81321),x81322),x81323)),f312(f312(f90(x81321),x81322),x81324)))
% 173.53/173.43 [8159]~P118(x81591)+~P22(f312(f312(f228(x81591),x81594),f2(x81591)))+P22(f312(f312(f228(x81591),x81592),x81593))+~P22(f312(f312(f228(x81591),f312(f312(f90(x81591),x81594),x81593)),f312(f312(f90(x81591),x81594),x81592)))
% 173.53/173.43 [8160]~P118(x81601)+~P22(f312(f312(f228(x81601),x81604),f2(x81601)))+P22(f312(f312(f227(x81601),x81602),x81603))+~P22(f312(f312(f227(x81601),f312(f312(f90(x81601),x81604),x81603)),f312(f312(f90(x81601),x81604),x81602)))
% 173.53/173.43 [8172]~P117(x81723)+~P22(f312(f312(f228(x81723),f87(x81723)),x81724))+P22(f312(f312(f228(a852),x81721),x81722))+~P22(f312(f312(f228(x81723),f312(f312(f240(x81723),x81724),x81721)),f312(f312(f240(x81723),x81724),x81722)))
% 173.53/173.43 [8174]~P117(x81743)+~P22(f312(f312(f228(x81743),f87(x81743)),x81744))+P22(f312(f312(f227(a852),x81741),x81742))+~P22(f312(f312(f227(x81743),f312(f312(f240(x81743),x81744),x81741)),f312(f312(f240(x81743),x81744),x81742)))
% 173.53/173.43 [8184]~P122(x81841)+P22(f312(f312(f228(x81841),x81842),x81843))+~P22(f312(f312(f227(x81841),f2(x81841)),x81844))+~P22(f312(f312(f228(x81841),f312(f312(f90(x81841),x81844),x81842)),f312(f312(f90(x81841),x81844),x81843)))
% 173.53/173.43 [8185]~P123(x81851)+P22(f312(f312(f228(x81851),x81852),x81853))+~P22(f312(f312(f227(x81851),f2(x81851)),x81854))+~P22(f312(f312(f228(x81851),f312(f312(f90(x81851),x81854),x81852)),f312(f312(f90(x81851),x81854),x81853)))
% 173.53/173.43 [8186]~P118(x81861)+P22(f312(f312(f228(x81861),x81862),x81863))+~P22(f312(f312(f228(x81861),f2(x81861)),x81864))+~P22(f312(f312(f228(x81861),f312(f312(f90(x81861),x81864),x81862)),f312(f312(f90(x81861),x81864),x81863)))
% 173.53/173.43 [8187]~P117(x81871)+~P22(f312(f312(f227(x81871),f2(x81871)),x81873))+P22(f312(f312(f228(x81871),x81872),x81873))+~P22(f312(f312(f228(x81871),f312(f312(f240(x81871),x81872),x81874)),f312(f312(f240(x81871),x81873),x81874)))
% 173.53/173.43 [8188]~P122(x81881)+P22(f312(f312(f228(x81881),x81882),x81883))+~P22(f312(f312(f227(x81881),f2(x81881)),x81884))+~P22(f312(f312(f228(x81881),f312(f312(f90(x81881),x81882),x81884)),f312(f312(f90(x81881),x81883),x81884)))
% 173.53/173.43 [8189]~P123(x81891)+P22(f312(f312(f228(x81891),x81892),x81893))+~P22(f312(f312(f227(x81891),f2(x81891)),x81894))+~P22(f312(f312(f228(x81891),f312(f312(f90(x81891),x81892),x81894)),f312(f312(f90(x81891),x81893),x81894)))
% 173.53/173.43 [8190]~P122(x81901)+P22(f312(f312(f227(x81901),x81902),x81903))+~P22(f312(f312(f228(x81901),f2(x81901)),x81904))+~P22(f312(f312(f227(x81901),f312(f312(f90(x81901),x81904),x81902)),f312(f312(f90(x81901),x81904),x81903)))
% 173.53/173.43 [8191]~P118(x81911)+P22(f312(f312(f227(x81911),x81912),x81913))+~P22(f312(f312(f228(x81911),f2(x81911)),x81914))+~P22(f312(f312(f227(x81911),f312(f312(f90(x81911),x81914),x81912)),f312(f312(f90(x81911),x81914),x81913)))
% 173.53/173.43 [8192]~P122(x81921)+P22(f312(f312(f227(x81921),x81922),x81923))+~P22(f312(f312(f228(x81921),f2(x81921)),x81924))+~P22(f312(f312(f227(x81921),f312(f312(f90(x81921),x81922),x81924)),f312(f312(f90(x81921),x81923),x81924)))
% 173.53/173.43 [8239]P22(f312(f312(f314(x82391),x82392),x82393))+~P22(f312(f312(f227(f860(x82391,a845)),x82393),x82394))+~P22(f312(f312(f228(f860(x82391,a845)),x82393),x82394))+P22(f312(f312(f228(f860(x82391,a845)),x82393),f312(f312(f289(x82391),x82392),x82394)))
% 173.53/173.43 [8613]E(f312(f312(f21(a1),f471(x86131,x86132,x86133,x86134)),f472(x86131,x86132,x86133,x86134)),x86134)+~P22(f312(f312(f228(a1),f2(a1)),x86133))+~P22(f312(f312(f227(a1),x86131),x86134))+P22(f312(f312(f227(a1),x86131),f312(f312(f89(a1),x86134),x86133)))
% 173.53/173.43 [8614]E(f312(f312(f21(a1),f479(x86141,x86142,x86143,x86144)),f480(x86141,x86142,x86143,x86144)),x86144)+~P22(f312(f312(f228(a1),f2(a1)),x86143))+~P22(f312(f312(f228(a1),x86141),x86144))+P22(f312(f312(f228(a1),x86141),f312(f312(f89(a1),x86144),x86143)))
% 173.53/173.43 [8749]~E(f312(f312(f161(x87491),x87493),f617(x87494,x87493,x87491,x87492)),f312(f312(f161(x87491),x87494),f617(x87494,x87493,x87491,x87492)))+E(f312(f312(f169(x87491),x87492),x87493),f312(f312(f169(x87491),x87492),x87494))+~P22(f312(f312(f227(a852),x87492),f312(f190(f853(x87491)),x87493)))+~P22(f312(f312(f227(a852),x87492),f312(f190(f853(x87491)),x87494)))
% 173.53/173.43 [8817]~P22(f312(f312(f228(a1),f2(a1)),x88173))+~P22(f312(f312(f227(a1),x88171),x88174))+P22(f312(f312(f314(a1),f471(x88171,x88172,x88173,x88174)),x88172))+P22(f312(f312(f227(a1),x88171),f312(f312(f89(a1),x88174),x88173)))
% 173.53/173.43 [8818]~P22(f312(f312(f228(a1),f2(a1)),x88183))+~P22(f312(f312(f228(a1),x88181),x88184))+P22(f312(f312(f314(a1),f479(x88181,x88182,x88183,x88184)),x88182))+P22(f312(f312(f228(a1),x88181),f312(f312(f89(a1),x88184),x88183)))
% 173.53/173.43 [8861]~P99(x88611)+~P22(f312(f70(x88611),x88613))+~P22(f312(f312(f314(x88611),x88614),x88613))+P22(f312(f312(f227(x88611),f312(f312(f73(x88611,x88611,f115(x88611)),x88612),x88613)),f312(f312(f115(x88611),x88614),x88612)))
% 173.53/173.43 [8862]~P103(x88621)+~P22(f312(f70(x88621),x88623))+~P22(f312(f312(f314(x88621),x88624),x88623))+P22(f312(f312(f227(x88621),f312(f312(f73(x88621,x88621,f225(x88621)),x88622),x88623)),f312(f312(f225(x88621),x88624),x88622)))
% 173.53/173.43 [8912]E(f312(f312(f169(x89121),x89122),x89123),f312(f312(f169(x89121),x89122),x89124))+P22(f312(f312(f228(a852),f617(x89123,x89124,x89121,x89122)),x89122))+~P22(f312(f312(f227(a852),x89122),f312(f190(f853(x89121)),x89123)))+~P22(f312(f312(f227(a852),x89122),f312(f190(f853(x89121)),x89124)))
% 173.53/173.43 [8917]~P22(f312(f312(f228(a1),f2(a1)),x89173))+~P22(f312(f312(f228(a1),x89171),x89172))+P22(f312(f312(f314(a1),f480(x89171,x89174,x89173,x89172)),f283(a1,f87(a1),x89173)))+P22(f312(f312(f228(a1),x89171),f312(f312(f89(a1),x89172),x89173)))
% 173.53/173.43 [8918]~P22(f312(f312(f228(a1),f2(a1)),x89183))+~P22(f312(f312(f227(a1),x89181),x89182))+P22(f312(f312(f314(a1),f472(x89181,x89184,x89183,x89182)),f283(a1,f87(a1),x89183)))+P22(f312(f312(f227(a1),x89181),f312(f312(f89(a1),x89182),x89183)))
% 173.53/173.43 [9076]~E(f312(f173(x90761,x90762),x90763),f312(f173(x90761,x90762),x90764))+E(f312(f168(f859(x90761,x90762)),x90763),f312(f168(f859(x90761,x90762)),x90764))+~P22(f312(f133(x90761),f312(f312(f150(f859(x90761,x90762),x90761),f246(x90761,x90762)),x90764)))+~P22(f312(f133(x90761),f312(f312(f150(f859(x90761,x90762),x90761),f246(x90761,x90762)),x90763)))
% 173.53/173.43 [9088]E(f312(f173(x90881,x90882),x90883),f312(f173(x90881,x90882),x90884))+~E(f312(f168(f859(x90881,x90882)),x90883),f312(f168(f859(x90881,x90882)),x90884))+~P22(f312(f133(x90881),f312(f312(f150(f859(x90881,x90882),x90881),f246(x90881,x90882)),x90884)))+~P22(f312(f133(x90881),f312(f312(f150(f859(x90881,x90882),x90881),f246(x90881,x90882)),x90883)))
% 173.53/173.43 [9358]~P22(f312(f312(f228(a1),f2(a1)),x93583))+~P22(f312(f312(f227(a1),f2(a1)),x93584))+~P22(f312(f312(f228(a1),x93584),x93581))+P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x93581),f54(a1,x93582,x93583))),x93584)),f312(f312(f90(a1),x93581),x93583)))
% 173.53/173.43 [9747]E(x97471,x97472)+P22(f312(f312(f314(f859(f853(x97473),f853(x97473))),f312(f312(f239(f853(x97473),f853(x97473)),x97472),x97471)),f143(x97473,x97474)))+P22(f312(f312(f314(f859(f853(x97473),f853(x97473))),f312(f312(f239(f853(x97473),f853(x97473)),x97471),x97472)),f143(x97473,x97474)))+~P22(f312(f312(f314(f859(x97473,x97473)),f312(f312(f239(x97473,x97473),f604(x97471,x97472,x97474,x97473)),f609(x97471,x97472,x97474,x97473))),x97474))
% 173.53/173.43 [9748]E(x97481,x97482)+P22(f312(f312(f314(f859(f853(x97483),f853(x97483))),f312(f312(f239(f853(x97483),f853(x97483)),x97482),x97481)),f143(x97483,x97484)))+P22(f312(f312(f314(f859(f853(x97483),f853(x97483))),f312(f312(f239(f853(x97483),f853(x97483)),x97481),x97482)),f143(x97483,x97484)))+~P22(f312(f312(f314(f859(x97483,x97483)),f312(f312(f239(x97483,x97483),f609(x97481,x97482,x97484,x97483)),f604(x97481,x97482,x97484,x97483))),x97484))
% 173.53/173.43 [7318]~P103(x73181)+~P22(f312(f312(f228(x73181),x73183),x73184))+~P22(f312(f312(f228(x73181),x73182),x73184))+P22(f312(f312(f228(x73181),f312(f312(f226(x73181),x73182),x73183)),x73184))
% 173.53/173.43 [7321]~P98(x73211)+~P22(f312(f312(f227(x73211),x73213),x73214))+~P22(f312(f312(f227(x73211),x73212),x73214))+P22(f312(f312(f227(x73211),f312(f312(f124(x73211),x73212),x73213)),x73214))
% 173.53/173.43 [7324]~P103(x73241)+~P22(f312(f312(f227(x73241),x73243),x73244))+~P22(f312(f312(f227(x73241),x73242),x73244))+P22(f312(f312(f227(x73241),f312(f312(f226(x73241),x73242),x73243)),x73244))
% 173.53/173.43 [7642]~E(x76421,x76423)+E(f135(a852,f312(f282(a852,x76421),x76422)),f312(f312(f147(a852),x76423),x76424))+~E(f135(a852,f312(f282(a852,f312(f312(f89(a852),x76421),f87(a852))),x76422)),x76424)+~P22(f312(f312(f228(a852),x76421),x76422))
% 173.53/173.43 [7653]~P103(x76531)+P22(f312(f312(f228(x76531),x76532),x76533))+P22(f312(f312(f228(x76531),x76534),x76533))+~P22(f312(f312(f228(x76531),f312(f312(f225(x76531),x76534),x76532)),x76533))
% 173.53/173.43 [7654]~P103(x76541)+P22(f312(f312(f227(x76541),x76542),x76543))+P22(f312(f312(f227(x76541),x76544),x76543))+~P22(f312(f312(f227(x76541),f312(f312(f225(x76541),x76544),x76542)),x76543))
% 173.53/173.43 [7925]~P66(x79251)+~P22(f312(f312(f228(x79251),f2(x79251)),x79253))+~P22(f312(f312(f228(x79251),x79252),f312(f312(f268(x79251),x79254),x79253)))+P22(f312(f312(f228(x79251),f312(f312(f90(x79251),x79252),x79253)),x79254))
% 173.53/173.43 [7926]~P67(x79261)+~P22(f312(f312(f228(x79261),f2(x79261)),x79263))+~P22(f312(f312(f228(x79261),x79262),f312(f312(f268(x79261),x79264),x79263)))+P22(f312(f312(f228(x79261),f312(f312(f90(x79261),x79262),x79263)),x79264))
% 173.53/173.43 [7928]~P66(x79281)+~P22(f312(f312(f228(x79281),f2(x79281)),x79283))+~P22(f312(f312(f228(x79281),x79282),f312(f312(f90(x79281),x79284),x79283)))+P22(f312(f312(f228(x79281),f312(f312(f268(x79281),x79282),x79283)),x79284))
% 173.53/173.43 [7929]~P67(x79291)+~P22(f312(f312(f228(x79291),f2(x79291)),x79293))+~P22(f312(f312(f228(x79291),x79292),f312(f312(f90(x79291),x79294),x79293)))+P22(f312(f312(f228(x79291),f312(f312(f268(x79291),x79292),x79293)),x79294))
% 173.53/173.43 [7930]~P66(x79301)+~P22(f312(f312(f228(x79301),f2(x79301)),x79303))+~P22(f312(f312(f227(x79301),x79302),f312(f312(f268(x79301),x79304),x79303)))+P22(f312(f312(f227(x79301),f312(f312(f90(x79301),x79302),x79303)),x79304))
% 173.53/173.43 [7931]~P67(x79311)+~P22(f312(f312(f228(x79311),f2(x79311)),x79313))+~P22(f312(f312(f227(x79311),x79312),f312(f312(f268(x79311),x79314),x79313)))+P22(f312(f312(f227(x79311),f312(f312(f90(x79311),x79312),x79313)),x79314))
% 173.53/173.43 [7933]~P66(x79331)+~P22(f312(f312(f228(x79331),f2(x79331)),x79333))+~P22(f312(f312(f227(x79331),x79332),f312(f312(f90(x79331),x79334),x79333)))+P22(f312(f312(f227(x79331),f312(f312(f268(x79331),x79332),x79333)),x79334))
% 173.53/173.43 [7934]~P67(x79341)+~P22(f312(f312(f228(x79341),f2(x79341)),x79343))+~P22(f312(f312(f227(x79341),x79342),f312(f312(f90(x79341),x79344),x79343)))+P22(f312(f312(f227(x79341),f312(f312(f268(x79341),x79342),x79343)),x79344))
% 173.53/173.43 [8070]~P66(x80701)+~P22(f312(f312(f228(x80701),f2(x80701)),x80704))+P22(f312(f312(f228(x80701),x80702),f312(f312(f90(x80701),x80703),x80704)))+~P22(f312(f312(f228(x80701),f312(f312(f268(x80701),x80702),x80704)),x80703))
% 173.53/173.43 [8072]~P66(x80721)+~P22(f312(f312(f228(x80721),f2(x80721)),x80724))+P22(f312(f312(f228(x80721),x80722),f312(f312(f268(x80721),x80723),x80724)))+~P22(f312(f312(f228(x80721),f312(f312(f90(x80721),x80722),x80724)),x80723))
% 173.53/173.43 [8073]~P67(x80731)+~P22(f312(f312(f228(x80731),f2(x80731)),x80734))+P22(f312(f312(f228(x80731),x80732),f312(f312(f90(x80731),x80733),x80734)))+~P22(f312(f312(f228(x80731),f312(f312(f268(x80731),x80732),x80734)),x80733))
% 173.53/173.43 [8074]~P67(x80741)+~P22(f312(f312(f228(x80741),f2(x80741)),x80744))+P22(f312(f312(f228(x80741),x80742),f312(f312(f268(x80741),x80743),x80744)))+~P22(f312(f312(f228(x80741),f312(f312(f90(x80741),x80742),x80744)),x80743))
% 173.53/173.43 [8075]~P66(x80751)+~P22(f312(f312(f228(x80751),f2(x80751)),x80754))+P22(f312(f312(f227(x80751),x80752),f312(f312(f90(x80751),x80753),x80754)))+~P22(f312(f312(f227(x80751),f312(f312(f268(x80751),x80752),x80754)),x80753))
% 173.53/173.43 [8077]~P66(x80771)+~P22(f312(f312(f228(x80771),f2(x80771)),x80774))+P22(f312(f312(f227(x80771),x80772),f312(f312(f268(x80771),x80773),x80774)))+~P22(f312(f312(f227(x80771),f312(f312(f90(x80771),x80772),x80774)),x80773))
% 173.53/173.43 [8078]~P67(x80781)+~P22(f312(f312(f228(x80781),f2(x80781)),x80784))+P22(f312(f312(f227(x80781),x80782),f312(f312(f90(x80781),x80783),x80784)))+~P22(f312(f312(f227(x80781),f312(f312(f268(x80781),x80782),x80784)),x80783))
% 173.53/173.43 [8079]~P67(x80791)+~P22(f312(f312(f228(x80791),f2(x80791)),x80794))+P22(f312(f312(f227(x80791),x80792),f312(f312(f268(x80791),x80793),x80794)))+~P22(f312(f312(f227(x80791),f312(f312(f90(x80791),x80792),x80794)),x80793))
% 173.53/173.43 [8238]~P22(f312(x82381,x82384))+P22(f312(x82381,f312(f47(a852,x82382),x82383)))+~P22(f312(f312(f228(a852),x82382),f312(f312(f90(a852),x82383),f312(a126,x82384))))+~P22(f312(f312(f227(a852),f312(f312(f90(a852),x82383),x82384)),x82382))
% 173.53/173.43 [8244]~P67(x82441)+~P22(f312(f312(f228(x82441),x82443),f2(x82441)))+~P22(f312(f312(f228(x82441),f312(f312(f268(x82441),x82444),x82443)),x82442))+P22(f312(f312(f228(x82441),f312(f312(f90(x82441),x82442),x82443)),x82444))
% 173.53/173.43 [8245]~P67(x82451)+~P22(f312(f312(f228(x82451),x82453),f2(x82451)))+~P22(f312(f312(f228(x82451),f312(f312(f90(x82451),x82454),x82453)),x82452))+P22(f312(f312(f228(x82451),f312(f312(f268(x82451),x82452),x82453)),x82454))
% 173.53/173.43 [8246]~P67(x82461)+~P22(f312(f312(f228(x82461),x82463),f2(x82461)))+~P22(f312(f312(f227(x82461),f312(f312(f268(x82461),x82464),x82463)),x82462))+P22(f312(f312(f227(x82461),f312(f312(f90(x82461),x82462),x82463)),x82464))
% 173.53/173.43 [8247]~P67(x82471)+~P22(f312(f312(f228(x82471),x82473),f2(x82471)))+~P22(f312(f312(f227(x82471),f312(f312(f90(x82471),x82474),x82473)),x82472))+P22(f312(f312(f227(x82471),f312(f312(f268(x82471),x82472),x82473)),x82474))
% 173.53/173.43 [8478]~P98(x84781)+~P22(f312(f70(x84781),x84784))+~P22(f312(f312(f314(x84781),x84782),x84784))+P22(f312(f312(f227(x84781),f312(f312(f124(x84781),x84782),x84783)),f312(f312(f73(x84781,x84781,f124(x84781)),x84783),x84784)))
% 173.53/173.43 [8479]~P103(x84791)+~P22(f312(f70(x84791),x84794))+~P22(f312(f312(f314(x84791),x84792),x84794))+P22(f312(f312(f227(x84791),f312(f312(f226(x84791),x84792),x84793)),f312(f312(f73(x84791,x84791,f226(x84791)),x84793),x84794)))
% 173.53/173.43 [8615]~P22(f312(f70(x86151),x86152))+E(f312(f53(x86151),f312(f312(f21(f860(x86151,a845)),x86152),f312(f312(f289(x86151),x86153),x86154))),f312(f312(f21(a852),f312(f53(x86151),f312(f312(f21(f860(x86151,a845)),x86152),x86154))),f87(a852)))+P22(f312(f312(f314(x86151),x86153),x86154))+~P22(f312(f312(f314(x86151),x86153),x86152))
% 173.53/173.43 [8686]E(f312(f312(f89(a1),f473(x86861,x86862,x86863,x86864)),f474(x86861,x86862,x86863,x86864)),x86864)+~P22(f312(f312(f228(a1),f2(a1)),x86863))+~P22(f312(f312(f227(a1),x86864),x86861))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x86864),x86863)),x86861))
% 173.53/173.43 [8687]E(f312(f312(f89(a1),f481(x86871,x86872,x86873,x86874)),f482(x86871,x86872,x86873,x86874)),x86874)+~P22(f312(f312(f228(a1),f2(a1)),x86873))+~P22(f312(f312(f228(a1),x86874),x86871))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x86874),x86873)),x86871))
% 173.53/173.43 [8897]~P22(f312(f312(f228(a1),f2(a1)),x88973))+~P22(f312(f312(f227(a1),x88974),x88971))+P22(f312(f312(f314(a1),f473(x88971,x88972,x88973,x88974)),x88972))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x88974),x88973)),x88971))
% 173.53/173.43 [8898]~P22(f312(f312(f228(a1),f2(a1)),x88983))+~P22(f312(f312(f228(a1),x88984),x88981))+P22(f312(f312(f314(a1),f481(x88981,x88982,x88983,x88984)),x88982))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x88984),x88983)),x88981))
% 173.53/173.43 [8980]~P22(f312(f312(f228(a1),f2(a1)),x89802))+~P22(f312(f312(f228(a1),x89801),x89803))+P22(f312(f312(f314(a1),f482(x89803,x89804,x89802,x89801)),f283(a1,f87(a1),x89802)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x89801),x89802)),x89803))
% 173.53/173.43 [8981]~P22(f312(f312(f228(a1),f2(a1)),x89812))+~P22(f312(f312(f227(a1),x89811),x89813))+P22(f312(f312(f314(a1),f474(x89813,x89814,x89812,x89811)),f283(a1,f87(a1),x89812)))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x89811),x89812)),x89813))
% 173.53/173.43 [8997]~P22(f312(f312(f228(a1),f2(a1)),x89973))+~P22(f312(f312(f227(a1),f2(a1)),x89974))+~P22(f312(f312(f228(a1),x89974),x89971))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x89971),f54(a1,x89972,x89973))),x89974)))
% 173.53/173.43 [9075]~P22(f312(f312(f227(a1),x90754),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x90752))+~P22(f312(f312(f228(a1),x90751),x90754))+P22(f312(f312(f228(a1),f312(f312(f90(a1),x90751),x90752)),f312(f312(f89(a1),f312(f312(f90(a1),x90751),f54(a1,x90753,x90752))),x90754)))
% 173.53/173.43 [9097]P22(f312(f70(x90971),x90972))+~P22(f312(f70(x90971),x90973))+~P22(f312(f312(f314(f860(x90971,a845)),x90972),f312(f312(f69(x90971),x90973),x90974)))+~P22(f312(f312(f227(f860(f859(x90971,x90971),a845)),x90974),f312(f312(f247(x90971,x90971),x90973),f312(f16(f860(x90971,a845),x90971),x90973))))
% 173.53/173.43 [9135]~P49(f860(x91351,a845),f860(x91351,a845),x91353)+~P22(f312(f312(f314(x91351),x91352),x91354))+P22(f312(f312(f314(x91351),x91352),f110(f860(x91351,a845),x91353)))+~P22(f312(f312(f227(f860(x91351,a845)),x91354),f312(x91353,f312(f312(f124(f860(x91351,a845)),x91354),f110(f860(x91351,a845),x91353)))))
% 173.53/173.43 [9310]~P49(f860(x93103,a845),f860(x93103,a845),x93104)+P22(f312(x93101,x93102))+~P22(f312(f312(f314(x93103),x93102),f109(f860(x93103,a845),x93104)))+P22(f312(f312(f314(x93103),f558(x93101,x93104,x93102,x93103)),f312(x93104,f312(f312(f115(f860(x93103,a845)),f109(f860(x93103,a845),x93104)),f312(f233(x93103),x93101)))))
% 173.53/173.43 [9520]~P22(f312(f70(x95202),x95204))+~P22(f312(f70(x95201),x95203))+~P22(f312(f312(f227(a852),f312(f53(x95202),x95204)),f312(f53(x95201),x95203)))+P22(f312(f312(f227(f860(x95201,a845)),f312(f290(x95202,x95201,f388(x95203,x95201,x95204,x95202)),x95204)),x95203))
% 173.53/173.43 [9175]~P22(f312(f312(f314(x91751),x91752),x91754))+P22(f312(f312(f314(x91751),x91752),x91753))+~P22(f312(f312(f228(f860(x91751,a845)),x91754),f312(f312(f289(x91751),x91752),x91753)))+P22(f312(f312(f228(f860(x91751,a845)),f312(f312(f21(f860(x91751,a845)),x91754),f312(f312(f289(x91751),x91752),f189(f860(x91751,a845))))),x91753))
% 173.53/173.43 [9335]~P22(f312(f312(f314(x93351),x93352),x93354))+P22(f312(f312(f314(x93351),x93352),x93353))+P22(f312(f312(f228(f860(x93351,a845)),x93354),f312(f312(f289(x93351),x93352),x93353)))+~P22(f312(f312(f228(f860(x93351,a845)),f312(f312(f21(f860(x93351,a845)),x93354),f312(f312(f289(x93351),x93352),f189(f860(x93351,a845))))),x93353))
% 173.53/173.43 [9361]P22(f312(f312(f314(x93611),x93612),x93613))+~P22(f312(f312(f227(f860(x93611,a845)),x93614),x93613))+P22(f312(f312(f228(f860(x93611,a845)),x93614),f312(f312(f289(x93611),x93612),x93613)))+~P22(f312(f312(f228(f860(x93611,a845)),f312(f312(f21(f860(x93611,a845)),x93614),f312(f312(f289(x93611),x93612),f189(f860(x93611,a845))))),x93613))
% 173.53/173.43 [9366]~P22(f312(f312(f314(x93661),x93663),x93662))+~P22(f312(f312(f228(f860(x93661,a845)),x93662),x93664))+P22(f312(f312(f228(f860(x93661,a845)),x93662),f312(f312(f289(x93661),x93663),x93664)))+~P22(f312(f312(f228(f860(x93661,a845)),f312(f312(f21(f860(x93661,a845)),x93662),f312(f312(f289(x93661),x93663),f189(f860(x93661,a845))))),x93664))
% 173.53/173.43 [9378]~P22(f312(f312(f227(f860(x93781,a845)),x93782),x93784))+~P22(f312(f312(f228(f860(x93781,a845)),x93782),x93784))+P22(f312(f312(f228(f860(x93781,a845)),x93782),f312(f312(f289(x93781),x93783),x93784)))+~P22(f312(f312(f228(f860(x93781,a845)),f312(f312(f21(f860(x93781,a845)),x93782),f312(f312(f289(x93781),x93783),f189(f860(x93781,a845))))),x93784))
% 173.53/173.43 [9424]~P105(x94242)+~P63(x94241)+~P22(f312(f312(f227(f860(x94241,x94242)),x94243),x94244))+P22(f312(f67(x94241),f312(f312(f18(x94241,x94242,a845),f312(f312(f8(x94242,f860(x94242,a845),x94241),f227(x94242)),x94243)),x94244)))
% 173.53/173.43 [9564]~P105(x95642)+~P63(x95641)+P22(f312(f312(f227(f860(x95641,x95642)),x95643),x95644))+~P22(f312(f67(x95641),f312(f312(f18(x95641,x95642,a845),f312(f312(f8(x95642,f860(x95642,a845),x95641),f227(x95642)),x95643)),x95644)))
% 173.53/173.43 [10050]~P49(f860(x100501,a845),f860(x100501,a845),x100503)+~P22(f312(f312(f314(x100501),x100502),x100504))+P22(f312(f312(f314(x100501),x100502),f110(f860(x100501,a845),x100503)))+~P22(f312(f312(f227(f860(x100501,a845)),x100504),f312(x100503,f109(f860(x100501,a845),f312(f312(f7(f860(x100501,a845),f860(x100501,a845),f860(x100501,a845)),f312(f312(f8(f860(x100501,a845),f860(f860(x100501,a845),f860(x100501,a845)),f860(x100501,a845)),f124(f860(x100501,a845))),f312(f312(f7(f860(x100501,a845),f860(x100501,a845),f860(x100501,a845)),f312(f312(f8(f860(x100501,a845),f860(f860(x100501,a845),f860(x100501,a845)),f860(x100501,a845)),f124(f860(x100501,a845))),x100503)),x100504))),f110(f860(x100501,a845),x100503))))))
% 173.53/173.43 [9730]E(f312(f312(f161(x97301),f312(f312(f161(f853(x97301)),f175(x97301,x97302)),x97303)),x97304),f312(f312(f161(x97301),f312(f312(f161(f853(x97301)),x97302),x97304)),x97303))+~P22(f312(f312(f228(a852),x97303),f312(f190(f853(f853(x97301))),f175(x97301,x97302))))+~P33(a852,f312(f165(a852),f312(f312(f150(f853(x97301),a852),f190(f853(x97301))),x97302)))+~P22(f312(f312(f228(a852),x97304),f312(f190(f853(f853(x97301))),f312(f132(f853(x97301),f312(f312(f8(a852,a845,f853(x97301)),f312(f228(a852),x97303)),f190(f853(x97301)))),x97302))))
% 173.53/173.43 [9759]~P22(f312(f312(f314(f859(a852,a852)),x97594),x97591))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x97594),x97592)),a45))+~P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97591),x97593)),a77))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97591),f312(f312(f289(f859(a852,a852)),x97592),x97593))),a77))
% 173.53/173.43 [9760]~P22(f312(f312(f314(f859(a852,a852)),x97604),x97601))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x97604),x97602)),a79))+~P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97601),x97603)),a80))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97601),f312(f312(f289(f859(a852,a852)),x97602),x97603))),a80))
% 173.53/173.43 [9648]~P105(x96482)+~P63(x96481)+~P22(f312(f312(f228(f860(x96481,x96482)),x96483),x96484))+P22(f312(f66(x96481),f312(f312(f8(a845,a845,x96481),a307),f312(f312(f18(x96481,x96482,a845),f312(f312(f8(x96482,f860(x96482,a845),x96481),a309),x96483)),x96484))))
% 173.53/173.43 [9773]~P22(f312(f312(f314(f859(a852,a852)),x97734),x97733))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x97731),x97734)),a45))+~P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97732),x97733)),a46))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f312(f312(f289(f859(a852,a852)),x97731),x97732)),x97733)),a46))
% 173.53/173.43 [9774]~P22(f312(f312(f314(f859(a852,a852)),x97744),x97743))+~P22(f312(f312(f314(f859(f859(a852,a852),f859(a852,a852))),f312(f312(f239(f859(a852,a852),f859(a852,a852)),x97741),x97744)),a79))+~P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),x97742),x97743)),a78))+P22(f312(f312(f314(f859(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845))),f312(f312(f239(f860(f859(a852,a852),a845),f860(f859(a852,a852),a845)),f312(f312(f289(f859(a852,a852)),x97741),x97742)),x97743)),a78))
% 173.53/173.43 [8824]~P36(x88241,x88242,x88244,x88245)+~P36(x88241,x88242,x88243,x88245)+~P36(x88241,x88242,x88243,f180(x88241,x88242,x88243,x88244))+P36(x88241,x88242,f180(x88241,x88242,x88243,x88244),x88245)
% 173.53/173.43 [5946]~P2(x59464,x59461)+~P22(f312(f312(x59461,x59462),x59465))+P22(f312(f312(x59461,x59462),x59463))+~P22(f312(f312(x59461,x59465),x59463))
% 173.53/173.43 [5219]~P30(x52195)+E(x52191,x52192)+~E(x52193,x52194)+~E(f312(f312(f21(x52195),x52193),x52194),f312(f312(f21(x52195),x52191),x52192))
% 173.53/173.43 [6046]~P12(x60465,x60461,x60463)+E(f312(f312(x60461,x60462),f312(x60463,x60464)),f312(x60463,x60464))+~P22(f312(f70(x60465),x60464))+~P22(f312(f312(f314(x60465),x60462),x60464))
% 173.53/173.43 [6235]~P76(x62351)+~E(f312(f312(f21(x62351),x62354),x62355),f312(f312(f21(x62351),x62352),x62353))+~P22(f312(f312(f228(x62351),x62354),x62355))+P22(f312(f312(f228(x62351),x62352),x62353))
% 173.53/173.43 [6237]~P76(x62371)+~E(f312(f312(f21(x62371),x62374),x62375),f312(f312(f21(x62371),x62372),x62373))+~P22(f312(f312(f227(x62371),x62374),x62375))+P22(f312(f312(f227(x62371),x62372),x62373))
% 173.53/173.43 [7186]~E(x71862,f312(f312(f147(x71861),x71864),x71865))+P22(f312(f312(f314(f853(x71861)),x71862),f157(x71861,x71863)))+~P22(f312(f312(f314(f853(x71861)),x71865),f157(x71861,x71863)))+~P22(f312(f312(f314(x71861),x71864),x71863))
% 173.53/173.43 [7593]~E(f312(f190(f853(x75931)),x75933),f312(f190(f853(x75932)),x75934))+~E(f312(f312(f150(f859(x75931,x75932),x75932),f248(x75931,x75932)),x75935),x75934)+~E(f312(f312(f150(f859(x75931,x75932),x75931),f246(x75931,x75932)),x75935),x75933)+E(f312(f312(f177(x75931,x75932),x75933),x75934),x75935)
% 173.53/173.43 [7922]~P105(x79221)+P22(f312(f312(f228(f860(x79221,a845)),f283(x79221,x79222,x79223)),f283(x79221,x79224,x79225)))+~P22(f312(f312(f227(x79221),x79224),x79225))+P22(f312(f312(f227(x79221),x79222),x79223))
% 173.53/173.43 [8021]~P105(x80211)+P22(f312(f312(f227(f860(x80211,a845)),f283(x80211,x80212,x80213)),f283(x80211,x80214,x80215)))+~P22(f312(f312(f227(x80211),x80213),x80215))+~P22(f312(f312(f227(x80211),x80214),x80212))
% 173.53/173.43 [8146]~P103(x81461)+P22(f312(f312(f227(x81461),x81462),x81463))+P22(f312(f312(f227(x81461),x81464),x81463))+~P22(f312(f312(f227(f860(x81461,a845)),f312(f282(x81461,x81463),x81462)),f312(f282(x81461,x81464),x81465)))
% 173.53/173.43 [8147]~P103(x81471)+P22(f312(f312(f227(x81471),x81472),x81473))+P22(f312(f312(f227(x81471),x81472),x81474))+~P22(f312(f312(f227(f860(x81471,a845)),f312(f282(x81471,x81473),x81472)),f312(f282(x81471,x81475),x81474)))
% 173.53/173.43 [8319]~P99(x83193)+~P99(x83191)+~P49(x83193,x83191,x83192)+P22(f312(f312(f227(x83191),f312(x83192,f312(f312(f115(x83193),x83194),x83195))),f312(f312(f115(x83191),f312(x83192,x83194)),f312(x83192,x83195))))
% 173.53/173.43 [8320]~P99(x83201)+~P103(x83203)+~P49(x83203,x83201,x83202)+P22(f312(f312(f227(x83201),f312(x83202,f312(f312(f225(x83203),x83204),x83205))),f312(f312(f115(x83201),f312(x83202,x83204)),f312(x83202,x83205))))
% 173.53/173.43 [8396]~P105(x83961)+~P22(f312(f312(f228(f860(x83961,a845)),f283(x83961,x83964,x83962)),f283(x83961,x83965,x83963)))+P22(f312(f312(f227(x83961),x83962),x83963))+~P22(f312(f312(f227(x83961),x83964),x83962))
% 173.53/173.43 [8397]~P105(x83971)+~P22(f312(f312(f227(f860(x83971,a845)),f283(x83971,x83974,x83972)),f283(x83971,x83975,x83973)))+P22(f312(f312(f227(x83971),x83972),x83973))+~P22(f312(f312(f227(x83971),x83974),x83972))
% 173.53/173.43 [8398]~P105(x83981)+~P22(f312(f312(f228(f860(x83981,a845)),f283(x83981,x83983,x83984)),f283(x83981,x83982,x83985)))+P22(f312(f312(f227(x83981),x83982),x83983))+~P22(f312(f312(f227(x83981),x83983),x83984))
% 173.53/173.43 [8399]~P105(x83991)+~P22(f312(f312(f227(f860(x83991,a845)),f283(x83991,x83993,x83994)),f283(x83991,x83992,x83995)))+P22(f312(f312(f227(x83991),x83992),x83993))+~P22(f312(f312(f227(x83991),x83993),x83994))
% 173.53/173.43 [5894]~P103(x58945)+~P103(x58941)+~P49(x58945,x58941,x58942)+E(f312(f312(f225(x58941),f312(x58942,x58943)),f312(x58942,x58944)),f312(x58942,f312(f312(f225(x58945),x58943),x58944)))
% 173.53/173.43 [5895]~P103(x58955)+~P103(x58951)+~P49(x58955,x58951,x58952)+E(f312(f312(f226(x58951),f312(x58952,x58953)),f312(x58952,x58954)),f312(x58952,f312(f312(f226(x58955),x58953),x58954)))
% 173.53/173.43 [5945]~P12(x59452,x59455,x59453)+E(x59451,f189(f860(x59452,a845)))+~P22(f312(f70(x59452),x59451))+E(f312(x59453,f312(f312(f289(x59452),x59454),x59451)),f312(f312(x59455,x59454),f312(x59453,x59451)))
% 173.53/173.43 [6694]~E(x66941,x66942)+~E(f312(f312(f115(f860(x66943,a845)),x66944),x66945),f189(f860(x66943,a845)))+~P22(f312(f312(f314(x66943),x66942),x66945))+~P22(f312(f312(f314(x66943),x66941),x66944))
% 173.53/173.43 [6835]~P72(x68352)+~P22(f312(f70(x68351),x68355))+E(f312(f312(f9(x68351,x68352),x68353),f312(f312(f289(x68351),x68354),x68355)),f312(f312(f90(x68352),f312(x68353,x68354)),f312(f312(f9(x68351,x68352),x68353),x68355)))+P22(f312(f312(f314(x68351),x68354),x68355))
% 173.53/173.43 [6837]~P26(x68372)+~P22(f312(f70(x68371),x68375))+E(f312(f312(f6(x68371,x68372),x68373),f312(f312(f289(x68371),x68374),x68375)),f312(f312(f89(x68372),f312(x68373,x68374)),f312(f312(f6(x68371,x68372),x68373),x68375)))+P22(f312(f312(f314(x68371),x68374),x68375))
% 173.53/173.43 [7335]~P13(x73352,x73355,x73351)+~P22(f312(f70(x73352),x73354))+E(f312(x73351,f312(f312(f289(x73352),x73353),x73354)),x73353)+~E(f312(f312(f21(f860(x73352,a845)),x73354),f312(f312(f289(x73352),x73353),f189(f860(x73352,a845)))),f189(f860(x73352,a845)))
% 173.53/173.43 [7647]~P22(f312(x76471,x76473))+~P22(f312(f312(f195(x76472),x76473),x76475))+~P22(f312(f312(f195(f35(x76471,x76472)),x76475),x76474))+P22(f312(f312(f195(f35(x76471,x76472)),x76473),x76474))
% 173.53/173.43 [7698]~P80(x76981)+~P22(f312(f312(f228(x76981),x76983),x76985))+~P22(f312(f312(f228(x76981),x76982),x76984))+P22(f312(f312(f228(x76981),f312(f312(f89(x76981),x76982),x76983)),f312(f312(f89(x76981),x76984),x76985)))
% 173.53/173.43 [7699]~P80(x76991)+~P22(f312(f312(f227(x76991),x76992),x76994))+~P22(f312(f312(f228(x76991),x76993),x76995))+P22(f312(f312(f228(x76991),f312(f312(f89(x76991),x76992),x76993)),f312(f312(f89(x76991),x76994),x76995)))
% 173.53/173.43 [7700]~P80(x77001)+~P22(f312(f312(f227(x77001),x77003),x77005))+~P22(f312(f312(f228(x77001),x77002),x77004))+P22(f312(f312(f228(x77001),f312(f312(f89(x77001),x77002),x77003)),f312(f312(f89(x77001),x77004),x77005)))
% 173.53/173.43 [7701]~P82(x77011)+~P22(f312(f312(f227(x77011),x77013),x77015))+~P22(f312(f312(f227(x77011),x77012),x77014))+P22(f312(f312(f227(x77011),f312(f312(f89(x77011),x77012),x77013)),f312(f312(f89(x77011),x77014),x77015)))
% 173.53/173.43 [7702]~P98(x77021)+~P22(f312(f312(f227(x77021),x77023),x77025))+~P22(f312(f312(f227(x77021),x77022),x77024))+P22(f312(f312(f227(x77021),f312(f312(f124(x77021),x77022),x77023)),f312(f312(f124(x77021),x77024),x77025)))
% 173.53/173.43 [7703]~P99(x77031)+~P22(f312(f312(f227(x77031),x77033),x77035))+~P22(f312(f312(f227(x77031),x77032),x77034))+P22(f312(f312(f227(x77031),f312(f312(f115(x77031),x77032),x77033)),f312(f312(f115(x77031),x77034),x77035)))
% 173.53/173.43 [7704]~P103(x77041)+~P22(f312(f312(f227(x77041),x77043),x77045))+~P22(f312(f312(f227(x77041),x77042),x77044))+P22(f312(f312(f227(x77041),f312(f312(f225(x77041),x77042),x77043)),f312(f312(f225(x77041),x77044),x77045)))
% 173.53/173.43 [7705]~P103(x77051)+~P22(f312(f312(f227(x77051),x77053),x77055))+~P22(f312(f312(f227(x77051),x77052),x77054))+P22(f312(f312(f227(x77051),f312(f312(f226(x77051),x77052),x77053)),f312(f312(f226(x77051),x77054),x77055)))
% 173.53/173.43 [7835]~P136(x78355)+E(x78351,x78352)+E(x78353,x78354)+~E(f312(f312(f89(x78355),f312(f312(f90(x78355),x78353),x78351)),f312(f312(f90(x78355),x78354),x78352)),f312(f312(f89(x78355),f312(f312(f90(x78355),x78353),x78352)),f312(f312(f90(x78355),x78354),x78351)))
% 173.53/173.43 [7973]P34(x79731,x79732,x79733)+~P21(x79731,x79734,x79735)+~P34(x79731,x79732,f638(x79735,x79734,x79731,x79732))+~P22(f312(f312(f314(f851(x79731)),x79733),x79735))
% 173.53/173.43 [8044]~P103(x80444)+~P22(f312(f133(x80441),x80443))+P22(f312(f312(f314(x80441),x80442),f312(f168(x80441),x80443)))+P22(f312(f133(x80441),f312(f312(f145(x80441,x80444,x80445),x80442),x80443)))
% 173.53/173.43 [8193]~P26(x81931)+E(f312(f312(f89(x81931),f312(f312(f6(a852,x81931),x81932),f312(f282(a852,x81933),x81934))),f312(f312(f6(a852,x81931),x81932),f312(f282(a852,x81934),x81935))),f312(f312(f6(a852,x81931),x81932),f312(f282(a852,x81933),x81935)))+~P22(f312(f312(f227(a852),x81934),x81935))+~P22(f312(f312(f227(a852),x81933),x81934))
% 173.53/173.43 [8194]~P30(x81941)+E(f312(f312(f21(x81941),f312(f312(f6(a852,x81941),x81942),f312(f282(a852,x81943),x81944))),f312(f312(f6(a852,x81941),x81942),f312(f282(a852,x81943),x81945))),f312(f312(f6(a852,x81941),x81942),f312(f282(a852,x81945),x81944)))+~P22(f312(f312(f227(a852),x81945),x81944))+~P22(f312(f312(f227(a852),x81943),x81945))
% 173.53/173.43 [8532]~P65(x85322)+E(x85321,f2(x85322))+E(x85323,f2(x85322))+E(f312(f312(f268(x85322),f312(f312(f89(x85322),f312(f312(f90(x85322),x85324),x85321)),f312(f312(f90(x85322),x85325),x85323))),f312(f312(f90(x85322),x85323),x85321)),f312(f312(f89(x85322),f312(f312(f268(x85322),x85324),x85323)),f312(f312(f268(x85322),x85325),x85321)))
% 173.53/173.43 [8533]~P65(x85332)+E(x85331,f2(x85332))+E(x85333,f2(x85332))+E(f312(f312(f268(x85332),f312(f312(f21(x85332),f312(f312(f90(x85332),x85334),x85331)),f312(f312(f90(x85332),x85335),x85333))),f312(f312(f90(x85332),x85333),x85331)),f312(f312(f21(x85332),f312(f312(f268(x85332),x85334),x85333)),f312(f312(f268(x85332),x85335),x85331)))
% 173.53/173.43 [8542]~E(x85422,f312(x85423,x85421))+E(x85421,f824(x85422,x85423,x85424,x85425))+~P19(x85425,x85424,x85423,f235(f860(x85425,a845)))+~P22(f312(f312(f314(x85424),x85422),f312(f290(x85425,x85424,x85423),f235(f860(x85425,a845)))))
% 173.53/173.43 [8734]~P112(x87341)+~P22(f312(f312(f228(x87341),f312(f84(x87341),x87342)),x87344))+P22(f312(f312(f228(x87341),f312(f312(f90(x87341),f312(f84(x87341),x87342)),f312(f84(x87341),x87343))),f312(f312(f90(x87341),x87344),x87345)))+~P22(f312(f312(f228(x87341),f312(f84(x87341),x87343)),x87345))
% 173.53/173.43 [8751]~P21(x87511,x87515,x87514)+P34(x87511,x87512,x87513)+P22(f312(f312(f314(f851(x87511)),f638(x87514,x87515,x87511,x87512)),x87515))+~P22(f312(f312(f314(f851(x87511)),x87513),x87514))
% 173.53/173.43 [8853]~P19(x88531,x88533,x88535,x88532)+~P22(f312(f70(x88533),x88534))+P22(f312(f312(f227(a852),f312(f53(x88531),x88532)),f312(f53(x88533),x88534)))+~P22(f312(f312(f227(f860(x88533,a845)),f312(f290(x88531,x88533,x88535),x88532)),x88534))
% 173.53/173.43 [8926]~P72(x89262)+~P19(x89261,x89261,x89264,x89265)+~P22(f312(f70(x89261),x89265))+E(f312(f312(f9(x89261,x89262),f312(f82(x89261,x89262,x89261,x89263),x89264)),x89265),f312(f312(f9(x89261,x89262),x89263),f312(f290(x89261,x89261,x89264),x89265)))
% 173.53/173.43 [8927]~P26(x89272)+~P19(x89271,x89271,x89274,x89275)+~P22(f312(f70(x89271),x89275))+E(f312(f312(f6(x89271,x89272),f312(f82(x89271,x89272,x89271,x89273),x89274)),x89275),f312(f312(f6(x89271,x89272),x89273),f312(f290(x89271,x89271,x89274),x89275)))
% 173.53/173.43 [9074]~P19(x90742,x90743,x90745,x90741)+E(x90741,f189(f860(x90742,a845)))+E(f312(f290(x90743,x90742,f829(x90744,x90743,x90742,x90741)),x90744),x90741)+~P22(f312(f312(f227(f860(x90743,a845)),f312(f290(x90742,x90743,x90745),x90741)),x90744))
% 173.53/173.43 [9545]~P103(x95455)+~P31(x95455)+P22(f312(f312(f314(x95451),f408(x95452,x95453,x95451,x95454,x95455)),x95453))+~P22(f312(f312(f228(x95455),x95454),f312(f312(f50(x95451,x95455),x95453),x95452)))
% 173.53/173.43 [9549]~P103(x95491)+~P31(x95491)+P22(f312(f312(f228(x95491),x95492),f312(x95493,f408(x95493,x95494,x95495,x95492,x95491))))+~P22(f312(f312(f228(x95491),x95492),f312(f312(f50(x95495,x95491),x95494),x95493)))
% 173.53/173.43 [9628]~P68(x96281)+~P22(f312(f75(x96281,x96281,f90(x96281),x96282,x96283),x96285))+P22(f312(f312(f314(x96281),x96282),x96283))+P22(f312(f75(x96281,x96281,f90(x96281),x96284,f312(f312(f289(x96281),x96282),x96283)),f312(f312(f90(x96281),x96284),x96285)))
% 173.53/173.43 [9846]~P72(x98462)+~P22(f312(f70(x98461),x98465))+E(f312(f312(f9(x98461,x98462),f312(f312(f7(x98461,x98462,x98462),f312(f312(f18(x98461,x98462,f860(x98462,x98462)),f312(f312(f8(a845,f860(x98462,f860(x98462,x98462)),x98461),f108(x98462)),f312(a309,x98463))),x98464)),f87(x98462))),x98465),f87(x98462))+P22(f312(f312(f314(x98461),x98463),x98465))
% 173.53/173.43 [9847]~P26(x98472)+~P22(f312(f70(x98471),x98475))+E(f312(f312(f6(x98471,x98472),f312(f312(f7(x98471,x98472,x98472),f312(f312(f18(x98471,x98472,f860(x98472,x98472)),f312(f312(f8(a845,f860(x98472,f860(x98472,x98472)),x98471),f108(x98472)),f312(a309,x98473))),x98474)),f2(x98472))),x98475),f2(x98472))+P22(f312(f312(f314(x98471),x98473),x98475))
% 173.53/173.43 [9848]~P72(x98482)+~P22(f312(f70(x98481),x98485))+E(f312(f312(f9(x98481,x98482),f312(f312(f7(x98481,x98482,x98482),f312(f312(f18(x98481,x98482,f860(x98482,x98482)),f312(f312(f8(a845,f860(x98482,f860(x98482,x98482)),x98481),f108(x98482)),f312(a309,x98483))),x98484)),f87(x98482))),x98485),f312(x98484,x98483))+~P22(f312(f312(f314(x98481),x98483),x98485))
% 173.53/173.43 [9849]~P26(x98492)+~P22(f312(f70(x98491),x98495))+E(f312(f312(f6(x98491,x98492),f312(f312(f7(x98491,x98492,x98492),f312(f312(f18(x98491,x98492,f860(x98492,x98492)),f312(f312(f8(a845,f860(x98492,f860(x98492,x98492)),x98491),f108(x98492)),f312(a309,x98493))),x98494)),f2(x98492))),x98495),f312(x98494,x98493))+~P22(f312(f312(f314(x98491),x98493),x98495))
% 173.53/173.43 [9909]~P72(x99092)+~P22(f312(f70(x99091),x99095))+E(f312(f312(f9(x99091,x99092),f312(f312(f7(x99091,x99092,x99092),f312(f312(f18(x99091,x99092,f860(x99092,x99092)),f312(f312(f8(a845,f860(x99092,f860(x99092,x99092)),x99091),f108(x99092)),f312(f312(f7(x99091,x99091,a845),a309),x99093))),x99094)),f87(x99092))),x99095),f87(x99092))+P22(f312(f312(f314(x99091),x99093),x99095))
% 173.53/173.43 [9910]~P26(x99102)+~P22(f312(f70(x99101),x99105))+E(f312(f312(f6(x99101,x99102),f312(f312(f7(x99101,x99102,x99102),f312(f312(f18(x99101,x99102,f860(x99102,x99102)),f312(f312(f8(a845,f860(x99102,f860(x99102,x99102)),x99101),f108(x99102)),f312(f312(f7(x99101,x99101,a845),a309),x99103))),x99104)),f2(x99102))),x99105),f2(x99102))+P22(f312(f312(f314(x99101),x99103),x99105))
% 173.53/173.43 [9912]~P72(x99122)+~P22(f312(f70(x99121),x99125))+E(f312(f312(f9(x99121,x99122),f312(f312(f7(x99121,x99122,x99122),f312(f312(f18(x99121,x99122,f860(x99122,x99122)),f312(f312(f8(a845,f860(x99122,f860(x99122,x99122)),x99121),f108(x99122)),f312(f312(f7(x99121,x99121,a845),a309),x99123))),x99124)),f87(x99122))),x99125),f312(x99124,x99123))+~P22(f312(f312(f314(x99121),x99123),x99125))
% 173.53/173.43 [9913]~P26(x99132)+~P22(f312(f70(x99131),x99135))+E(f312(f312(f6(x99131,x99132),f312(f312(f7(x99131,x99132,x99132),f312(f312(f18(x99131,x99132,f860(x99132,x99132)),f312(f312(f8(a845,f860(x99132,f860(x99132,x99132)),x99131),f108(x99132)),f312(f312(f7(x99131,x99131,a845),a309),x99133))),x99134)),f2(x99132))),x99135),f312(x99134,x99133))+~P22(f312(f312(f314(x99131),x99133),x99135))
% 173.53/173.43 [7697]~P30(x76972)+~P22(f312(f70(x76971),x76974))+E(f312(f312(f6(x76971,x76972),x76973),f312(f312(f21(f860(x76971,a845)),x76974),f312(f312(f289(x76971),x76975),f189(f860(x76971,a845))))),f312(f312(f6(x76971,x76972),x76973),x76974))+P22(f312(f312(f314(x76971),x76975),x76974))
% 173.53/173.43 [8200]~P120(x82002)+~P22(f312(f70(x82001),x82004))+E(f312(f312(f6(x82001,x82002),x82003),f312(f312(f21(f860(x82001,a845)),x82004),f312(f312(f289(x82001),x82005),f189(f860(x82001,a845))))),f312(f312(f21(x82002),f312(f312(f6(x82001,x82002),x82003),x82004)),f312(x82003,x82005)))+~P22(f312(f312(f314(x82001),x82005),x82004))
% 173.53/173.43 [8201]~P30(x82012)+~P22(f312(f70(x82011),x82014))+E(f312(f312(f6(x82011,x82012),x82013),f312(f312(f21(f860(x82011,a845)),x82014),f312(f312(f289(x82011),x82015),f189(f860(x82011,a845))))),f312(f312(f21(x82012),f312(f312(f6(x82011,x82012),x82013),x82014)),f312(x82013,x82015)))+~P22(f312(f312(f314(x82011),x82015),x82014))
% 173.53/173.43 [8234]~P30(x82341)+~P22(f312(f70(x82342),x82344))+E(f312(f312(f21(x82341),f312(f312(f6(x82342,x82341),x82343),x82344)),f312(f312(f6(x82342,x82341),x82343),x82345)),f312(f312(f6(x82342,x82341),x82343),f312(f312(f21(f860(x82342,a845)),x82344),x82345)))+~P22(f312(f312(f227(f860(x82342,a845)),x82345),x82344))
% 173.53/173.43 [8256]P22(f312(f70(x82561),f312(x82562,x82563)))+~P22(f312(f70(x82564),x82565))+~P22(f312(f312(f314(x82564),x82563),x82565))+~P22(f312(f70(x82561),f312(f312(f50(x82564,f860(x82561,a845)),x82565),x82562)))
% 173.53/173.43 [8374]~P98(x83745)+~P98(x83741)+~P49(x83745,x83741,x83742)+P22(f312(f312(f227(x83741),f312(f312(f124(x83741),f312(x83742,x83743)),f312(x83742,x83744))),f312(x83742,f312(f312(f124(x83745),x83743),x83744))))
% 173.53/173.43 [8375]~P98(x83751)+~P103(x83755)+~P49(x83755,x83751,x83752)+P22(f312(f312(f227(x83751),f312(f312(f124(x83751),f312(x83752,x83753)),f312(x83752,x83754))),f312(x83752,f312(f312(f226(x83755),x83753),x83754))))
% 173.53/173.43 [8697]~P3(x86971,x86975,x86974)+~E(f312(f264(x86971,x86971,x86974),f312(f312(f289(x86971),x86972),f189(f860(x86971,a845)))),f312(f264(x86971,x86971,x86974),f312(f312(f289(x86971),x86973),f189(f860(x86971,a845)))))+~P22(f312(f312(f314(x86971),x86973),x86975))+P22(f312(f312(f314(f859(x86971,x86971)),f312(f312(f239(x86971,x86971),x86972),x86973)),x86974))
% 173.53/173.43 [8995]~P22(f312(x89951,x89955))+P22(f312(x89951,f807(x89951,x89952,x89953,x89954)))+P22(f312(x89951,f806(x89951,x89952,x89953,x89954)))+~P22(f312(f312(f314(x89954),x89955),f312(f312(f124(f860(x89954,a845)),x89953),x89952)))
% 173.53/173.43 [9180]~P22(f312(x91801,x91805))+P22(f312(x91801,f806(x91801,x91802,x91803,x91804)))+P22(f312(f312(f314(x91804),f807(x91801,x91802,x91803,x91804)),x91802))+~P22(f312(f312(f314(x91804),x91805),f312(f312(f124(f860(x91804,a845)),x91803),x91802)))
% 173.53/173.43 [9181]~P22(f312(x91811,x91815))+P22(f312(x91811,f807(x91811,x91812,x91813,x91814)))+P22(f312(f312(f314(x91814),f806(x91811,x91812,x91813,x91814)),x91813))+~P22(f312(f312(f314(x91814),x91815),f312(f312(f124(f860(x91814,a845)),x91813),x91812)))
% 173.53/173.43 [9187]P22(f312(x91871,x91872))+~P22(f312(x91871,f810(x91871,x91873,x91874,x91875)))+~P22(f312(x91871,f809(x91871,x91873,x91874,x91875)))+~P22(f312(f312(f314(x91875),x91872),f312(f312(f124(f860(x91875,a845)),x91874),x91873)))
% 173.53/173.43 [9228]E(x92281,x92282)+~P22(f312(f312(f314(f859(x92283,x92283)),f312(f312(f239(x92283,x92283),x92281),x92282)),f287(x92283,x92285)))+P22(f312(f312(f314(x92283),x92281),x92284))+~P22(f312(f312(f227(f860(f859(x92283,x92283),a845)),x92285),f312(f312(f247(x92283,x92283),x92284),f312(f16(f860(x92283,a845),x92283),x92284))))
% 173.53/173.43 [9245]P22(f312(x92451,x92452))+~P22(f312(x92451,f809(x92451,x92454,x92455,x92453)))+P22(f312(f312(f314(x92453),f810(x92451,x92454,x92455,x92453)),x92454))+~P22(f312(f312(f314(x92453),x92452),f312(f312(f124(f860(x92453,a845)),x92455),x92454)))
% 173.53/173.43 [9246]P22(f312(x92461,x92462))+~P22(f312(x92461,f810(x92461,x92464,x92465,x92463)))+P22(f312(f312(f314(x92463),f809(x92461,x92464,x92465,x92463)),x92465))+~P22(f312(f312(f314(x92463),x92462),f312(f312(f124(f860(x92463,a845)),x92465),x92464)))
% 173.53/173.43 [9306]P22(f312(x93061,x93062))+P22(f312(f312(f314(x93063),f810(x93061,x93064,x93065,x93063)),x93064))+P22(f312(f312(f314(x93063),f809(x93061,x93064,x93065,x93063)),x93065))+~P22(f312(f312(f314(x93063),x93062),f312(f312(f124(f860(x93063,a845)),x93065),x93064)))
% 173.53/173.43 [9308]~P22(f312(x93082,x93085))+P22(f312(f312(f314(x93081),f807(x93082,x93083,x93084,x93081)),x93083))+P22(f312(f312(f314(x93081),f806(x93082,x93083,x93084,x93081)),x93084))+~P22(f312(f312(f314(x93081),x93085),f312(f312(f124(f860(x93081,a845)),x93084),x93083)))
% 173.53/173.43 [9456]~P3(x94561,x94565,x94564)+~P22(f312(f312(f314(x94561),x94563),x94565))+P22(f312(f312(f314(f859(x94561,x94561)),f312(f312(f239(x94561,x94561),x94562),x94563)),x94564))+~P22(f312(f312(f227(f860(x94561,a845)),f312(f264(x94561,x94561,x94564),f312(f312(f289(x94561),x94563),f189(f860(x94561,a845))))),f312(f264(x94561,x94561,x94564),f312(f312(f289(x94561),x94562),f189(f860(x94561,a845))))))
% 173.53/173.43 [9574]~P103(x95745)+~P31(x95745)+P22(f312(f312(f314(x95741),f640(x95742,x95743,x95744,x95741,x95745)),x95744))+~P22(f312(f312(f228(x95745),f312(f312(f51(x95741,x95745),x95744),x95743)),x95742))
% 173.53/173.43 [9606]~P25(x96065)+~P82(x96065)+P22(f312(f312(f314(x96061),f612(x96062,x96063,x96064,x96061,x96065)),f312(f168(x96061),x96064)))+P22(f312(f312(f227(x96065),f312(f162(x96065),f312(f312(f150(x96061,x96065),x96063),x96064))),f312(f162(x96065),f312(f312(f150(x96061,x96065),x96062),x96064))))
% 173.53/173.43 [9718]~P103(x97181)+~P31(x97181)+P22(f312(f312(f228(x97181),f312(x97182,f640(x97183,x97182,x97184,x97185,x97181))),x97183))+~P22(f312(f312(f228(x97181),f312(f312(f51(x97185,x97181),x97184),x97182)),x97183))
% 173.53/173.43 [9865]~P25(x98651)+~P82(x98651)+~P22(f312(f312(f227(x98651),f312(x98653,f612(x98655,x98653,x98654,x98652,x98651))),f312(x98655,f612(x98655,x98653,x98654,x98652,x98651))))+P22(f312(f312(f227(x98651),f312(f162(x98651),f312(f312(f150(x98652,x98651),x98653),x98654))),f312(f162(x98651),f312(f312(f150(x98652,x98651),x98655),x98654))))
% 173.53/173.43 [8549]~P72(x85491)+~P22(f312(f70(x85494),x85495))+~P22(f312(f312(f314(x85494),x85493),x85495))+E(f312(f312(f90(x85491),f312(x85492,x85493)),f312(f312(f9(x85494,x85491),x85492),f312(f312(f21(f860(x85494,a845)),x85495),f312(f312(f289(x85494),x85493),f189(f860(x85494,a845)))))),f312(f312(f9(x85494,x85491),x85492),x85495))
% 173.53/173.43 [8551]~P26(x85511)+~P22(f312(f70(x85514),x85515))+~P22(f312(f312(f314(x85514),x85513),x85515))+E(f312(f312(f89(x85511),f312(x85512,x85513)),f312(f312(f6(x85514,x85511),x85512),f312(f312(f21(f860(x85514,a845)),x85515),f312(f312(f289(x85514),x85513),f189(f860(x85514,a845)))))),f312(f312(f6(x85514,x85511),x85512),x85515))
% 173.53/173.43 [8604]~P13(x86041,x86044,x86045)+~P22(f312(f70(x86041),x86042))+E(f312(f312(f21(f860(x86041,a845)),x86042),f312(f312(f289(x86041),x86043),f189(f860(x86041,a845)))),f189(f860(x86041,a845)))+E(f312(f312(x86044,x86043),f312(x86045,f312(f312(f21(f860(x86041,a845)),x86042),f312(f312(f289(x86041),x86043),f189(f860(x86041,a845)))))),f312(x86045,f312(f312(f289(x86041),x86043),x86042)))
% 173.53/173.43 [8975]~P26(x89751)+~P22(f312(f70(x89752),x89755))+~P22(f312(f70(x89752),x89754))+E(f312(f312(f89(x89751),f312(f312(f6(x89752,x89751),x89753),f312(f312(f124(f860(x89752,a845)),x89754),x89755))),f312(f312(f6(x89752,x89751),x89753),f312(f312(f115(f860(x89752,a845)),x89754),x89755))),f312(f312(f89(x89751),f312(f312(f6(x89752,x89751),x89753),x89754)),f312(f312(f6(x89752,x89751),x89753),x89755)))
% 173.53/173.43 [8977]~P72(x89771)+~P22(f312(f70(x89772),x89775))+~P22(f312(f70(x89772),x89774))+E(f312(f312(f90(x89771),f312(f312(f9(x89772,x89771),x89773),f312(f312(f124(f860(x89772,a845)),x89774),x89775))),f312(f312(f9(x89772,x89771),x89773),f312(f312(f115(f860(x89772,a845)),x89774),x89775))),f312(f312(f90(x89771),f312(f312(f9(x89772,x89771),x89773),x89774)),f312(f312(f9(x89772,x89771),x89773),x89775)))
% 173.53/173.43 [9116]~P30(x91161)+~P22(f312(f70(x91162),x91165))+~P22(f312(f70(x91162),x91164))+E(f312(f312(f21(x91161),f312(f312(f89(x91161),f312(f312(f6(x91162,x91161),x91163),x91164)),f312(f312(f6(x91162,x91161),x91163),x91165))),f312(f312(f6(x91162,x91161),x91163),f312(f312(f115(f860(x91162,a845)),x91164),x91165))),f312(f312(f6(x91162,x91161),x91163),f312(f312(f124(f860(x91162,a845)),x91164),x91165)))
% 173.53/173.43 [9318]~P19(x93181,x93182,x93183,x93185)+~P19(x93181,x93182,x93183,x93184)+P19(x93181,x93182,x93183,f312(f312(f124(f860(x93181,a845)),x93184),x93185))+~E(f312(f312(f115(f860(x93182,a845)),f312(f290(x93181,x93182,x93183),f312(f312(f21(f860(x93181,a845)),x93184),x93185))),f312(f290(x93181,x93182,x93183),f312(f312(f21(f860(x93181,a845)),x93185),x93184))),f189(f860(x93182,a845)))
% 173.53/173.43 [9425]E(x94251,f2(a1))+~P22(f312(f312(f228(a1),f2(a1)),x94253))+~P22(f312(f57(x94252,x94251),f312(f312(f239(a1,a1),x94254),x94255)))+P22(f312(f57(x94252,f312(f312(f90(a1),x94251),x94253)),f312(f312(f239(a1,a1),f312(f47(a1,x94254),x94253)),f312(f312(f89(a1),f312(f312(f90(a1),x94251),f54(a1,x94254,x94253))),x94255))))
% 173.53/173.43 [9433]~P22(f312(f312(f228(a852),f2(a852)),x94333))+~P22(f312(f312(f228(a852),f2(a852)),x94332))+~P22(f312(f56(x94331,x94332),f312(f312(f239(a852,a852),x94334),x94335)))+P22(f312(f56(x94331,f312(f312(f90(a852),x94332),x94333)),f312(f312(f239(a852,a852),f312(f47(a852,x94334),x94333)),f312(f312(f89(a852),f312(f312(f90(a852),x94332),f54(a852,x94334,x94333))),x94335))))
% 173.53/173.43 [9490]~P72(x94901)+~P22(f312(f70(x94902),x94905))+~P22(f312(f70(x94902),x94904))+E(f312(f312(f90(x94901),f312(f312(f312(f74(x94901,x94902,f90(x94901)),x94903),f87(x94901)),f312(f312(f124(f860(x94902,a845)),x94904),x94905))),f312(f312(f312(f74(x94901,x94902,f90(x94901)),x94903),f87(x94901)),f312(f312(f115(f860(x94902,a845)),x94904),x94905))),f312(f312(f90(x94901),f312(f312(f312(f74(x94901,x94902,f90(x94901)),x94903),f87(x94901)),x94904)),f312(f312(f312(f74(x94901,x94902,f90(x94901)),x94903),f87(x94901)),x94905)))
% 173.53/173.43 [9492]~E(f312(f312(f169(x94921),x94925),x94922),f312(f312(f169(x94921),x94925),x94923))+P22(f312(f312(f314(f859(f853(x94921),f853(x94921))),f312(f312(f239(f853(x94921),f853(x94921)),x94922),x94923)),f143(x94921,x94924)))+~P22(f312(f312(f228(a852),x94925),f312(f312(f225(a852),f312(f190(f853(x94921)),x94922)),f312(f190(f853(x94921)),x94923))))+~P22(f312(f312(f314(f859(x94921,x94921)),f312(f312(f239(x94921,x94921),f312(f312(f161(x94921),x94922),x94925)),f312(f312(f161(x94921),x94923),x94925))),x94924))
% 173.53/173.43 [9594]~P23(x95945)+~P82(x95945)+P22(f312(f312(f314(x95941),f487(x95942,x95943,x95944,x95941,x95945)),x95944))+P22(f312(f312(f227(x95945),f312(f312(f6(x95941,x95945),x95943),x95944)),f312(f312(f90(x95945),f312(f114(x95945),f312(f53(x95941),x95944))),x95942)))
% 173.53/173.43 [9791]~P23(x97911)+~P82(x97911)+~P22(f312(f312(f227(x97911),f312(x97913,f487(x97915,x97913,x97914,x97912,x97911))),x97915))+P22(f312(f312(f227(x97911),f312(f312(f6(x97912,x97911),x97913),x97914)),f312(f312(f90(x97911),f312(f114(x97911),f312(f53(x97912),x97914))),x97915)))
% 173.53/173.43 [8576]E(f312(f312(f129(x85761),x85762),x85763),f312(f312(f129(x85761),x85764),x85765))+~E(f312(f312(f169(x85761),f312(f190(f853(x85761)),x85762)),x85764),x85762)+~E(f312(f312(f129(x85761),f312(f312(f134(x85761),f312(f190(f853(x85761)),x85762)),x85764)),x85765),x85763)+P22(f312(f312(f227(a852),f312(f190(f853(x85761)),x85764)),f312(f190(f853(x85761)),x85762)))
% 173.53/173.43 [8696]E(f312(f312(f129(x86961),x86962),x86963),f312(f312(f129(x86961),x86964),x86965))+~E(f312(f312(f169(x86961),f312(f190(f853(x86961)),x86962)),x86964),x86962)+~E(x86963,f312(f312(f129(x86961),f312(f312(f134(x86961),f312(f190(f853(x86961)),x86962)),x86964)),x86965))+~P22(f312(f312(f227(a852),f312(f190(f853(x86961)),x86962)),f312(f190(f853(x86961)),x86964)))
% 173.53/173.43 [9931]~P22(f312(x99315,x99314))+~P22(f312(f70(x99312),f312(f233(x99312),x99315)))+P22(f312(f70(x99311),f312(f233(x99311),f312(f312(f7(x99311,x99312,a845),x99313),x99314))))+~P22(f312(f70(x99311),f312(f233(x99311),f312(f312(f8(f860(x99312,a845),a845,x99311),f96(x99312)),f312(f312(f8(f860(x99312,a845),f860(x99312,a845),x99311),f312(f18(x99312,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99312),a310),x99315))),x99313)))))
% 173.53/173.43 [8371]~P14(x83715,x83711,x83716,x83712)+E(f312(f82(x83711,x83711,x83711,f312(x83712,x83713)),f312(x83712,x83714)),f312(f82(x83711,x83711,x83711,f312(x83712,x83714)),f312(x83712,x83713)))+~P22(f312(f70(x83715),x83714))+~P22(f312(f70(x83715),x83713))
% 173.53/173.43 [7755]~P19(x77551,x77552,x77554,x77553)+~E(f312(x77554,x77556),x77555)+E(f312(f86(x77551,x77552,x77553,x77554),x77555),x77556)+~P22(f312(f312(f314(x77551),x77556),x77553))
% 173.53/173.43 [7942]~P15(x79426,x79421,x79424,x79422)+E(f312(f82(x79421,x79421,x79421,f312(x79422,x79423)),f312(x79424,x79425)),f312(x79422,x79423))+~P22(f312(f70(x79426),x79423))+~P22(f312(f312(f314(x79426),x79425),x79423))
% 173.53/173.43 [9164]~P14(x91643,x91641,x91646,x91642)+E(f312(f82(x91641,x91641,x91641,f312(x91642,f312(f312(f21(f860(x91643,a845)),x91644),f312(f312(f289(x91643),x91645),f189(f860(x91643,a845)))))),f312(x91646,x91645)),f312(x91642,x91644))+~P22(f312(f70(x91643),x91644))+~P22(f312(f312(f314(x91643),x91645),x91644))
% 173.53/173.43 [6841]~P60(x68411)+~E(f54(x68411,x68413,x68414),f54(x68411,x68416,x68414))+~E(f54(x68411,x68412,x68414),f54(x68411,x68415,x68414))+E(f54(x68411,f312(f312(f89(x68411),x68412),x68413),x68414),f54(x68411,f312(f312(f89(x68411),x68415),x68416),x68414))
% 173.53/173.43 [6842]~P61(x68421)+~E(f54(x68421,x68423,x68424),f54(x68421,x68426,x68424))+~E(f54(x68421,x68422,x68424),f54(x68421,x68425,x68424))+E(f54(x68421,f312(f312(f21(x68421),x68422),x68423),x68424),f54(x68421,f312(f312(f21(x68421),x68425),x68426),x68424))
% 173.53/173.43 [6843]~P60(x68431)+~E(f54(x68431,x68433,x68434),f54(x68431,x68436,x68434))+~E(f54(x68431,x68432,x68434),f54(x68431,x68435,x68434))+E(f54(x68431,f312(f312(f90(x68431),x68432),x68433),x68434),f54(x68431,f312(f312(f90(x68431),x68435),x68436),x68434))
% 173.53/173.43 [7712]~P31(x77121)+P22(f312(f312(f227(x77121),x77122),f312(x77123,x77124)))+~P22(f312(f312(f314(x77125),x77124),x77126))+~P22(f312(f312(f227(x77121),x77122),f312(f312(f51(x77125,x77121),x77126),x77123)))
% 173.53/173.43 [7958]~P103(x79583)+~P22(f312(x79582,x79585))+~P33(x79583,f312(f312(f150(x79581,x79583),x79584),x79586))+E(f312(f132(x79581,x79582),f312(f312(f145(x79581,x79583,x79584),x79585),x79586)),f312(f312(f145(x79581,x79583,x79584),x79585),f312(f132(x79581,x79582),x79586)))
% 173.53/173.43 [7981]E(x79811,x79812)+E(x79813,f2(a1))+~P22(f312(f57(x79814,x79813),f312(f312(f239(a1,a1),x79815),x79812)))+~P22(f312(f57(x79814,x79813),f312(f312(f239(a1,a1),x79816),x79811)))
% 173.53/173.43 [7982]E(x79821,x79822)+E(x79823,f2(a1))+~P22(f312(f57(x79824,x79823),f312(f312(f239(a1,a1),x79822),x79825)))+~P22(f312(f57(x79824,x79823),f312(f312(f239(a1,a1),x79821),x79826)))
% 173.53/173.43 [8002]~P14(x80022,x80025,x80026,x80021)+~P22(f312(f70(x80022),x80024))+E(f312(x80021,f312(f312(f289(x80022),x80023),x80024)),f312(f82(x80025,x80025,x80025,f312(x80021,x80024)),f312(x80026,x80023)))+P22(f312(f312(f314(x80022),x80023),x80024))
% 173.53/173.43 [8237]~P15(x82375,x82371,x82376,x82372)+E(f312(f82(x82371,x82371,x82371,f312(x82372,x82373)),f312(x82372,x82374)),f312(x82372,x82373))+~P22(f312(f70(x82375),x82373))+~P22(f312(f312(f227(f860(x82375,a845)),x82374),x82373))
% 173.53/173.43 [9363]~P19(x93631,x93632,x93634,x93633)+~P22(f312(f312(f314(x93632),x93635),f312(f290(x93631,x93632,x93634),x93633)))+P22(f312(f312(f314(x93631),f312(f86(x93631,x93632,x93633,x93634),x93635)),x93636))+~P22(f312(f312(f227(f860(x93631,a845)),x93633),x93636))
% 173.53/173.43 [9733]~P26(x97332)+~E(f502(x97331,x97333,x97335,x97336,x97334,x97332),f503(x97331,x97333,x97335,x97336,x97334,x97332))+~P22(f312(f70(x97334),x97336))+E(f312(f312(f6(x97331,x97332),x97333),f312(f290(x97334,x97331,x97335),x97336)),f312(f312(f6(x97334,x97332),f312(f82(x97331,x97332,x97334,x97333),x97335)),x97336))
% 173.53/173.43 [9769]~P26(x97696)+E(f312(x97691,f502(x97692,x97693,x97691,x97694,x97695,x97696)),f312(x97691,f503(x97692,x97693,x97691,x97694,x97695,x97696)))+E(f312(f312(f6(x97692,x97696),x97693),f312(f290(x97695,x97692,x97691),x97694)),f312(f312(f6(x97695,x97696),f312(f82(x97692,x97696,x97695,x97693),x97691)),x97694))+~P22(f312(f70(x97695),x97694))
% 173.53/173.43 [9814]~P26(x98142)+~E(f312(x98143,f312(x98145,f503(x98141,x98143,x98145,x98146,x98144,x98142))),f2(x98142))+~P22(f312(f70(x98144),x98146))+E(f312(f312(f6(x98141,x98142),x98143),f312(f290(x98144,x98141,x98145),x98146)),f312(f312(f6(x98144,x98142),f312(f82(x98141,x98142,x98144,x98143),x98145)),x98146))
% 173.53/173.43 [9875]~P26(x98752)+~P22(f312(f70(x98754),x98756))+E(f312(f312(f6(x98751,x98752),x98753),f312(f290(x98754,x98751,x98755),x98756)),f312(f312(f6(x98754,x98752),f312(f82(x98751,x98752,x98754,x98753),x98755)),x98756))+P22(f312(f312(f314(x98754),f503(x98751,x98753,x98755,x98756,x98754,x98752)),x98756))
% 173.53/173.43 [9876]~P26(x98762)+~P22(f312(f70(x98764),x98766))+E(f312(f312(f6(x98761,x98762),x98763),f312(f290(x98764,x98761,x98765),x98766)),f312(f312(f6(x98764,x98762),f312(f82(x98761,x98762,x98764,x98763),x98765)),x98766))+P22(f312(f312(f314(x98764),f502(x98761,x98763,x98765,x98766,x98764,x98762)),x98766))
% 173.53/173.43 [9953]~P49(f860(f859(x99534,x99535),a845),f860(f859(x99534,x99535),a845),x99536)+~P22(f312(f312(x99531,f564(x99531,x99536,x99533,x99532,x99535,x99534)),f565(x99531,x99536,x99533,x99532,x99535,x99534)))+P22(f312(f312(x99531,x99532),x99533))+~P22(f312(f312(f314(f859(x99534,x99535)),f312(f312(f239(x99534,x99535),x99532),x99533)),f109(f860(f859(x99534,x99535),a845),x99536)))
% 173.53/173.43 [9990]~P72(x99901)+~P22(f312(f70(x99902),x99906))+E(f312(f312(f312(f74(x99901,x99902,f90(x99901)),f312(f312(f18(x99902,f860(x99903,a845),x99901),f312(f312(f7(x99902,x99901,f860(f860(x99903,a845),x99901)),f312(f312(f8(f860(x99903,x99901),f860(x99901,f860(f860(x99903,a845),x99901)),x99902),f74(x99901,x99903,f90(x99901))),x99904)),f87(x99901))),x99905)),f87(x99901)),x99906),f312(f312(f312(f74(x99901,f859(x99902,x99903),f90(x99901)),f312(f249(x99902,x99903,x99901),x99904)),f87(x99901)),f312(f312(f247(x99902,x99903),x99906),x99905)))+P22(f312(f312(f314(x99902),f530(x99904,x99905,x99903,x99906,x99902,x99901)),x99906))
% 173.53/173.43 [10010]~P72(x100101)+~P22(f312(f70(x100102),x100106))+E(f312(f312(f312(f74(x100101,x100102,f90(x100101)),f312(f312(f18(x100102,f860(x100103,a845),x100101),f312(f312(f7(x100102,x100101,f860(f860(x100103,a845),x100101)),f312(f312(f8(f860(x100103,x100101),f860(x100101,f860(f860(x100103,a845),x100101)),x100102),f74(x100101,x100103,f90(x100101))),x100104)),f87(x100101))),x100105)),f87(x100101)),x100106),f312(f312(f312(f74(x100101,f859(x100102,x100103),f90(x100101)),f312(f249(x100102,x100103,x100101),x100104)),f87(x100101)),f312(f312(f247(x100102,x100103),x100106),x100105)))+~P22(f312(f70(x100103),f312(x100105,f530(x100104,x100105,x100103,x100106,x100102,x100101))))
% 173.53/173.43 [8145]~P15(x81452,x81455,x81456,x81451)+~P22(f312(f70(x81452),x81454))+~P22(f312(f70(x81452),x81453))+E(f312(x81451,f312(f312(f124(f860(x81452,a845)),x81453),x81454)),f312(f82(x81455,x81455,x81455,f312(x81451,x81453)),f312(x81451,x81454)))
% 173.53/173.43 [8372]~P31(x83721)+P22(f312(f312(f227(x83721),f312(x83722,x83723)),x83724))+~P22(f312(f312(f314(x83725),x83723),x83726))+~P22(f312(f312(f227(x83721),f312(f312(f50(x83725,x83721),x83726),x83722)),x83724))
% 173.53/173.43 [8774]~P19(x87742,x87741,x87743,x87746)+E(f312(f312(f21(f860(x87741,a845)),f312(f290(x87742,x87741,x87743),x87744)),f312(f290(x87742,x87741,x87743),x87745)),f312(f290(x87742,x87741,x87743),f312(f312(f21(f860(x87742,a845)),x87744),x87745)))+~P22(f312(f312(f227(f860(x87742,a845)),x87745),x87746))+~P22(f312(f312(f227(f860(x87742,a845)),x87744),x87746))
% 173.53/173.43 [8775]~P19(x87752,x87751,x87753,x87756)+E(f312(f312(f115(f860(x87751,a845)),f312(f290(x87752,x87751,x87753),x87754)),f312(f290(x87752,x87751,x87753),x87755)),f312(f290(x87752,x87751,x87753),f312(f312(f115(f860(x87752,a845)),x87754),x87755)))+~P22(f312(f312(f227(f860(x87752,a845)),x87755),x87756))+~P22(f312(f312(f227(f860(x87752,a845)),x87754),x87756))
% 173.53/173.43 [8810]~P22(f312(x88101,x88103))+~P22(f312(f312(f312(f312(a198,x88102),x88103),x88104),x88106))+~P22(f312(f312(f312(f312(a198,f35(x88101,x88102)),x88106),x88104),x88105))+P22(f312(f312(f312(f312(a198,f35(x88101,x88102)),x88103),x88104),x88105))
% 173.53/173.43 [9041]E(x90411,x90412)+~P54(x90413,x90414,x90415)+~P22(f312(f312(f314(f859(x90413,x90414)),f312(f312(f239(x90413,x90414),x90416),x90412)),x90415))+~P22(f312(f312(f314(f859(x90413,x90414)),f312(f312(f239(x90413,x90414),x90416),x90411)),x90415))
% 173.53/173.43 [9809]~P68(x98091)+~E(f312(x98093,f746(x98094,x98096,x98093,x98095,x98092,x98091)),f312(x98096,f746(x98094,x98096,x98093,x98095,x98092,x98091)))+~P22(f312(f70(x98092),x98095))+E(f312(f312(f312(f74(x98091,x98092,f90(x98091)),x98093),x98094),x98095),f312(f312(f312(f74(x98091,x98092,f90(x98091)),x98096),x98094),x98095))
% 173.53/173.43 [9872]~P68(x98721)+~P22(f312(f70(x98722),x98725))+E(f312(f312(f312(f74(x98721,x98722,f90(x98721)),x98723),x98724),x98725),f312(f312(f312(f74(x98721,x98722,f90(x98721)),x98726),x98724),x98725))+P22(f312(f312(f314(x98722),f746(x98724,x98723,x98726,x98725,x98722,x98721)),x98725))
% 173.53/173.43 [8589]~P68(x85891)+~P22(f312(f70(x85892),x85896))+P22(f312(f312(f314(x85892),x85895),x85896))+E(f312(f312(f312(f74(x85891,x85892,f90(x85891)),x85893),x85894),f312(f312(f289(x85892),x85895),x85896)),f312(f312(f90(x85891),f312(x85893,x85895)),f312(f312(f312(f74(x85891,x85892,f90(x85891)),x85893),x85894),x85896)))
% 173.53/173.43 [8636]~P3(x86361,x86366,x86363)+~P9(x86361,f860(x86362,a845),x86363,x86365)+~P22(f312(f312(f314(x86361),x86364),x86366))+E(f312(f312(f50(x86361,f860(x86362,a845)),f312(f264(x86361,x86361,x86363),f312(f312(f289(x86361),x86364),f189(f860(x86361,a845))))),x86365),f312(x86365,x86364))
% 173.53/173.43 [9053]~P14(x90533,x90531,x90536,x90532)+~P22(f312(f70(x90533),x90535))+~P22(f312(f70(x90533),x90534))+E(f312(f82(x90531,x90531,x90531,f312(x90532,f312(f312(f124(f860(x90533,a845)),x90534),x90535))),f312(x90532,f312(f312(f115(f860(x90533,a845)),x90534),x90535))),f312(f82(x90531,x90531,x90531,f312(x90532,x90534)),f312(x90532,x90535)))
% 173.53/173.43 [10012]~P49(f860(f859(x100124,x100125),a845),f860(f859(x100124,x100125),a845),x100126)+P22(f312(f312(x100121,x100122),x100123))+~P22(f312(f312(f314(f859(x100124,x100125)),f312(f312(f239(x100124,x100125),x100122),x100123)),f109(f860(f859(x100124,x100125),a845),x100126)))+P22(f312(f312(f314(f859(x100124,x100125)),f312(f312(f239(x100124,x100125),f564(x100121,x100126,x100123,x100122,x100125,x100124)),f565(x100121,x100126,x100123,x100122,x100125,x100124))),f312(x100126,f312(f312(f115(f860(f859(x100124,x100125),a845)),f109(f860(f859(x100124,x100125),a845),x100126)),f312(f233(f859(x100124,x100125)),f312(f249(x100124,x100125,a845),x100121))))))
% 173.53/173.43 [9382]~E(x93823,f312(f312(f155(x93821,x93822),x93825),x93826))+P22(f312(f312(f314(f859(f853(x93821),f853(x93821))),f312(f312(f239(f853(x93821),f853(x93821)),x93822),x93823)),f153(x93821,x93824)))+~P22(f312(f312(f228(a852),x93825),f312(f190(f853(x93821)),x93822)))+~P22(f312(f312(f314(f859(x93821,x93821)),f312(f312(f239(x93821,x93821),f312(f312(f161(x93821),x93822),x93825)),x93826)),x93824))
% 173.53/173.43 [9889]~P72(x98892)+~P22(f312(f70(x98891),x98896))+P22(f312(f312(f314(x98891),f529(x98894,x98895,x98893,x98896,x98891,x98892)),x98896))+E(f312(f312(f9(x98891,x98892),f312(f312(f18(x98891,f860(x98893,a845),x98892),f312(f312(f8(f860(x98893,x98892),f860(f860(x98893,a845),x98892),x98891),f9(x98893,x98892)),x98894)),x98895)),x98896),f312(f312(f9(f859(x98891,x98893),x98892),f312(f249(x98891,x98893,x98892),x98894)),f312(f312(f247(x98891,x98893),x98896),x98895)))
% 173.53/173.43 [9890]~P26(x98902)+~P22(f312(f70(x98901),x98906))+P22(f312(f312(f314(x98901),f531(x98904,x98905,x98903,x98906,x98901,x98902)),x98906))+E(f312(f312(f6(x98901,x98902),f312(f312(f18(x98901,f860(x98903,a845),x98902),f312(f312(f8(f860(x98903,x98902),f860(f860(x98903,a845),x98902),x98901),f6(x98903,x98902)),x98904)),x98905)),x98906),f312(f312(f6(f859(x98901,x98903),x98902),f312(f249(x98901,x98903,x98902),x98904)),f312(f312(f247(x98901,x98903),x98906),x98905)))
% 173.53/173.43 [9928]~P72(x99282)+~P22(f312(f70(x99281),x99286))+~P22(f312(f70(x99283),f312(x99285,f529(x99284,x99285,x99283,x99286,x99281,x99282))))+E(f312(f312(f9(x99281,x99282),f312(f312(f18(x99281,f860(x99283,a845),x99282),f312(f312(f8(f860(x99283,x99282),f860(f860(x99283,a845),x99282),x99281),f9(x99283,x99282)),x99284)),x99285)),x99286),f312(f312(f9(f859(x99281,x99283),x99282),f312(f249(x99281,x99283,x99282),x99284)),f312(f312(f247(x99281,x99283),x99286),x99285)))
% 173.53/173.43 [9929]~P26(x99292)+~P22(f312(f70(x99291),x99296))+~P22(f312(f70(x99293),f312(x99295,f531(x99294,x99295,x99293,x99296,x99291,x99292))))+E(f312(f312(f6(x99291,x99292),f312(f312(f18(x99291,f860(x99293,a845),x99292),f312(f312(f8(f860(x99293,x99292),f860(f860(x99293,a845),x99292),x99291),f6(x99293,x99292)),x99294)),x99295)),x99296),f312(f312(f6(f859(x99291,x99293),x99292),f312(f249(x99291,x99293,x99292),x99294)),f312(f312(f247(x99291,x99293),x99296),x99295)))
% 173.53/173.43 [9911]~P72(x99112)+~P22(f312(f70(x99111),x99116))+P22(f312(f312(f314(x99111),x99113),x99116))+E(f312(f312(f9(x99111,x99112),f312(f312(f7(x99111,x99112,x99112),f312(f312(f18(x99111,x99112,f860(x99112,x99112)),f312(f312(f8(a845,f860(x99112,f860(x99112,x99112)),x99111),f108(x99112)),f312(f312(f7(x99111,x99111,a845),a309),x99113))),x99114)),x99115)),x99116),f312(f312(f240(x99112),x99115),f312(f53(x99111),x99116)))
% 173.53/173.43 [9916]~P72(x99162)+~P22(f312(f70(x99161),x99166))+~P22(f312(f312(f314(x99161),x99163),x99166))+E(f312(f312(f9(x99161,x99162),f312(f312(f7(x99161,x99162,x99162),f312(f312(f18(x99161,x99162,f860(x99162,x99162)),f312(f312(f8(a845,f860(x99162,f860(x99162,x99162)),x99161),f108(x99162)),f312(f312(f7(x99161,x99161,a845),a309),x99163))),x99164)),x99165)),x99166),f312(f312(f90(x99162),f312(x99164,x99163)),f312(f312(f240(x99162),x99165),f312(f312(f21(a852),f312(f53(x99161),x99166)),f87(a852)))))
% 173.53/173.43 [9982]~P22(f312(f70(x99821),x99825))+~P22(f312(f70(x99822),x99823))+P22(f312(f312(f314(x99822),f561(x99826,x99824,x99823,x99822,x99825,x99821)),x99823))+E(f312(f312(f6(x99821,a852),f312(f312(f8(f860(x99822,a845),a852,x99821),f53(x99822)),f312(f312(f8(f860(x99822,a845),f860(x99822,a845),x99821),f233(x99822)),f312(f312(f8(f860(x99822,a845),f860(x99822,a845),x99821),f312(f18(x99822,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99822),a310),f312(f312(f7(x99822,f860(x99822,a845),a845),f314(x99822)),x99823)))),x99824)))),x99825),f312(f312(f90(a852),x99826),f312(f53(x99822),x99823)))
% 173.53/173.43 [9983]~P22(f312(f70(x99831),x99835))+~P22(f312(f70(x99832),x99833))+P22(f312(f312(f314(x99832),f566(x99836,x99834,x99833,x99832,x99835,x99831)),x99833))+E(f312(f312(f6(x99831,a852),f312(f312(f8(f860(x99832,a845),a852,x99831),f53(x99832)),f312(f312(f8(f860(x99832,a845),f860(x99832,a845),x99831),f233(x99832)),f312(f312(f8(f860(x99832,a845),f860(x99832,a845),x99831),f312(f18(x99832,a845,a845),f312(f312(f8(a845,f860(a845,a845),x99832),a310),f312(f312(f7(x99832,f860(x99832,a845),a845),f314(x99832)),x99833)))),x99834)))),x99835),f312(f312(f6(x99832,a852),x99836),x99833))
% 173.53/173.43 [10015]~P22(f312(f70(x100152),x100153))+~P22(f312(f70(x100151),x100155))+~E(f312(f53(x100151),f312(f233(x100151),f312(f312(f18(x100151,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100151),a310),f312(f312(f7(x100151,f860(x100151,a845),a845),f314(x100151)),x100155))),f312(f312(f7(x100151,x100152,a845),x100154),f561(x100156,x100154,x100153,x100152,x100155,x100151))))),x100156)+E(f312(f312(f6(x100151,a852),f312(f312(f8(f860(x100152,a845),a852,x100151),f53(x100152)),f312(f312(f8(f860(x100152,a845),f860(x100152,a845),x100151),f233(x100152)),f312(f312(f8(f860(x100152,a845),f860(x100152,a845),x100151),f312(f18(x100152,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100152),a310),f312(f312(f7(x100152,f860(x100152,a845),a845),f314(x100152)),x100153)))),x100154)))),x100155),f312(f312(f90(a852),x100156),f312(f53(x100152),x100153)))
% 173.53/173.43 [10017]~P22(f312(f70(x100172),x100173))+~P22(f312(f70(x100171),x100175))+~E(f312(f53(x100171),f312(f233(x100171),f312(f312(f18(x100171,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100171),a310),f312(f312(f7(x100171,f860(x100171,a845),a845),f314(x100171)),x100175))),f312(f312(f7(x100171,x100172,a845),x100174),f566(x100176,x100174,x100173,x100172,x100175,x100171))))),f312(x100176,f566(x100176,x100174,x100173,x100172,x100175,x100171)))+E(f312(f312(f6(x100171,a852),f312(f312(f8(f860(x100172,a845),a852,x100171),f53(x100172)),f312(f312(f8(f860(x100172,a845),f860(x100172,a845),x100171),f233(x100172)),f312(f312(f8(f860(x100172,a845),f860(x100172,a845),x100171),f312(f18(x100172,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100172),a310),f312(f312(f7(x100172,f860(x100172,a845),a845),f314(x100172)),x100173)))),x100174)))),x100175),f312(f312(f6(x100172,a852),x100176),x100173))
% 173.53/173.43 [9459]P22(f312(x94591,x94592))+~P22(f312(f312(f314(x94597),x94592),f312(x94596,x94594)))+~P22(f312(x94591,f404(x94591,x94596,x94595,x94593,x94597)))+~P22(f312(f312(f314(x94593),x94594),x94595))
% 173.53/173.43 [9359]~P68(x93591)+~P19(x93595,x93592,x93596,x93597)+~P22(f312(f70(x93595),x93597))+E(f312(f312(f312(f74(x93591,x93592,f90(x93591)),x93593),x93594),f312(f290(x93595,x93592,x93596),x93597)),f312(f312(f312(f74(x93591,x93595,f90(x93591)),f312(f82(x93592,x93591,x93595,x93593),x93596)),x93594),x93597))
% 173.53/173.43 [9484]~E(f312(f312(f289(x94841),x94845),x94846),f312(f312(f289(x94841),x94842),x94843))+~P22(f312(f75(x94841,x94841,x94844,x94842,x94843),x94847))+P22(f312(f312(f314(x94841),x94842),x94843))+P22(f312(f71(x94841,x94844,f312(f312(f289(x94841),x94845),x94846)),x94847))
% 173.53/173.43 [9563]P22(f312(x95631,x95632))+~P22(f312(f312(f314(x95633),x95632),f312(x95634,x95637)))+~P22(f312(f312(f314(x95636),x95637),x95635))+P22(f312(f312(f314(x95633),f404(x95631,x95634,x95635,x95636,x95633)),f312(f312(f50(x95636,f860(x95633,a845)),x95635),x95634)))
% 173.53/173.43 [9575]~P19(x95752,x95751,x95755,x95754)+~P19(x95751,x95753,x95756,f312(f290(x95752,x95751,x95755),x95754))+E(f312(f312(f82(x95751,x95752,x95753,f86(x95752,x95751,x95754,x95755)),f86(x95751,x95753,f312(f290(x95752,x95751,x95755),x95754),x95756)),x95757),f312(f86(x95752,x95753,x95754,f312(f82(x95751,x95753,x95752,x95756),x95755)),x95757))+~P22(f312(f312(f314(x95753),x95757),f312(f290(x95751,x95753,x95756),f312(f290(x95752,x95751,x95755),x95754))))
% 173.53/173.43 [9636]E(x96361,f2(a1))+~P22(f312(f57(x96363,x96361),f312(f312(f239(a1,a1),x96365),x96367)))+~P22(f312(f57(x96362,x96361),f312(f312(f239(a1,a1),x96364),x96366)))+P22(f312(f57(f312(f312(f89(a1),x96362),x96363),x96361),f312(f312(f239(a1,a1),f312(f312(f89(a1),f312(f312(f89(a1),x96364),x96365)),f312(f47(a1,f312(f312(f89(a1),x96366),x96367)),x96361))),f54(a1,f312(f312(f89(a1),x96366),x96367),x96361))))
% 173.53/173.43 [9642]~P22(f312(f312(f228(a852),f2(a852)),x96423))+~P22(f312(f56(x96422,x96423),f312(f312(f239(a852,a852),x96425),x96427)))+~P22(f312(f56(x96421,x96423),f312(f312(f239(a852,a852),x96424),x96426)))+P22(f312(f56(f312(f312(f89(a852),x96421),x96422),x96423),f312(f312(f239(a852,a852),f312(f312(f89(a852),f312(f312(f89(a852),x96424),x96425)),f312(f47(a852,f312(f312(f89(a852),x96426),x96427)),x96423))),f54(a852,f312(f312(f89(a852),x96426),x96427),x96423))))
% 173.53/173.43 [10014]~P26(x100142)+~P22(f312(f70(x100143),x100145))+~P22(f312(f70(x100141),x100147))+E(f312(f312(f6(x100141,x100142),f312(f312(f18(x100141,f860(x100143,a845),x100142),f312(f312(f8(f860(x100143,x100142),f860(f860(x100143,a845),x100142),x100141),f6(x100143,x100142)),x100144)),f312(f312(f8(f860(x100143,a845),f860(x100143,a845),x100141),f233(x100143)),f312(f312(f8(f860(x100143,a845),f860(x100143,a845),x100141),f312(f18(x100143,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100143),a310),f312(f312(f7(x100143,f860(x100143,a845),a845),f314(x100143)),x100145)))),x100146)))),x100147),f312(f312(f6(x100143,x100142),f312(f312(f18(x100143,f860(x100141,a845),x100142),f312(f312(f8(f860(x100141,x100142),f860(f860(x100141,a845),x100142),x100143),f6(x100141,x100142)),f312(f7(x100141,x100143,x100142),x100144))),f312(f312(f8(f860(x100141,a845),f860(x100141,a845),x100143),f233(x100141)),f312(f312(f8(f860(x100141,a845),f860(x100141,a845),x100143),f312(f18(x100141,a845,a845),f312(f312(f8(a845,f860(a845,a845),x100141),a310),f312(f312(f7(x100141,f860(x100141,a845),a845),f314(x100141)),x100147)))),f312(f7(x100141,x100143,a845),x100146))))),x100145))
% 173.53/173.43 [9523]~P10(x95236,x95231,x95232,x95238,x95233,x95234)+~P3(x95236,x95237,x95238)+P9(x95231,x95232,x95233,f312(x95234,x95235))+~P22(f312(f312(f314(x95236),x95235),x95237))
% 173.53/173.43 [7959]~P34(x79598,x79597,f312(f312(f312(f100(x79598),x79594),x79596),x79591))+P22(f312(f312(x79591,x79592),x79593))+~P22(f312(f312(x79594,x79592),x79595))+~P22(f312(f312(f312(f312(a198,x79596),x79595),x79597),x79593))
% 173.53/173.43 [9147]~P14(x91477,x91471,x91478,x91473)+~P22(f312(f70(x91477),x91475))+~P22(f312(f70(x91477),x91474))+E(f312(f82(x91471,x91471,x91472,f312(x91473,x91474)),f312(f82(x91471,x91471,x91472,f312(x91473,x91475)),x91476)),f312(f82(x91471,x91471,x91472,f312(x91473,x91475)),f312(f82(x91471,x91471,x91472,f312(x91473,x91474)),x91476)))
% 173.53/173.43 [9154]~P39(x91541,x91542,x91543,x91544,x91547)+P39(x91541,x91542,x91543,f312(f312(f155(x91541,x91544),x91545),x91546),f312(f312(f155(x91542,x91547),x91545),x91548))+~P22(f312(f312(x91543,x91546),x91548))+~P22(f312(f312(f228(a852),x91545),f312(f190(f853(x91541)),x91544)))
% 173.53/173.43 [9155]~P39(x91551,x91552,x91553,x91554,x91557)+P39(x91551,x91552,x91553,f312(f312(f155(x91551,x91554),x91555),x91556),f312(f312(f155(x91552,x91557),x91555),x91558))+~P22(f312(f312(x91553,x91556),x91558))+~P22(f312(f312(f228(a852),x91555),f312(f190(f853(x91552)),x91557)))
% 173.53/173.43 [9233]~P19(x92332,x92332,x92335,x92336)+~P16(x92333,x92332,x92337,x92338,x92331)+~P22(f312(f70(x92332),x92336))+E(f312(f312(x92331,f312(f82(x92332,x92333,x92332,x92334),x92335)),x92336),f312(f312(x92331,x92334),f312(f290(x92332,x92332,x92335),x92336)))
% 173.53/173.43 [9521]~P17(x95217,x95212,x95215,x95218,x95216,x95211)+~P22(f312(f70(x95212),x95214))+E(f312(x95211,f312(f312(f289(x95212),x95213),x95214)),f312(f312(x95215,f312(x95216,x95213)),f312(x95211,x95214)))+P22(f312(f312(f314(x95212),x95213),x95214))
% 173.53/173.43 [9132]P22(f312(f312(f314(f859(f853(x91321),f853(x91321))),f312(f312(f239(f853(x91321),f853(x91321)),x91322),x91323)),f153(x91321,x91324)))+~E(x91323,f312(f312(f129(x91321),x91325),f312(f312(f147(x91321),x91326),x91327)))+~E(x91322,f312(f312(f129(x91321),x91325),f312(f312(f147(x91321),x91328),x91327)))+~P22(f312(f312(f314(f859(x91321,x91321)),f312(f312(f239(x91321,x91321),x91328),x91326)),x91324))
% 173.53/173.43 [10056]~P19(x100564,x100562,x100565,x100568)+E(f312(f312(f51(x100561,f860(x100562,a845)),x100563),f312(f312(f8(f860(x100564,a845),f860(x100562,a845),x100561),f290(x100564,x100562,x100565)),x100566)),f312(f290(x100564,x100562,x100565),f312(f312(f51(x100561,f860(x100564,a845)),x100563),x100566)))+~P22(f312(f312(f314(x100561),x100567),x100563))+P22(f312(f312(f314(x100561),f673(x100567,x100566,x100563,x100561,x100568,x100565,x100562,x100564)),x100563))
% 173.53/173.43 [10079]~P19(x100794,x100792,x100795,x100797)+E(f312(f312(f51(x100791,f860(x100792,a845)),x100793),f312(f312(f8(f860(x100794,a845),f860(x100792,a845),x100791),f290(x100794,x100792,x100795)),x100796)),f312(f290(x100794,x100792,x100795),f312(f312(f51(x100791,f860(x100794,a845)),x100793),x100796)))+~P22(f312(f312(f314(x100791),x100798),x100793))+~P22(f312(f312(f227(f860(x100794,a845)),f312(x100796,f673(x100798,x100796,x100793,x100791,x100797,x100795,x100792,x100794))),x100797))
% 173.53/173.43 [9583]~P17(x95837,x95835,x95831,x95838,x95832,x95834)+~P22(f312(f70(x95835),x95836))+~P22(f312(f312(f314(x95835),x95833),x95836))+E(f312(f312(x95831,f312(x95832,x95833)),f312(x95834,f312(f312(f21(f860(x95835,a845)),x95836),f312(f312(f289(x95835),x95833),f189(f860(x95835,a845)))))),f312(x95834,x95836))
% 173.53/173.43 [9591]~P17(x95916,x95913,x95911,x95917,x95918,x95912)+~P22(f312(f70(x95913),x95915))+~P22(f312(f70(x95913),x95914))+E(f312(f312(x95911,f312(x95912,f312(f312(f124(f860(x95913,a845)),x95914),x95915))),f312(x95912,f312(f312(f115(f860(x95913,a845)),x95914),x95915))),f312(f312(x95911,f312(x95912,x95914)),f312(x95912,x95915)))
% 173.53/173.43 [9683]P45(x96831,x96832,x96833,x96834,x96835,f312(f312(x96833,x96836),x96837))+~P45(x96831,x96832,x96833,x96834,f312(f312(f21(f860(x96831,a845)),x96835),f312(f312(f289(x96831),x96838),f189(f860(x96831,a845)))),x96839)+~E(f312(f312(x96833,x96836),x96837),f312(f312(x96833,x96838),x96839))+~P22(f312(f312(f314(x96831),x96838),x96835))
% 173.53/173.43 [10094]P18(x100941,x100942,f312(f312(f289(f851(x100941)),f312(f312(f312(f100(x100941),f312(x100943,f370(x100944,x100945,x100946,x100947,x100943,x100942,x100941,x100948,x100949))),f312(x100947,f370(x100944,x100945,x100946,x100947,x100943,x100942,x100941,x100948,x100949))),f312(x100946,f370(x100944,x100945,x100946,x100947,x100943,x100942,x100941,x100948,x100949)))),f189(f860(f851(x100941),a845))))+~P22(f312(f70(x100949),x100948))+~P18(x100941,x100942,f312(f290(x100949,f851(x100941),f312(f312(f18(x100949,f860(x100941,f860(a847,a845)),f851(x100941)),f312(f312(f18(x100949,a846,f860(f860(x100941,f860(a847,a845)),f851(x100941))),f312(f312(f8(f860(x100941,f860(a847,a845)),f860(a846,f860(f860(x100941,f860(a847,a845)),f851(x100941))),x100949),f100(x100941)),x100943)),x100947)),x100946)),x100948))+P18(x100941,x100942,f312(f290(x100949,f851(x100941),f312(f312(f18(x100949,f860(x100941,f860(a847,a845)),f851(x100941)),f312(f312(f18(x100949,a846,f860(f860(x100941,f860(a847,a845)),f851(x100941))),f312(f312(f8(f860(x100941,f860(a847,a845)),f860(a846,f860(f860(x100941,f860(a847,a845)),f851(x100941))),x100949),f100(x100941)),x100945)),x100947)),x100944)),x100948))
% 173.53/173.43 [10095]~P18(x100951,x100952,f312(f312(f289(f851(x100951)),f312(f312(f312(f100(x100951),f312(x100954,f370(x100956,x100954,x100958,x100955,x100959,x100952,x100951,x100957,x100953))),f312(x100955,f370(x100956,x100954,x100958,x100955,x100959,x100952,x100951,x100957,x100953))),f312(x100956,f370(x100956,x100954,x100958,x100955,x100959,x100952,x100951,x100957,x100953)))),f189(f860(f851(x100951),a845))))+~P22(f312(f70(x100953),x100957))+~P18(x100951,x100952,f312(f290(x100953,f851(x100951),f312(f312(f18(x100953,f860(x100951,f860(a847,a845)),f851(x100951)),f312(f312(f18(x100953,a846,f860(f860(x100951,f860(a847,a845)),f851(x100951))),f312(f312(f8(f860(x100951,f860(a847,a845)),f860(a846,f860(f860(x100951,f860(a847,a845)),f851(x100951))),x100953),f100(x100951)),x100959)),x100955)),x100958)),x100957))+P18(x100951,x100952,f312(f290(x100953,f851(x100951),f312(f312(f18(x100953,f860(x100951,f860(a847,a845)),f851(x100951)),f312(f312(f18(x100953,a846,f860(f860(x100951,f860(a847,a845)),f851(x100951))),f312(f312(f8(f860(x100951,f860(a847,a845)),f860(a846,f860(f860(x100951,f860(a847,a845)),f851(x100951))),x100953),f100(x100951)),x100954)),x100955)),x100956)),x100957))
% 173.53/173.43 [9619]~P10(x96196,x96197,x96198,x96199,x961910,x96191)+E(f312(f312(x96191,x96192),x96193),f312(f312(x96191,x96194),x96195))+~P22(f312(f312(f314(f859(x96197,x96197)),f312(f312(f239(x96197,x96197),x96193),x96195)),x961910))+~P22(f312(f312(f314(f859(x96196,x96196)),f312(f312(f239(x96196,x96196),x96192),x96194)),x96199))
% 173.53/173.43 [9235]~P87(x92352)+E(x92351,f189(f860(x92352,a845)))+~P22(f312(f70(x92352),x92351))+P22(f312(f312(f314(x92352),f11(x92352,x92351)),x92351))+~P22(f312(f312(f314(x92352),f312(f312(f115(x92352),f374(x92351,x92352)),f375(x92351,x92352))),f312(f312(f289(x92352),f374(x92351,x92352)),f312(f312(f289(x92352),f375(x92351,x92352)),f189(f860(x92352,a845))))))
% 173.53/173.43 [9236]~P87(x92362)+E(x92361,f189(f860(x92362,a845)))+~P22(f312(f70(x92362),x92361))+P22(f312(f312(f314(x92362),f10(x92362,x92361)),x92361))+~P22(f312(f312(f314(x92362),f312(f312(f124(x92362),f377(x92361,x92362)),f382(x92361,x92362))),f312(f312(f289(x92362),f377(x92361,x92362)),f312(f312(f289(x92362),f382(x92361,x92362)),f189(f860(x92362,a845))))))
% 173.53/173.43 [9267]~P68(x92672)+E(x92671,f189(f860(x92672,a845)))+~P22(f312(f70(x92672),x92671))+P22(f312(f312(f314(x92672),f312(f72(x92672,f90(x92672)),x92671)),x92671))+~P22(f312(f312(f314(x92672),f312(f312(f90(x92672),f545(x92671,x92672)),f546(x92671,x92672))),f312(f312(f289(x92672),f545(x92671,x92672)),f312(f312(f289(x92672),f546(x92671,x92672)),f189(f860(x92672,a845))))))
% 173.53/173.43 [9273]~P103(x92732)+E(x92731,f189(f860(x92732,a845)))+~P22(f312(f70(x92732),x92731))+P22(f312(f312(f314(x92732),f12(x92732,f226(x92732),x92731)),x92731))+~P22(f312(f312(f314(x92732),f312(f312(f226(x92732),f389(x92731,x92732)),f390(x92731,x92732))),f312(f312(f289(x92732),f389(x92731,x92732)),f312(f312(f289(x92732),f390(x92731,x92732)),f189(f860(x92732,a845))))))
% 173.53/173.43 [9274]~P103(x92742)+E(x92741,f189(f860(x92742,a845)))+~P22(f312(f70(x92742),x92741))+P22(f312(f312(f314(x92742),f13(x92742,f225(x92742),x92741)),x92741))+~P22(f312(f312(f314(x92742),f312(f312(f225(x92742),f391(x92741,x92742)),f392(x92741,x92742))),f312(f312(f289(x92742),f391(x92741,x92742)),f312(f312(f289(x92742),f392(x92741,x92742)),f189(f860(x92742,a845))))))
% 173.53/173.43 [6421]~P84(x64212)+E(x64211,f2(x64212))+~E(f312(f312(f89(x64212),x64213),x64211),f2(x64212))+~P22(f312(f312(f227(x64212),f2(x64212)),x64213))+~P22(f312(f312(f227(x64212),f2(x64212)),x64211))
% 173.53/173.43 [6422]~P84(x64222)+E(x64221,f2(x64222))+~E(f312(f312(f89(x64222),x64221),x64223),f2(x64222))+~P22(f312(f312(f227(x64222),f2(x64222)),x64223))+~P22(f312(f312(f227(x64222),f2(x64222)),x64221))
% 173.53/173.43 [6947]~P103(x69472)+~P33(x69472,x69471)+E(x69471,f127(x69472))+~P22(f312(f312(f314(x69472),x69473),f312(f168(x69472),f649(x69471,x69472))))+P22(f312(f312(f227(x69472),f688(x69471,x69472)),x69473))
% 173.53/173.43 [7114]~P103(x71141)+E(f15(x71141,x71142),x71143)+~P22(f312(f70(x71141),x71142))+~P22(f312(f312(f227(x71141),x71143),f745(x71143,x71142,x71141)))+~P22(f312(f312(f314(x71141),x71143),x71142))
% 173.53/173.43 [7143]~P103(x71431)+~P33(x71431,x71432)+~P33(x71431,x71433)+P33(x71431,f312(f312(f129(x71431),x71432),x71433))+P22(f312(f312(f314(x71431),f646(x71433,x71432,x71431)),f312(f168(x71431),x71432)))
% 173.53/173.43 [7144]~P103(x71441)+~P33(x71441,x71442)+~P33(x71441,x71443)+P33(x71441,f312(f312(f129(x71441),x71442),x71443))+P22(f312(f312(f314(x71441),f647(x71443,x71442,x71441)),f312(f168(x71441),x71443)))
% 173.53/173.43 [7190]~P103(x71901)+E(f14(x71901,x71902),x71903)+~P22(f312(f70(x71901),x71902))+P22(f312(f312(f314(x71901),f747(x71903,x71902,x71901)),x71902))+~P22(f312(f312(f314(x71901),x71903),x71902))
% 173.53/173.43 [7191]~P103(x71911)+E(f15(x71911,x71912),x71913)+~P22(f312(f70(x71911),x71912))+P22(f312(f312(f314(x71911),f745(x71913,x71912,x71911)),x71912))+~P22(f312(f312(f314(x71911),x71913),x71912))
% 173.53/173.43 [7770]~P103(x77701)+E(f14(x77701,x77702),x77703)+~P22(f312(f70(x77701),x77702))+~P22(f312(f312(f314(x77701),x77703),x77702))+~P22(f312(f312(f227(x77701),f747(x77703,x77702,x77701)),x77703))
% 173.53/173.43 [8092]~P103(x80921)+~P33(x80921,x80922)+~P33(x80921,x80923)+P33(x80921,f312(f312(f129(x80921),x80922),x80923))+~P22(f312(f312(f227(x80921),f646(x80923,x80922,x80921)),f647(x80923,x80922,x80921)))
% 173.53/173.43 [8879]~P87(x88792)+E(x88791,f189(f860(x88792,a845)))+~E(f312(f312(f115(x88792),f312(x88793,f433(x88791,x88793,x88792))),f312(x88793,f440(x88791,x88793,x88792))),f312(x88793,f312(f312(f115(x88792),f433(x88791,x88793,x88792)),f440(x88791,x88793,x88792))))+E(f11(x88792,f312(f290(x88792,x88792,x88793),x88791)),f312(x88793,f11(x88792,x88791)))+~P22(f312(f70(x88792),x88791))
% 173.53/173.43 [8880]~P87(x88802)+E(x88801,f189(f860(x88802,a845)))+~E(f312(f312(f124(x88802),f312(x88803,f441(x88801,x88803,x88802))),f312(x88803,f442(x88801,x88803,x88802))),f312(x88803,f312(f312(f124(x88802),f441(x88801,x88803,x88802)),f442(x88801,x88803,x88802))))+E(f10(x88802,f312(f290(x88802,x88802,x88803),x88801)),f312(x88803,f10(x88802,x88801)))+~P22(f312(f70(x88802),x88801))
% 173.53/173.43 [8881]~P103(x88812)+E(x88811,f189(f860(x88812,a845)))+~E(f312(f312(f226(x88812),f312(x88813,f434(x88811,x88813,x88812))),f312(x88813,f437(x88811,x88813,x88812))),f312(x88813,f312(f312(f226(x88812),f434(x88811,x88813,x88812)),f437(x88811,x88813,x88812))))+E(f14(x88812,f312(f290(x88812,x88812,x88813),x88811)),f312(x88813,f14(x88812,x88811)))+~P22(f312(f70(x88812),x88811))
% 173.53/173.43 [8882]~P103(x88822)+E(x88821,f189(f860(x88822,a845)))+~E(f312(f312(f225(x88822),f312(x88823,f438(x88821,x88823,x88822))),f312(x88823,f439(x88821,x88823,x88822))),f312(x88823,f312(f312(f225(x88822),f438(x88821,x88823,x88822)),f439(x88821,x88823,x88822))))+E(f15(x88822,f312(f290(x88822,x88822,x88823),x88821)),f312(x88823,f15(x88822,x88821)))+~P22(f312(f70(x88822),x88821))
% 173.53/173.43 [8953]~P103(x89532)+E(x89531,f189(f860(x89532,a845)))+~E(f312(f312(f226(x89532),f312(x89533,f426(x89531,x89533,x89532))),f312(x89533,f428(x89531,x89533,x89532))),f312(x89533,f312(f312(f226(x89532),f426(x89531,x89533,x89532)),f428(x89531,x89533,x89532))))+E(f12(x89532,f226(x89532),f312(f290(x89532,x89532,x89533),x89531)),f312(x89533,f12(x89532,f226(x89532),x89531)))+~P22(f312(f70(x89532),x89531))
% 173.53/173.43 [8954]~P103(x89542)+E(x89541,f189(f860(x89542,a845)))+~E(f312(f312(f225(x89542),f312(x89543,f435(x89541,x89543,x89542))),f312(x89543,f436(x89541,x89543,x89542))),f312(x89543,f312(f312(f225(x89542),f435(x89541,x89543,x89542)),f436(x89541,x89543,x89542))))+E(f13(x89542,f225(x89542),f312(f290(x89542,x89542,x89543),x89541)),f312(x89543,f13(x89542,f225(x89542),x89541)))+~P22(f312(f70(x89542),x89541))
% 173.53/173.43 [6433]~P68(x64332)+E(x64331,f189(f860(x64332,a845)))+~P22(f312(f70(x64332),x64331))+E(f312(f72(x64332,f90(x64332)),f312(f312(f289(x64332),x64333),x64331)),f312(f312(f90(x64332),x64333),f312(f72(x64332,f90(x64332)),x64331)))+P22(f312(f312(f314(x64332),x64333),x64331))
% 173.53/173.43 [6952]~P87(x69522)+E(f312(f312(f124(x69522),f10(x69522,x69521)),f10(x69522,x69523)),f10(x69522,x69523))+E(x69521,f189(f860(x69522,a845)))+~P22(f312(f70(x69522),x69523))+~P22(f312(f312(f227(f860(x69522,a845)),x69521),x69523))
% 173.53/173.43 [6953]~P87(x69532)+E(f312(f312(f115(x69532),f11(x69532,x69531)),f11(x69532,x69533)),f11(x69532,x69533))+E(x69531,f189(f860(x69532,a845)))+~P22(f312(f70(x69532),x69533))+~P22(f312(f312(f227(f860(x69532,a845)),x69531),x69533))
% 173.53/173.43 [6954]~P103(x69542)+E(f312(f312(f225(x69542),f15(x69542,x69541)),f15(x69542,x69543)),f15(x69542,x69543))+E(x69541,f189(f860(x69542,a845)))+~P22(f312(f70(x69542),x69543))+~P22(f312(f312(f227(f860(x69542,a845)),x69541),x69543))
% 173.53/173.43 [6955]~P103(x69552)+E(f312(f312(f226(x69552),f14(x69552,x69551)),f14(x69552,x69553)),f14(x69552,x69553))+E(x69551,f189(f860(x69552,a845)))+~P22(f312(f70(x69552),x69553))+~P22(f312(f312(f227(f860(x69552,a845)),x69551),x69553))
% 173.53/173.43 [7246]~P103(x72462)+E(x72461,f189(f860(x72462,a845)))+~P22(f312(f70(x72462),x72463))+P22(f312(f312(f227(x72462),f14(x72462,x72461)),f14(x72462,x72463)))+~P22(f312(f312(f227(f860(x72462,a845)),x72461),x72463))
% 173.53/173.43 [7247]~P103(x72472)+E(x72471,f189(f860(x72472,a845)))+~P22(f312(f70(x72472),x72473))+P22(f312(f312(f227(x72472),f15(x72472,x72473)),f15(x72472,x72471)))+~P22(f312(f312(f227(f860(x72472,a845)),x72471),x72473))
% 173.53/173.43 [7304]~P87(x73041)+E(f11(x73041,x73042),x73043)+~P22(f312(f70(x73041),x73042))+~E(f312(f312(f21(f860(x73041,a845)),x73042),f312(f312(f289(x73041),x73043),f189(f860(x73041,a845)))),f189(f860(x73041,a845)))+~P22(f312(f312(f314(x73041),x73043),x73042))
% 173.53/173.43 [7305]~P87(x73051)+E(f10(x73051,x73052),x73053)+~P22(f312(f70(x73051),x73052))+~E(f312(f312(f21(f860(x73051,a845)),x73052),f312(f312(f289(x73051),x73053),f189(f860(x73051,a845)))),f189(f860(x73051,a845)))+~P22(f312(f312(f314(x73051),x73053),x73052))
% 173.53/173.43 [7306]~P103(x73061)+E(f14(x73061,x73062),x73063)+~P22(f312(f70(x73061),x73062))+~E(f312(f312(f21(f860(x73061,a845)),x73062),f312(f312(f289(x73061),x73063),f189(f860(x73061,a845)))),f189(f860(x73061,a845)))+~P22(f312(f312(f314(x73061),x73063),x73062))
% 173.53/173.43 [7307]~P103(x73071)+E(f15(x73071,x73072),x73073)+~P22(f312(f70(x73071),x73072))+~E(f312(f312(f21(f860(x73071,a845)),x73072),f312(f312(f289(x73071),x73073),f189(f860(x73071,a845)))),f189(f860(x73071,a845)))+~P22(f312(f312(f314(x73071),x73073),x73072))
% 173.53/173.43 [7401]~P103(x74011)+E(f12(x74011,f226(x74011),x74012),x74013)+~P22(f312(f70(x74011),x74012))+~E(f312(f312(f21(f860(x74011,a845)),x74012),f312(f312(f289(x74011),x74013),f189(f860(x74011,a845)))),f189(f860(x74011,a845)))+~P22(f312(f312(f314(x74011),x74013),x74012))
% 173.53/173.43 [7402]~P103(x74021)+E(f13(x74021,f225(x74021),x74022),x74023)+~P22(f312(f70(x74021),x74022))+~E(f312(f312(f21(f860(x74021,a845)),x74022),f312(f312(f289(x74021),x74023),f189(f860(x74021,a845)))),f189(f860(x74021,a845)))+~P22(f312(f312(f314(x74021),x74023),x74022))
% 173.53/173.43 [7438]~P103(x74382)+E(x74381,f189(f860(x74382,a845)))+~P22(f312(f70(x74382),x74381))+~P22(f312(f312(f228(x74382),x74383),f540(x74383,x74381,x74382)))+P22(f312(f312(f228(x74382),x74383),f312(f72(x74382,f225(x74382)),x74381)))
% 173.53/173.43 [7439]~P99(x74392)+E(x74391,f189(f860(x74392,a845)))+~P22(f312(f70(x74392),x74391))+~P22(f312(f312(f227(x74392),x74393),f524(x74393,x74391,x74392)))+P22(f312(f312(f227(x74392),x74393),f312(f72(x74392,f115(x74392)),x74391)))
% 173.53/173.43 [7440]~P103(x74402)+E(x74401,f189(f860(x74402,a845)))+~P22(f312(f70(x74402),x74401))+~P22(f312(f312(f227(x74402),x74403),f536(x74403,x74401,x74402)))+P22(f312(f312(f227(x74402),x74403),f312(f72(x74402,f225(x74402)),x74401)))
% 173.53/173.43 [7527]~P99(x75272)+E(x75271,f189(f860(x75272,a845)))+~P22(f312(f70(x75272),x75271))+P22(f312(f312(f314(x75272),f524(x75273,x75271,x75272)),x75271))+P22(f312(f312(f227(x75272),x75273),f312(f72(x75272,f115(x75272)),x75271)))
% 173.53/173.43 [7528]~P103(x75282)+E(x75281,f189(f860(x75282,a845)))+~P22(f312(f70(x75282),x75281))+P22(f312(f312(f314(x75282),f536(x75283,x75281,x75282)),x75281))+P22(f312(f312(f227(x75282),x75283),f312(f72(x75282,f225(x75282)),x75281)))
% 173.53/173.43 [7529]~P103(x75292)+E(x75291,f189(f860(x75292,a845)))+~P22(f312(f70(x75292),x75291))+P22(f312(f312(f314(x75292),f540(x75293,x75291,x75292)),x75291))+P22(f312(f312(f228(x75292),x75293),f312(f72(x75292,f225(x75292)),x75291)))
% 173.53/173.43 [7651]~P103(x76512)+E(x76511,f189(f860(x76512,a845)))+E(f312(f312(f225(x76512),f13(x76512,f225(x76512),x76511)),f13(x76512,f225(x76512),x76513)),f13(x76512,f225(x76512),x76513))+~P22(f312(f70(x76512),x76513))+~P22(f312(f312(f227(f860(x76512,a845)),x76511),x76513))
% 173.53/173.43 [7652]~P103(x76522)+E(x76521,f189(f860(x76522,a845)))+E(f312(f312(f226(x76522),f12(x76522,f226(x76522),x76521)),f12(x76522,f226(x76522),x76523)),f12(x76522,f226(x76522),x76523))+~P22(f312(f70(x76522),x76523))+~P22(f312(f312(f227(f860(x76522,a845)),x76521),x76523))
% 173.53/173.43 [7843]~E(f690(x78431,x78433,x78432),f691(x78431,x78433,x78432))+~E(f312(f53(x78432),f692(x78431,x78433,x78432)),x78431)+E(f312(f312(f90(a852),x78431),f312(f53(f860(x78432,a845)),x78433)),f312(f53(x78432),f48(f860(x78432,a845),x78433)))+~P22(f312(f70(x78432),f48(f860(x78432,a845),x78433)))+~P22(f312(f70(f860(x78432,a845)),x78433))
% 173.53/173.43 [8026]~P103(x80262)+E(x80261,f189(f860(x80262,a845)))+~P22(f312(f70(x80262),x80263))+P22(f312(f312(f227(x80262),f312(f72(x80262,f225(x80262)),x80263)),f312(f72(x80262,f225(x80262)),x80261)))+~P22(f312(f312(f227(f860(x80262,a845)),x80261),x80263))
% 173.53/173.43 [8341]~E(f690(x83411,x83413,x83412),f691(x83411,x83413,x83412))+E(f312(f312(f90(a852),x83411),f312(f53(f860(x83412,a845)),x83413)),f312(f53(x83412),f48(f860(x83412,a845),x83413)))+P22(f312(f312(f314(f860(x83412,a845)),f692(x83411,x83413,x83412)),x83413))+~P22(f312(f70(x83412),f48(f860(x83412,a845),x83413)))+~P22(f312(f70(f860(x83412,a845)),x83413))
% 173.53/173.43 [8368]~E(f312(f53(x83682),f692(x83681,x83683,x83682)),x83681)+E(f312(f312(f90(a852),x83681),f312(f53(f860(x83682,a845)),x83683)),f312(f53(x83682),f48(f860(x83682,a845),x83683)))+P22(f312(f312(f314(f860(x83682,a845)),f691(x83681,x83683,x83682)),x83683))+~P22(f312(f70(x83682),f48(f860(x83682,a845),x83683)))+~P22(f312(f70(f860(x83682,a845)),x83683))
% 173.53/173.43 [8369]~E(f312(f53(x83692),f692(x83691,x83693,x83692)),x83691)+E(f312(f312(f90(a852),x83691),f312(f53(f860(x83692,a845)),x83693)),f312(f53(x83692),f48(f860(x83692,a845),x83693)))+P22(f312(f312(f314(f860(x83692,a845)),f690(x83691,x83693,x83692)),x83693))+~P22(f312(f70(x83692),f48(f860(x83692,a845),x83693)))+~P22(f312(f70(f860(x83692,a845)),x83693))
% 173.53/173.43 [8400]~E(f312(f53(x84002),f692(x84001,x84003,x84002)),x84001)+~E(f312(f312(f115(f860(x84002,a845)),f691(x84001,x84003,x84002)),f690(x84001,x84003,x84002)),f189(f860(x84002,a845)))+E(f312(f312(f90(a852),x84001),f312(f53(f860(x84002,a845)),x84003)),f312(f53(x84002),f48(f860(x84002,a845),x84003)))+~P22(f312(f70(f860(x84002,a845)),x84003))+~P22(f312(f70(x84002),f48(f860(x84002,a845),x84003)))
% 173.53/173.43 [8642]E(f312(f312(f90(a852),x86421),f312(f53(f860(x86422,a845)),x86423)),f312(f53(x86422),f48(f860(x86422,a845),x86423)))+P22(f312(f312(f314(f860(x86422,a845)),f692(x86421,x86423,x86422)),x86423))+P22(f312(f312(f314(f860(x86422,a845)),f691(x86421,x86423,x86422)),x86423))+~P22(f312(f70(f860(x86422,a845)),x86423))+~P22(f312(f70(x86422),f48(f860(x86422,a845),x86423)))
% 173.53/173.43 [8643]E(f312(f312(f90(a852),x86431),f312(f53(f860(x86432,a845)),x86433)),f312(f53(x86432),f48(f860(x86432,a845),x86433)))+P22(f312(f312(f314(f860(x86432,a845)),f692(x86431,x86433,x86432)),x86433))+P22(f312(f312(f314(f860(x86432,a845)),f690(x86431,x86433,x86432)),x86433))+~P22(f312(f70(f860(x86432,a845)),x86433))+~P22(f312(f70(x86432),f48(f860(x86432,a845),x86433)))
% 173.53/173.43 [8668]~E(f312(f312(f115(f860(x86682,a845)),f691(x86681,x86683,x86682)),f690(x86681,x86683,x86682)),f189(f860(x86682,a845)))+E(f312(f312(f90(a852),x86681),f312(f53(f860(x86682,a845)),x86683)),f312(f53(x86682),f48(f860(x86682,a845),x86683)))+~P22(f312(f70(f860(x86682,a845)),x86683))+P22(f312(f312(f314(f860(x86682,a845)),f692(x86681,x86683,x86682)),x86683))+~P22(f312(f70(x86682),f48(f860(x86682,a845),x86683)))
% 173.53/173.43 [8928]~P93(x89282)+E(x89281,f189(f860(x89282,a845)))+~E(f312(f312(f90(x89282),f312(x89283,f544(x89281,x89283,x89282))),f312(x89283,f547(x89281,x89283,x89282))),f312(x89283,f312(f312(f90(x89282),f544(x89281,x89283,x89282)),f547(x89281,x89283,x89282))))+~P22(f312(f70(x89282),x89281))+E(f312(f72(x89282,f90(x89282)),f312(f290(x89282,x89282,x89283),x89281)),f312(x89283,f312(f72(x89282,f90(x89282)),x89281)))
% 173.53/173.43 [9844]P22(f312(f312(x98441,x98442),x98443))+P22(f312(f312(f228(a1),f349(x98441,x98443,x98442)),f354(x98441,x98443,x98442)))+P22(f312(f312(f227(a1),f354(x98441,x98443,x98442)),f2(a1)))+P22(f312(f312(x98441,f349(x98441,x98443,x98442)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f354(x98441,x98443,x98442))))+~P22(f312(f300(f859(a1,a1),a65),f312(f312(f239(a1,a1),x98442),x98443)))
% 173.53/173.43 [9850]P22(f312(f312(x98501,x98502),x98503))+P22(f312(f312(f227(a1),f348(x98501,x98503,x98502)),f2(a1)))+P22(f312(f312(x98501,f347(x98501,x98503,x98502)),f312(f312(f90(a1),f312(f117(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f348(x98501,x98503,x98502))))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f347(x98501,x98503,x98502)),f348(x98501,x98503,x98502))))+~P22(f312(f300(f859(a1,a1),a60),f312(f312(f239(a1,a1),x98502),x98503)))
% 173.53/173.43 [7815]~P112(x78151)+~P22(f312(f312(f227(x78151),x78152),f87(x78151)))+~P22(f312(f312(f227(x78151),f2(x78151)),x78152))+~P22(f312(f312(f227(x78151),f2(x78151)),x78153))+P22(f312(f312(f227(x78151),f312(f312(f90(x78151),x78152),x78153)),x78153))
% 173.53/173.43 [7816]~P112(x78161)+~P22(f312(f312(f227(x78161),x78163),f87(x78161)))+~P22(f312(f312(f227(x78161),f2(x78161)),x78163))+~P22(f312(f312(f227(x78161),f2(x78161)),x78162))+P22(f312(f312(f227(x78161),f312(f312(f90(x78161),x78162),x78163)),x78162))
% 173.53/173.43 [8178]~P103(x81782)+E(x81781,f189(f860(x81782,a845)))+~P22(f312(f70(x81782),x81781))+P22(f312(f312(f314(x81782),f537(x81783,x81781,x81782)),x81781))+~P22(f312(f312(f227(x81782),f312(f72(x81782,f225(x81782)),x81781)),x81783))
% 173.53/173.43 [8179]~P103(x81792)+E(x81791,f189(f860(x81792,a845)))+~P22(f312(f70(x81792),x81791))+P22(f312(f312(f314(x81792),f543(x81793,x81791,x81792)),x81791))+~P22(f312(f312(f228(x81792),f312(f72(x81792,f225(x81792)),x81791)),x81793))
% 173.53/173.43 [8180]~P103(x81802)+E(x81801,f189(f860(x81802,a845)))+~P22(f312(f70(x81802),x81801))+P22(f312(f312(f228(x81802),f543(x81803,x81801,x81802)),x81803))+~P22(f312(f312(f228(x81802),f312(f72(x81802,f225(x81802)),x81801)),x81803))
% 173.53/173.43 [8181]~P103(x81812)+E(x81811,f189(f860(x81812,a845)))+~P22(f312(f70(x81812),x81811))+P22(f312(f312(f227(x81812),f537(x81813,x81811,x81812)),x81813))+~P22(f312(f312(f227(x81812),f312(f72(x81812,f225(x81812)),x81811)),x81813))
% 173.53/173.43 [8267]~P22(f312(x82671,x82673))+P22(f312(x82671,f475(x82671,x82672)))+P22(f312(x82671,f470(x82671,x82672)))+~P22(f312(f312(f228(a1),f2(a1)),x82672))+P22(f312(x82671,f312(f312(f21(a1),f470(x82671,x82672)),f312(f312(f90(a1),f476(x82671,x82672)),x82672))))
% 173.53/173.43 [8500]~P22(f312(x85001,x85003))+P22(f312(x85001,f470(x85001,x85002)))+~P22(f312(f312(f228(a1),f2(a1)),x85002))+P22(f312(f312(f314(a1),f475(x85001,x85002)),f283(a1,f87(a1),x85002)))+P22(f312(x85001,f312(f312(f21(a1),f470(x85001,x85002)),f312(f312(f90(a1),f476(x85001,x85002)),x85002))))
% 173.53/173.43 [8689]~P22(f312(x86891,x86893))+~P22(f312(x86891,f470(x86891,x86892)))+P22(f312(x86891,f475(x86891,x86892)))+~P22(f312(f312(f228(a1),f2(a1)),x86892))+~P22(f312(x86891,f312(f312(f21(a1),f470(x86891,x86892)),f312(f312(f90(a1),f476(x86891,x86892)),x86892))))
% 173.53/173.43 [8808]~P22(f312(x88081,x88083))+~P22(f312(x88081,f470(x88081,x88082)))+~P22(f312(f312(f228(a1),f2(a1)),x88082))+P22(f312(f312(f314(a1),f475(x88081,x88082)),f283(a1,f87(a1),x88082)))+~P22(f312(x88081,f312(f312(f21(a1),f470(x88081,x88082)),f312(f312(f90(a1),f476(x88081,x88082)),x88082))))
% 173.53/173.43 [8600]~P87(x86001)+~P22(f312(f70(x86001),x86002))+E(f312(f312(f21(f860(x86001,a845)),x86002),f312(f312(f289(x86001),x86003),f189(f860(x86001,a845)))),f189(f860(x86001,a845)))+~P22(f312(f312(f314(x86001),x86003),x86002))+E(f312(f312(f115(x86001),x86003),f11(x86001,f312(f312(f21(f860(x86001,a845)),x86002),f312(f312(f289(x86001),x86003),f189(f860(x86001,a845)))))),f11(x86001,x86002))
% 173.53/173.43 [8601]~P87(x86011)+~P22(f312(f70(x86011),x86012))+E(f312(f312(f21(f860(x86011,a845)),x86012),f312(f312(f289(x86011),x86013),f189(f860(x86011,a845)))),f189(f860(x86011,a845)))+~P22(f312(f312(f314(x86011),x86013),x86012))+E(f312(f312(f124(x86011),x86013),f10(x86011,f312(f312(f21(f860(x86011,a845)),x86012),f312(f312(f289(x86011),x86013),f189(f860(x86011,a845)))))),f10(x86011,x86012))
% 173.53/173.43 [8602]~P103(x86021)+~P22(f312(f70(x86021),x86022))+E(f312(f312(f21(f860(x86021,a845)),x86022),f312(f312(f289(x86021),x86023),f189(f860(x86021,a845)))),f189(f860(x86021,a845)))+~P22(f312(f312(f314(x86021),x86023),x86022))+E(f312(f312(f226(x86021),x86023),f14(x86021,f312(f312(f21(f860(x86021,a845)),x86022),f312(f312(f289(x86021),x86023),f189(f860(x86021,a845)))))),f14(x86021,x86022))
% 173.53/173.43 [8603]~P103(x86031)+~P22(f312(f70(x86031),x86032))+E(f312(f312(f21(f860(x86031,a845)),x86032),f312(f312(f289(x86031),x86033),f189(f860(x86031,a845)))),f189(f860(x86031,a845)))+~P22(f312(f312(f314(x86031),x86033),x86032))+E(f312(f312(f225(x86031),x86033),f15(x86031,f312(f312(f21(f860(x86031,a845)),x86032),f312(f312(f289(x86031),x86033),f189(f860(x86031,a845)))))),f15(x86031,x86032))
% 173.53/173.43 [8662]~P103(x86621)+~P22(f312(f70(x86621),x86622))+E(f312(f312(f21(f860(x86621,a845)),x86622),f312(f312(f289(x86621),x86623),f189(f860(x86621,a845)))),f189(f860(x86621,a845)))+~P22(f312(f312(f314(x86621),x86623),x86622))+E(f312(f312(f226(x86621),x86623),f12(x86621,f226(x86621),f312(f312(f21(f860(x86621,a845)),x86622),f312(f312(f289(x86621),x86623),f189(f860(x86621,a845)))))),f12(x86621,f226(x86621),x86622))
% 173.53/173.43 [8663]~P103(x86631)+~P22(f312(f70(x86631),x86632))+E(f312(f312(f21(f860(x86631,a845)),x86632),f312(f312(f289(x86631),x86633),f189(f860(x86631,a845)))),f189(f860(x86631,a845)))+~P22(f312(f312(f314(x86631),x86633),x86632))+E(f312(f312(f225(x86631),x86633),f13(x86631,f225(x86631),f312(f312(f21(f860(x86631,a845)),x86632),f312(f312(f289(x86631),x86633),f189(f860(x86631,a845)))))),f13(x86631,f225(x86631),x86632))
% 173.53/173.43 [8676]~P87(x86761)+~P22(f312(f70(x86761),x86763))+~P22(f312(f70(x86761),x86762))+E(f312(f312(f115(f860(x86761,a845)),x86762),x86763),f189(f860(x86761,a845)))+E(f312(f312(f124(x86761),f10(x86761,f312(f312(f124(f860(x86761,a845)),x86762),x86763))),f10(x86761,f312(f312(f115(f860(x86761,a845)),x86762),x86763))),f312(f312(f124(x86761),f10(x86761,x86762)),f10(x86761,x86763)))
% 173.53/173.43 [8677]~P87(x86771)+~P22(f312(f70(x86771),x86773))+~P22(f312(f70(x86771),x86772))+E(f312(f312(f115(f860(x86771,a845)),x86772),x86773),f189(f860(x86771,a845)))+E(f312(f312(f115(x86771),f11(x86771,f312(f312(f124(f860(x86771,a845)),x86772),x86773))),f11(x86771,f312(f312(f115(f860(x86771,a845)),x86772),x86773))),f312(f312(f115(x86771),f11(x86771,x86772)),f11(x86771,x86773)))
% 173.53/173.43 [8678]~P103(x86781)+~P22(f312(f70(x86781),x86783))+~P22(f312(f70(x86781),x86782))+E(f312(f312(f115(f860(x86781,a845)),x86782),x86783),f189(f860(x86781,a845)))+E(f312(f312(f225(x86781),f15(x86781,f312(f312(f124(f860(x86781,a845)),x86782),x86783))),f15(x86781,f312(f312(f115(f860(x86781,a845)),x86782),x86783))),f312(f312(f225(x86781),f15(x86781,x86782)),f15(x86781,x86783)))
% 173.53/173.43 [8679]~P103(x86791)+~P22(f312(f70(x86791),x86793))+~P22(f312(f70(x86791),x86792))+E(f312(f312(f115(f860(x86791,a845)),x86792),x86793),f189(f860(x86791,a845)))+E(f312(f312(f226(x86791),f14(x86791,f312(f312(f124(f860(x86791,a845)),x86792),x86793))),f14(x86791,f312(f312(f115(f860(x86791,a845)),x86792),x86793))),f312(f312(f226(x86791),f14(x86791,x86792)),f14(x86791,x86793)))
% 173.53/173.43 [8900]~P103(x89001)+~P22(f312(f70(x89001),x89003))+~P22(f312(f70(x89001),x89002))+E(f312(f312(f115(f860(x89001,a845)),x89002),x89003),f189(f860(x89001,a845)))+E(f312(f312(f225(x89001),f13(x89001,f225(x89001),f312(f312(f124(f860(x89001,a845)),x89002),x89003))),f13(x89001,f225(x89001),f312(f312(f115(f860(x89001,a845)),x89002),x89003))),f312(f312(f225(x89001),f13(x89001,f225(x89001),x89002)),f13(x89001,f225(x89001),x89003)))
% 173.53/173.43 [8901]~P103(x89011)+~P22(f312(f70(x89011),x89013))+~P22(f312(f70(x89011),x89012))+E(f312(f312(f115(f860(x89011,a845)),x89012),x89013),f189(f860(x89011,a845)))+E(f312(f312(f226(x89011),f12(x89011,f226(x89011),f312(f312(f124(f860(x89011,a845)),x89012),x89013))),f12(x89011,f226(x89011),f312(f312(f115(f860(x89011,a845)),x89012),x89013))),f312(f312(f226(x89011),f12(x89011,f226(x89011),x89012)),f12(x89011,f226(x89011),x89013)))
% 173.53/173.43 [9680]~P117(x96803)+E(x96801,x96802)+~P22(f312(f312(f227(x96803),f2(x96803)),x96802))+~P22(f312(f312(f227(x96803),f2(x96803)),x96801))+~E(f312(f312(f240(x96803),x96801),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f240(x96803),x96802),f312(f117(a852),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 173.53/173.43 [6239]E(f495(x62391,x62392,x62393),x62394)+E(f312(x62391,x62394),f2(a852))+~E(f312(f312(f6(x62393,a852),x62391),x62392),f87(a852))+~P22(f312(f70(x62393),x62392))+~P22(f312(f312(f314(x62393),x62394),x62392))
% 173.53/173.43 [6303]E(f492(x63031,x63032,x63033),x63034)+E(f312(x63031,x63034),f2(a852))+~E(f312(f312(f6(x63033,a852),x63031),x63032),f312(a126,f2(a852)))+~P22(f312(f70(x63033),x63032))+~P22(f312(f312(f314(x63033),x63034),x63032))
% 173.53/173.43 [6406]~P103(x64061)+~P31(x64061)+P22(f312(f312(f228(x64061),x64062),f48(x64061,x64063)))+~P22(f312(f312(f228(x64061),x64062),x64064))+~P22(f312(f312(f314(x64061),x64064),x64063))
% 173.53/173.43 [6574]~P103(x65741)+~P31(x65741)+~P22(f312(f312(f228(x65741),x65744),x65743))+P22(f312(f312(f228(x65741),f49(x65741,x65742)),x65743))+~P22(f312(f312(f314(x65741),x65744),x65742))
% 173.53/173.43 [6826]~P117(x68263)+E(x68261,x68262)+~E(f312(f312(f240(x68263),x68261),f312(a126,x68264)),f312(f312(f240(x68263),x68262),f312(a126,x68264)))+~P22(f312(f312(f227(x68263),f2(x68263)),x68262))+~P22(f312(f312(f227(x68263),f2(x68263)),x68261))
% 173.53/173.43 [7040]~E(f496(x70402,x70403,x70401,x70404),x70404)+~E(f312(x70402,x70404),f87(a852))+E(f312(f312(f6(x70401,a852),x70402),x70403),f87(a852))+~P22(f312(f70(x70401),x70403))+~P22(f312(f312(f314(x70401),x70404),x70403))
% 173.53/173.43 [7047]~P107(x70474)+~P127(x70474)+E(f312(x70471,f396(x70471,x70472,x70473,x70474)),f2(x70474))+~E(f312(f312(f9(x70473,x70474),x70471),x70472),f2(x70474))+~P22(f312(f70(x70473),x70472))
% 173.53/173.43 [7134]~E(f493(x71342,x71343,x71341,x71344),x71344)+~E(f312(x71342,x71344),f312(a126,f2(a852)))+E(f312(f312(f6(x71341,a852),x71342),x71343),f312(a126,f2(a852)))+~P22(f312(f70(x71341),x71343))+~P22(f312(f312(f314(x71341),x71344),x71343))
% 173.53/173.43 [7854]~E(f312(x78542,x78544),f87(a852))+~E(f312(x78542,f496(x78542,x78543,x78541,x78544)),f2(a852))+E(f312(f312(f6(x78541,a852),x78542),x78543),f87(a852))+~P22(f312(f70(x78541),x78543))+~P22(f312(f312(f314(x78541),x78544),x78543))
% 173.53/173.43 [7897]~E(f312(x78972,x78974),f312(a126,f2(a852)))+~E(f312(x78972,f493(x78972,x78973,x78971,x78974)),f2(a852))+E(f312(f312(f6(x78971,a852),x78972),x78973),f312(a126,f2(a852)))+~P22(f312(f70(x78971),x78973))+~P22(f312(f312(f314(x78971),x78974),x78973))
% 173.53/173.43 [8468]~P103(x84681)+~P33(x84681,x84684)+P33(x84681,x84682)+~E(x84682,f312(f312(f147(x84681),x84683),x84684))+~P22(f312(f312(f227(x84681),x84683),f693(x84682,x84681,x84684,x84683)))
% 173.53/173.43 [8504]E(x85041,x85042)+E(f312(f312(f89(a1),f459(x85043,x85042,x85044,x85041)),f460(x85043,x85042,x85044,x85041)),x85041)+~E(f312(f312(f21(a1),x85041),x85044),x85042)+~P22(f312(f312(f228(a1),f2(a1)),x85044))+~P22(f312(f312(f314(a1),x85042),x85043))
% 173.53/173.43 [8505]E(x85051,x85052)+E(f312(f312(f21(a1),f447(x85053,x85052,x85054,x85051)),f448(x85053,x85052,x85054,x85051)),x85051)+~E(f312(f312(f89(a1),x85051),x85054),x85052)+~P22(f312(f312(f228(a1),f2(a1)),x85054))+~P22(f312(f312(f314(a1),x85052),x85053))
% 173.53/173.43 [8674]E(f312(x86741,f323(x86742,x86741,x86743,x86744)),x86742)+P22(f312(f312(f227(a852),x86744),f324(x86742,x86741,x86743,x86744)))+~P22(f312(f312(f227(a1),x86742),f312(x86741,x86743)))+~P22(f312(f312(f228(a852),x86744),x86743))+~P22(f312(f312(f227(a1),f312(x86741,x86744)),x86742))
% 173.53/173.43 [8675]~P103(x86751)+~P33(x86751,x86753)+P33(x86751,x86752)+~E(x86752,f312(f312(f147(x86751),x86754),x86753))+P22(f312(f312(f314(x86751),f693(x86752,x86751,x86753,x86754)),f312(f168(x86751),x86753)))
% 173.53/173.43 [8692]~P107(x86924)+~P127(x86924)+~E(f312(f312(f9(x86921,x86924),x86922),x86923),f2(x86924))+~P22(f312(f70(x86921),x86923))+P22(f312(f312(f314(x86921),f396(x86922,x86923,x86921,x86924)),x86923))
% 173.53/173.43 [8727]~E(f312(x87272,x87274),f87(a852))+E(f312(f312(f6(x87271,a852),x87272),x87273),f87(a852))+~P22(f312(f70(x87271),x87273))+~P22(f312(f312(f314(x87271),x87274),x87273))+P22(f312(f312(f314(x87271),f496(x87272,x87273,x87271,x87274)),x87273))
% 173.53/173.43 [8735]E(x87351,x87352)+~E(f312(f312(f89(a1),x87352),x87354),x87351)+~P22(f312(f312(f228(a1),f2(a1)),x87354))+~P22(f312(f312(f314(a1),x87351),x87353))+P22(f312(f312(f314(a1),f447(x87353,x87351,x87354,x87352)),x87353))
% 173.53/173.43 [8736]E(x87361,x87362)+~E(f312(f312(f21(a1),x87362),x87364),x87361)+~P22(f312(f312(f228(a1),f2(a1)),x87364))+~P22(f312(f312(f314(a1),x87361),x87363))+P22(f312(f312(f314(a1),f459(x87363,x87361,x87364,x87362)),x87363))
% 173.53/173.43 [8738]~E(f312(x87382,x87384),f312(a126,f2(a852)))+E(f312(f312(f6(x87381,a852),x87382),x87383),f312(a126,f2(a852)))+~P22(f312(f70(x87381),x87383))+~P22(f312(f312(f314(x87381),x87384),x87383))+P22(f312(f312(f314(x87381),f493(x87382,x87383,x87381,x87384)),x87383))
% 173.53/173.43 [8743]P58(x87432,x87433,x87434,x87431)+E(x87431,f189(f860(x87432,a845)))+~P22(f312(f70(x87432),x87434))+~P22(f312(f70(x87432),x87431))+P22(f312(f312(f314(x87432),f511(x87431,x87434,x87433,x87432)),x87434))
% 173.53/173.43 [8822]E(x88221,x88222)+~E(f312(f312(f89(a1),x88222),x88224),x88221)+~P22(f312(f312(f228(a1),f2(a1)),x88224))+~P22(f312(f312(f314(a1),x88221),x88223))+P22(f312(f312(f314(a1),f448(x88223,x88221,x88224,x88222)),f283(a1,f87(a1),x88224)))
% 173.53/173.43 [8823]E(x88231,x88232)+~E(f312(f312(f21(a1),x88232),x88234),x88231)+~P22(f312(f312(f228(a1),f2(a1)),x88234))+~P22(f312(f312(f314(a1),x88231),x88233))+P22(f312(f312(f314(a1),f460(x88233,x88231,x88234,x88232)),f283(a1,f87(a1),x88234)))
% 173.53/173.43 [8906]P22(f312(f312(f227(a852),x89061),f323(x89062,x89063,x89064,x89061)))+~P22(f312(f312(f227(a1),x89062),f312(x89063,x89064)))+P22(f312(f312(f227(a852),x89061),f324(x89062,x89063,x89064,x89061)))+~P22(f312(f312(f228(a852),x89061),x89064))+~P22(f312(f312(f227(a1),f312(x89063,x89061)),x89062))
% 173.53/173.43 [9014]E(f312(x90141,f323(x90142,x90141,x90143,x90144)),x90142)+~P22(f312(f312(f227(a1),x90142),f312(x90141,x90143)))+P22(f312(f312(f228(a852),f324(x90142,x90141,x90143,x90144)),x90143))+~P22(f312(f312(f228(a852),x90144),x90143))+~P22(f312(f312(f227(a1),f312(x90141,x90144)),x90142))
% 173.53/173.43 [9144]~P22(f312(f312(f227(a1),x91442),f312(x91443,x91444)))+P22(f312(f312(f227(a852),x91441),f324(x91442,x91443,x91444,x91441)))+P22(f312(f312(f227(a852),f323(x91442,x91443,x91444,x91441)),x91444))+~P22(f312(f312(f228(a852),x91441),x91444))+~P22(f312(f312(f227(a1),f312(x91443,x91441)),x91442))
% 173.53/173.43 [9145]~P22(f312(f312(f227(a1),x91452),f312(x91453,x91454)))+P22(f312(f312(f227(a852),x91451),f323(x91452,x91453,x91454,x91451)))+P22(f312(f312(f228(a852),f324(x91452,x91453,x91454,x91451)),x91454))+~P22(f312(f312(f228(a852),x91451),x91454))+~P22(f312(f312(f227(a1),f312(x91453,x91451)),x91452))
% 173.53/173.43 [9250]~P22(f312(f312(f227(a1),x92501),f312(x92502,x92503)))+P22(f312(f312(f227(a852),f323(x92501,x92502,x92503,x92504)),x92503))+~P22(f312(f312(f228(a852),x92504),x92503))+~P22(f312(f312(f227(a1),f312(x92502,x92504)),x92501))+P22(f312(f312(f228(a852),f324(x92501,x92502,x92503,x92504)),x92503))
% 173.53/173.43 [9329]E(x93291,f189(f860(x93292,a845)))+~P22(f312(f70(x93292),x93294))+~P22(f312(f70(x93292),x93291))+P22(f312(f312(f314(f859(f860(x93292,a845),f860(x93292,a845))),f312(f312(f239(f860(x93292,a845),f860(x93292,a845)),x93294),x93291)),f303(x93292,x93293)))+P22(f312(f312(f314(x93292),f516(x93293,x93291,x93294,x93292)),x93294))
% 173.53/173.43 [9330]E(x93301,f189(f860(x93302,a845)))+~P22(f312(f70(x93302),x93304))+~P22(f312(f70(x93302),x93301))+P22(f312(f312(f314(f859(f860(x93302,a845),f860(x93302,a845))),f312(f312(f239(f860(x93302,a845),f860(x93302,a845)),x93304),x93301)),f303(x93302,x93303)))+P22(f312(f312(f314(x93302),f740(x93303,x93301,x93304,x93302)),x93304))
% 173.53/173.43 [9991]E(f312(x99911,f323(x99912,x99911,x99913,x99914)),x99912)+~P22(f312(f312(f227(a1),x99912),f312(x99911,x99913)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99911,f312(f312(f89(a852),f324(x99912,x99911,x99913,x99914)),f87(a852)))),f312(x99911,f324(x99912,x99911,x99913,x99914))))),f87(a1)))+~P22(f312(f312(f228(a852),x99914),x99913))+~P22(f312(f312(f227(a1),f312(x99911,x99914)),x99912))
% 173.53/173.43 [9992]~P22(f312(f312(f227(a1),x99922),f312(x99923,x99924)))+P22(f312(f312(f227(a852),x99921),f323(x99922,x99923,x99924,x99921)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99923,f312(f312(f89(a852),f324(x99922,x99923,x99924,x99921)),f87(a852)))),f312(x99923,f324(x99922,x99923,x99924,x99921))))),f87(a1)))+~P22(f312(f312(f228(a852),x99921),x99924))+~P22(f312(f312(f227(a1),f312(x99923,x99921)),x99922))
% 173.53/173.43 [9993]~P22(f312(f312(f227(a1),x99931),f312(x99932,x99933)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99932,f312(f312(f89(a852),f324(x99931,x99932,x99933,x99934)),f87(a852)))),f312(x99932,f324(x99931,x99932,x99933,x99934))))),f87(a1)))+~P22(f312(f312(f228(a852),x99934),x99933))+~P22(f312(f312(f227(a1),f312(x99932,x99934)),x99931))+P22(f312(f312(f227(a852),f323(x99931,x99932,x99933,x99934)),x99933))
% 173.53/173.43 [7104]~P66(x71041)+P22(f312(f312(f228(x71041),x71042),f2(x71041)))+~P22(f312(f312(f228(x71041),x71043),f2(x71041)))+P22(f312(f312(f228(x71041),f2(x71041)),x71042))+P22(f312(f312(f228(x71041),x71043),f312(f312(f268(x71041),x71044),x71042)))
% 173.53/173.43 [7105]~P66(x71051)+P22(f312(f312(f228(x71051),x71052),f2(x71051)))+~P22(f312(f312(f227(x71051),x71053),f2(x71051)))+P22(f312(f312(f228(x71051),f2(x71051)),x71052))+P22(f312(f312(f227(x71051),x71053),f312(f312(f268(x71051),x71054),x71052)))
% 173.53/173.43 [7341]~P66(x73411)+P22(f312(f312(f228(x73411),x73412),f2(x73411)))+P22(f312(f312(f228(x73411),x73413),f2(x73411)))+P22(f312(f312(f228(x73411),f2(x73411)),x73413))+~P22(f312(f312(f228(x73411),x73412),f312(f312(f268(x73411),x73414),x73413)))
% 173.53/173.43 [7342]~P66(x73421)+P22(f312(f312(f228(x73421),x73422),f2(x73421)))+P22(f312(f312(f227(x73421),x73423),f2(x73421)))+P22(f312(f312(f228(x73421),f2(x73421)),x73422))+~P22(f312(f312(f227(x73421),x73423),f312(f312(f268(x73421),x73424),x73422)))
% 173.53/173.43 [7459]E(x74591,x74592)+~E(f312(f312(f161(x74593),x74594),x74591),f312(f312(f161(x74593),x74594),x74592))+~P22(f312(f133(x74593),x74594))+~P22(f312(f312(f228(a852),x74592),f312(f190(f853(x74593)),x74594)))+~P22(f312(f312(f228(a852),x74591),f312(f190(f853(x74593)),x74594)))
% 173.53/173.43 [7817]~P66(x78171)+~P22(f312(f312(f228(x78171),x78173),f2(x78171)))+P22(f312(f312(f228(x78171),f2(x78171)),x78172))+~P22(f312(f312(f228(x78171),x78174),f312(f312(f90(x78171),x78173),x78172)))+P22(f312(f312(f228(x78171),x78173),f312(f312(f268(x78171),x78174),x78172)))
% 173.53/173.43 [7818]~P66(x78181)+~P22(f312(f312(f227(x78181),x78183),f2(x78181)))+P22(f312(f312(f228(x78181),f2(x78181)),x78182))+~P22(f312(f312(f227(x78181),x78184),f312(f312(f90(x78181),x78183),x78182)))+P22(f312(f312(f227(x78181),x78183),f312(f312(f268(x78181),x78184),x78182)))
% 173.53/173.43 [7819]~P66(x78191)+~P22(f312(f312(f228(x78191),x78192),f2(x78191)))+P22(f312(f312(f228(x78191),f2(x78191)),x78192))+~P22(f312(f312(f228(x78191),x78194),f312(f312(f90(x78191),x78193),x78192)))+P22(f312(f312(f228(x78191),x78193),f312(f312(f268(x78191),x78194),x78192)))
% 173.53/173.43 [7820]~P66(x78201)+~P22(f312(f312(f228(x78201),x78202),f2(x78201)))+P22(f312(f312(f228(x78201),f2(x78201)),x78202))+~P22(f312(f312(f228(x78201),x78204),f312(f312(f268(x78201),x78203),x78202)))+P22(f312(f312(f228(x78201),x78203),f312(f312(f90(x78201),x78204),x78202)))
% 173.53/173.43 [7821]~P66(x78211)+~P22(f312(f312(f228(x78211),x78212),f2(x78211)))+P22(f312(f312(f228(x78211),f2(x78211)),x78212))+~P22(f312(f312(f227(x78211),x78214),f312(f312(f90(x78211),x78213),x78212)))+P22(f312(f312(f227(x78211),x78213),f312(f312(f268(x78211),x78214),x78212)))
% 173.53/173.43 [7822]~P66(x78221)+~P22(f312(f312(f228(x78221),x78222),f2(x78221)))+P22(f312(f312(f228(x78221),f2(x78221)),x78222))+~P22(f312(f312(f227(x78221),x78224),f312(f312(f268(x78221),x78223),x78222)))+P22(f312(f312(f227(x78221),x78223),f312(f312(f90(x78221),x78224),x78222)))
% 173.53/173.43 [7963]~P103(x79631)+~P33(x79631,x79632)+~P22(f312(f312(f227(a852),x79633),x79634))+P22(f312(f312(f227(x79631),f312(f312(f161(x79631),x79632),x79633)),f312(f312(f161(x79631),x79632),x79634)))+~P22(f312(f312(f228(a852),x79634),f312(f190(f853(x79631)),x79632)))
% 173.53/173.43 [8017]~P117(x80171)+~P22(f312(f312(f228(x80171),x80172),f87(x80171)))+~P22(f312(f312(f228(x80171),f2(x80171)),x80172))+~P22(f312(f312(f228(a852),x80174),x80173))+P22(f312(f312(f228(x80171),f312(f312(f240(x80171),x80172),x80173)),f312(f312(f240(x80171),x80172),x80174)))
% 173.53/173.43 [8018]~P117(x80181)+~P22(f312(f312(f227(x80181),x80182),f87(x80181)))+~P22(f312(f312(f227(x80181),f2(x80181)),x80182))+~P22(f312(f312(f227(a852),x80184),x80183))+P22(f312(f312(f227(x80181),f312(f312(f240(x80181),x80182),x80183)),f312(f312(f240(x80181),x80182),x80184)))
% 173.53/173.43 [8019]~P117(x80191)+~P22(f312(f312(f227(x80191),f2(x80191)),x80192))+~P22(f312(f312(f228(a852),f2(a852)),x80193))+~P22(f312(f312(f228(x80191),x80192),x80194))+P22(f312(f312(f228(x80191),f312(f312(f240(x80191),x80192),x80193)),f312(f312(f240(x80191),x80194),x80193)))
% 173.53/173.43 [8039]~P103(x80391)+~P33(x80391,f312(f165(x80391),x80392))+~P22(f312(f312(f227(a852),x80394),x80393))+P22(f312(f312(f227(x80391),f312(f312(f161(x80391),x80392),x80393)),f312(f312(f161(x80391),x80392),x80394)))+~P22(f312(f312(f228(a852),x80393),f312(f190(f853(x80391)),x80392)))
% 173.53/173.43 [8289]~P67(x82891)+~P22(f312(f312(f228(x82891),x82892),f2(x82891)))+~P22(f312(f312(f228(x82891),x82893),x82894))+~P22(f312(f312(f228(x82891),f2(x82891)),f312(f312(f90(x82891),x82893),x82894)))+P22(f312(f312(f228(x82891),f312(f312(f268(x82891),x82892),x82893)),f312(f312(f268(x82891),x82892),x82894)))
% 173.53/173.43 [8290]~P66(x82901)+~P22(f312(f312(f227(x82901),x82902),f2(x82901)))+~P22(f312(f312(f227(x82901),x82903),x82904))+~P22(f312(f312(f228(x82901),f2(x82901)),f312(f312(f90(x82901),x82903),x82904)))+P22(f312(f312(f227(x82901),f312(f312(f268(x82901),x82902),x82903)),f312(f312(f268(x82901),x82902),x82904)))
% 173.53/173.43 [8301]~P67(x83011)+~P22(f312(f312(f228(x83011),x83014),x83013))+~P22(f312(f312(f228(x83011),f2(x83011)),x83012))+~P22(f312(f312(f228(x83011),f2(x83011)),f312(f312(f90(x83011),x83013),x83014)))+P22(f312(f312(f228(x83011),f312(f312(f268(x83011),x83012),x83013)),f312(f312(f268(x83011),x83012),x83014)))
% 173.53/173.43 [8302]~P67(x83021)+~P22(f312(f312(f227(x83021),x83024),x83023))+~P22(f312(f312(f227(x83021),f2(x83021)),x83022))+~P22(f312(f312(f228(x83021),f2(x83021)),f312(f312(f90(x83021),x83023),x83024)))+P22(f312(f312(f227(x83021),f312(f312(f268(x83021),x83022),x83023)),f312(f312(f268(x83021),x83022),x83024)))
% 173.53/173.43 [8414]P22(f312(x84141,x84142))+~P22(f312(f70(x84144),x84142))+P22(f312(x84141,f506(x84141,x84143,x84142,x84144)))+~P22(f312(x84141,f189(f860(x84144,a845))))+~P22(f312(f312(f227(f860(x84144,a845)),x84142),x84143))
% 173.53/173.43 [8422]P22(f312(x84221,x84222))+P22(f312(f70(x84223),f506(x84221,x84224,x84222,x84223)))+~P22(f312(f70(x84223),x84222))+~P22(f312(x84221,f189(f860(x84223,a845))))+~P22(f312(f312(f227(f860(x84223,a845)),x84222),x84224))
% 173.53/173.43 [8670]E(f312(f312(f89(a1),f467(x86701,x86702,x86703,x86704)),f461(x86701,x86702,x86703,x86704)),x86704)+~P22(f312(f312(f228(a1),f2(a1)),x86703))+~P22(f312(f312(f228(a1),x86702),x86704))+~P22(f312(f312(f314(a1),x86702),x86701))+P22(f312(f312(f228(a1),x86702),f312(f312(f21(a1),x86704),x86703)))
% 173.53/173.43 [8885]~P22(f312(f312(f228(a1),f2(a1)),x88853))+~P22(f312(f312(f228(a1),x88852),x88854))+~P22(f312(f312(f314(a1),x88852),x88851))+P22(f312(f312(f314(a1),f467(x88851,x88852,x88853,x88854)),x88851))+P22(f312(f312(f228(a1),x88852),f312(f312(f21(a1),x88854),x88853)))
% 173.53/173.43 [8899]P22(f312(x88991,x88992))+~P22(f312(f70(x88993),x88992))+P22(f312(f312(f314(x88993),f507(x88991,x88994,x88992,x88993)),x88994))+~P22(f312(x88991,f189(f860(x88993,a845))))+~P22(f312(f312(f227(f860(x88993,a845)),x88992),x88994))
% 173.53/173.43 [8916]E(f312(f312(f89(a1),f449(x89161,x89162,x89163,x89164)),f450(x89161,x89162,x89163,x89164)),x89164)+~P22(f312(f312(f228(a1),f2(a1)),x89163))+~P22(f312(f312(f227(a1),x89162),x89164))+P22(f312(f312(f227(a1),x89162),f312(f312(f21(a1),x89164),x89163)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x89162),f87(a1))),x89161))
% 173.53/173.43 [8966]~P22(f312(f312(f228(a1),f2(a1)),x89663))+~P22(f312(f312(f228(a1),x89661),x89662))+~P22(f312(f312(f314(a1),x89661),x89664))+P22(f312(f312(f314(a1),f461(x89664,x89661,x89663,x89662)),f283(a1,f87(a1),x89663)))+P22(f312(f312(f228(a1),x89661),f312(f312(f21(a1),x89662),x89663)))
% 173.53/173.43 [9060]~P22(f312(f312(f228(a1),f2(a1)),x90603))+~P22(f312(f312(f227(a1),x90602),x90604))+P22(f312(f312(f314(a1),f449(x90601,x90602,x90603,x90604)),x90601))+P22(f312(f312(f227(a1),x90602),f312(f312(f21(a1),x90604),x90603)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x90602),f87(a1))),x90601))
% 173.53/173.43 [9098]~P22(f312(f312(f228(a1),f2(a1)),x90983))+~P22(f312(f312(f227(a1),x90981),x90982))+P22(f312(f312(f314(a1),f450(x90984,x90981,x90983,x90982)),f283(a1,f87(a1),x90983)))+P22(f312(f312(f227(a1),x90981),f312(f312(f21(a1),x90982),x90983)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x90981),f87(a1))),x90984))
% 173.53/173.43 [9333]P22(f312(x93331,x93332))+~P22(f312(f312(f314(x93333),f507(x93331,x93334,x93332,x93333)),f506(x93331,x93334,x93332,x93333)))+~P22(f312(f70(x93333),x93332))+~P22(f312(x93331,f189(f860(x93333,a845))))+~P22(f312(f312(f227(f860(x93333,a845)),x93332),x93334))
% 173.53/173.43 [9542]P22(f312(x95421,x95422))+~P22(f312(f70(x95423),x95422))+~P22(f312(x95421,f312(f312(f289(x95423),f507(x95421,x95424,x95422,x95423)),f506(x95421,x95424,x95422,x95423))))+~P22(f312(x95421,f189(f860(x95423,a845))))+~P22(f312(f312(f227(f860(x95423,a845)),x95422),x95424))
% 173.53/173.43 [7594]~P66(x75941)+P22(f312(f312(f228(x75941),x75942),f2(x75941)))+P22(f312(f312(f228(x75941),f2(x75941)),x75942))+~P22(f312(f312(f228(x75941),f2(x75941)),x75944))+P22(f312(f312(f228(x75941),f312(f312(f268(x75941),x75943),x75942)),x75944))
% 173.53/173.43 [7595]~P66(x75951)+P22(f312(f312(f228(x75951),x75952),f2(x75951)))+~P22(f312(f312(f227(x75951),f2(x75951)),x75954))+P22(f312(f312(f228(x75951),f2(x75951)),x75952))+P22(f312(f312(f227(x75951),f312(f312(f268(x75951),x75953),x75952)),x75954))
% 173.53/173.43 [7807]~P31(x78071)+~P49(x78071,x78071,x78074)+~E(x78073,f110(x78071,x78074))+P22(f312(f312(f227(x78071),x78072),x78073))+~P22(f312(f312(f227(x78071),x78072),f312(x78074,f312(f312(f124(x78071),x78072),x78073))))
% 173.53/173.43 [7869]~P22(f312(f312(f227(a1),x78694),f2(a1)))+~E(x78692,f312(f312(f89(a1),f312(f312(f90(a1),x78691),x78693)),x78694))+P22(f312(f312(f228(a1),f2(a1)),x78691))+~P22(f312(f312(f228(a1),x78691),x78694))+P22(f312(f57(x78692,x78691),f312(f312(f239(a1,a1),x78693),x78694)))
% 173.53/173.43 [7906]~P22(f312(x79061,x79064))+P22(f312(x79061,f837(x79062,x79061,x79063)))+~P22(f312(f312(f228(a1),f2(a1)),x79063))+~P22(f312(f312(f227(a1),f2(a1)),x79062))+P22(f312(x79061,f312(f312(f21(a1),x79064),f312(f312(f90(a1),x79062),x79063))))
% 173.53/173.43 [7907]~P22(f312(x79071,x79074))+P22(f312(x79071,f839(x79072,x79071,x79073)))+~P22(f312(f312(f228(a1),f2(a1)),x79073))+~P22(f312(f312(f227(a1),f2(a1)),x79072))+P22(f312(x79071,f312(f312(f89(a1),x79074),f312(f312(f90(a1),x79072),x79073))))
% 173.53/173.43 [7908]~P66(x79081)+P22(f312(f312(f228(x79081),x79082),f2(x79081)))+P22(f312(f312(f228(x79081),f2(x79081)),x79082))+P22(f312(f312(f228(x79081),f2(x79081)),x79083))+~P22(f312(f312(f228(x79081),f312(f312(f268(x79081),x79084),x79082)),x79083))
% 173.53/173.43 [7909]~P66(x79091)+P22(f312(f312(f228(x79091),x79092),f2(x79091)))+P22(f312(f312(f228(x79091),f2(x79091)),x79092))+P22(f312(f312(f227(x79091),f2(x79091)),x79093))+~P22(f312(f312(f227(x79091),f312(f312(f268(x79091),x79094),x79092)),x79093))
% 173.53/173.43 [7957]~E(x79571,f312(f312(f89(a1),f312(f312(f90(a1),x79572),x79573)),x79574))+~P22(f312(f312(f228(a1),f2(a1)),x79572))+~P22(f312(f312(f227(a1),f2(a1)),x79574))+~P22(f312(f312(f228(a1),x79574),x79572))+P22(f312(f57(x79571,x79572),f312(f312(f239(a1,a1),x79573),x79574)))
% 173.53/173.43 [8083]~P66(x80831)+P22(f312(f312(f228(x80831),x80832),f2(x80831)))+~P22(f312(f312(f228(x80831),f2(x80831)),x80834))+~P22(f312(f312(f228(x80831),x80833),f312(f312(f90(x80831),x80834),x80832)))+P22(f312(f312(f228(x80831),f312(f312(f268(x80831),x80833),x80832)),x80834))
% 173.53/173.43 [8084]~P66(x80841)+P22(f312(f312(f228(x80841),x80842),f2(x80841)))+~P22(f312(f312(f227(x80841),f2(x80841)),x80844))+~P22(f312(f312(f227(x80841),x80843),f312(f312(f90(x80841),x80844),x80842)))+P22(f312(f312(f227(x80841),f312(f312(f268(x80841),x80843),x80842)),x80844))
% 173.53/173.43 [8166]~P66(x81661)+P22(f312(f312(f228(x81661),x81662),f2(x81661)))+~P22(f312(f312(f228(x81661),x81663),f2(x81661)))+P22(f312(f312(f228(x81661),x81663),f312(f312(f268(x81661),x81664),x81662)))+~P22(f312(f312(f228(x81661),f312(f312(f90(x81661),x81663),x81662)),x81664))
% 173.53/173.43 [8167]~P66(x81671)+P22(f312(f312(f228(x81671),x81672),f2(x81671)))+~P22(f312(f312(f227(x81671),x81673),f2(x81671)))+P22(f312(f312(f227(x81671),x81673),f312(f312(f268(x81671),x81674),x81672)))+~P22(f312(f312(f227(x81671),f312(f312(f90(x81671),x81673),x81672)),x81674))
% 173.53/173.43 [8329]~P66(x83291)+~P22(f312(f312(f228(x83291),x83292),f2(x83291)))+P22(f312(f312(f228(x83291),f2(x83291)),x83292))+~P22(f312(f312(f228(x83291),f312(f312(f268(x83291),x83294),x83292)),x83293))+P22(f312(f312(f228(x83291),f312(f312(f90(x83291),x83293),x83292)),x83294))
% 173.53/173.43 [8330]~P66(x83301)+~P22(f312(f312(f228(x83301),x83302),f2(x83301)))+P22(f312(f312(f228(x83301),f2(x83301)),x83302))+~P22(f312(f312(f228(x83301),f312(f312(f90(x83301),x83304),x83302)),x83303))+P22(f312(f312(f228(x83301),f312(f312(f268(x83301),x83303),x83302)),x83304))
% 173.53/173.43 [8331]~P66(x83311)+~P22(f312(f312(f228(x83311),x83312),f2(x83311)))+P22(f312(f312(f228(x83311),f2(x83311)),x83312))+~P22(f312(f312(f227(x83311),f312(f312(f268(x83311),x83314),x83312)),x83313))+P22(f312(f312(f227(x83311),f312(f312(f90(x83311),x83313),x83312)),x83314))
% 173.53/173.43 [8332]~P66(x83321)+~P22(f312(f312(f228(x83321),x83322),f2(x83321)))+P22(f312(f312(f228(x83321),f2(x83321)),x83322))+~P22(f312(f312(f227(x83321),f312(f312(f90(x83321),x83324),x83322)),x83323))+P22(f312(f312(f227(x83321),f312(f312(f268(x83321),x83323),x83322)),x83324))
% 173.53/173.43 [8356]~P66(x83561)+~P22(f312(f312(f228(x83561),f2(x83561)),x83564))+P22(f312(f312(f228(x83561),f2(x83561)),x83562))+~P22(f312(f312(f228(x83561),f312(f312(f90(x83561),x83564),x83562)),x83563))+P22(f312(f312(f228(x83561),f312(f312(f268(x83561),x83563),x83562)),x83564))
% 173.53/173.43 [8357]~P66(x83571)+~P22(f312(f312(f227(x83571),f2(x83571)),x83574))+P22(f312(f312(f228(x83571),f2(x83571)),x83572))+~P22(f312(f312(f227(x83571),f312(f312(f90(x83571),x83574),x83572)),x83573))+P22(f312(f312(f227(x83571),f312(f312(f268(x83571),x83573),x83572)),x83574))
% 173.53/173.43 [8430]~P66(x84301)+~P22(f312(f312(f228(x84301),x84304),f2(x84301)))+~P22(f312(f312(f228(x84301),x84303),f312(f312(f90(x84301),x84302),x84304)))+P22(f312(f312(f228(x84301),x84302),f312(f312(f268(x84301),x84303),x84304)))+~P22(f312(f312(f228(x84301),f312(f312(f90(x84301),x84302),x84304)),x84303))
% 173.53/173.43 [8431]~P66(x84311)+~P22(f312(f312(f228(x84311),x84312),f2(x84311)))+~P22(f312(f312(f228(x84311),x84313),f312(f312(f90(x84311),x84312),x84314)))+P22(f312(f312(f228(x84311),x84312),f312(f312(f268(x84311),x84313),x84314)))+~P22(f312(f312(f228(x84311),f312(f312(f90(x84311),x84312),x84314)),x84313))
% 173.53/173.43 [8432]~P66(x84321)+~P22(f312(f312(f228(x84321),x84324),f2(x84321)))+~P22(f312(f312(f227(x84321),x84323),f312(f312(f90(x84321),x84322),x84324)))+P22(f312(f312(f227(x84321),x84322),f312(f312(f268(x84321),x84323),x84324)))+~P22(f312(f312(f227(x84321),f312(f312(f90(x84321),x84322),x84324)),x84323))
% 173.53/173.43 [8433]~P66(x84331)+~P22(f312(f312(f227(x84331),x84332),f2(x84331)))+~P22(f312(f312(f227(x84331),x84333),f312(f312(f90(x84331),x84332),x84334)))+P22(f312(f312(f227(x84331),x84332),f312(f312(f268(x84331),x84333),x84334)))+~P22(f312(f312(f227(x84331),f312(f312(f90(x84331),x84332),x84334)),x84333))
% 173.53/173.43 [8547]~P66(x85471)+~P22(f312(f312(f228(x85471),x85473),f2(x85471)))+~P22(f312(f312(f228(x85471),x85472),f312(f312(f90(x85471),x85474),x85473)))+~P22(f312(f312(f228(x85471),f312(f312(f90(x85471),x85474),x85473)),x85472))+P22(f312(f312(f228(x85471),f312(f312(f268(x85471),x85472),x85473)),x85474))
% 173.53/173.43 [8548]~P66(x85481)+~P22(f312(f312(f228(x85481),x85483),f2(x85481)))+~P22(f312(f312(f227(x85481),x85482),f312(f312(f90(x85481),x85484),x85483)))+~P22(f312(f312(f227(x85481),f312(f312(f90(x85481),x85484),x85483)),x85482))+P22(f312(f312(f227(x85481),f312(f312(f268(x85481),x85482),x85483)),x85484))
% 173.53/173.43 [8562]~P66(x85621)+~P22(f312(f312(f228(x85621),f2(x85621)),x85624))+~P22(f312(f312(f228(x85621),x85622),f312(f312(f90(x85621),x85624),x85623)))+~P22(f312(f312(f228(x85621),f312(f312(f90(x85621),x85624),x85623)),x85622))+P22(f312(f312(f228(x85621),f312(f312(f268(x85621),x85622),x85623)),x85624))
% 173.53/173.43 [8563]~P66(x85631)+~P22(f312(f312(f227(x85631),f2(x85631)),x85634))+~P22(f312(f312(f227(x85631),x85632),f312(f312(f90(x85631),x85634),x85633)))+~P22(f312(f312(f227(x85631),f312(f312(f90(x85631),x85634),x85633)),x85632))+P22(f312(f312(f227(x85631),f312(f312(f268(x85631),x85632),x85633)),x85634))
% 173.53/173.43 [8729]E(f312(f312(f21(a1),f468(x87291,x87292,x87293,x87294)),f469(x87291,x87292,x87293,x87294)),x87294)+~P22(f312(f312(f228(a1),f2(a1)),x87293))+~P22(f312(f312(f314(a1),x87292),x87291))+~P22(f312(f312(f228(a1),x87294),x87292))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x87294),x87293)),x87292))
% 173.53/173.43 [8804]~P22(f312(x88041,x88042))+~P22(f312(f312(f228(a1),f2(a1)),x88044))+~P22(f312(f312(f227(a1),f2(a1)),x88043))+~P22(f312(x88041,f312(f312(f89(a1),f839(x88043,x88041,x88044)),x88044)))+P22(f312(x88041,f312(f312(f89(a1),x88042),f312(f312(f90(a1),x88043),x88044))))
% 173.53/173.43 [8805]~P22(f312(x88051,x88052))+~P22(f312(f312(f228(a1),f2(a1)),x88054))+~P22(f312(f312(f227(a1),f2(a1)),x88053))+~P22(f312(x88051,f312(f312(f21(a1),f837(x88053,x88051,x88054)),x88054)))+P22(f312(x88051,f312(f312(f21(a1),x88052),f312(f312(f90(a1),x88053),x88054))))
% 173.53/173.43 [8961]~P22(f312(f312(f228(a1),f2(a1)),x89613))+~P22(f312(f312(f314(a1),x89612),x89611))+~P22(f312(f312(f228(a1),x89614),x89612))+P22(f312(f312(f314(a1),f468(x89611,x89612,x89613,x89614)),x89611))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x89614),x89613)),x89612))
% 173.53/173.43 [8979]E(f312(f312(f21(a1),f451(x89791,x89792,x89793,x89794)),f452(x89791,x89792,x89793,x89794)),x89794)+~P22(f312(f312(f228(a1),f2(a1)),x89793))+~P22(f312(f312(f227(a1),x89794),x89792))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x89792),f87(a1))),x89791))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x89794),x89793)),x89792))
% 173.53/173.43 [9004]~P22(f312(f312(f228(a1),f2(a1)),x90042))+~P22(f312(f312(f314(a1),x90043),x90044))+~P22(f312(f312(f228(a1),x90041),x90043))+P22(f312(f312(f314(a1),f469(x90044,x90043,x90042,x90041)),f283(a1,f87(a1),x90042)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x90041),x90042)),x90043))
% 173.53/173.43 [9093]~P22(f312(f312(f228(a1),f2(a1)),x90933))+~P22(f312(f312(f227(a1),x90934),x90932))+P22(f312(f312(f314(a1),f451(x90931,x90932,x90933,x90934)),x90931))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x90932),f87(a1))),x90931))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x90934),x90933)),x90932))
% 173.53/173.43 [9140]~P22(f312(f312(f228(a1),f2(a1)),x91402))+~P22(f312(f312(f227(a1),x91401),x91403))+P22(f312(f312(f314(a1),f452(x91404,x91403,x91402,x91401)),f283(a1,f87(a1),x91402)))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x91403),f87(a1))),x91404))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x91401),x91402)),x91403))
% 173.53/173.43 [9423]~P41(x94231,x94233)+~P20(x94231,x94234)+P41(x94231,f312(f312(f124(f860(f859(x94231,x94231),a845)),x94232),x94233))+~P22(f312(f312(f227(f860(f859(x94231,x94231),a845)),x94232),f312(f246(f860(f859(x94231,x94231),a845),f860(f859(x94231,x94231),a845)),x94234)))+~P22(f312(f312(f227(f860(f859(x94231,x94231),a845)),x94233),f312(f248(f860(f859(x94231,x94231),a845),f860(f859(x94231,x94231),a845)),x94234)))
% 173.53/173.43 [9706]~E(f312(f351(x97061,x97064,x97063,x97062),f353(x97061,x97064,x97063,x97062)),f192(f853(a308)))+P22(f312(f312(f228(a1),f352(x97061,x97064,x97063,x97062)),f353(x97061,x97064,x97063,x97062)))+P22(f312(f312(f312(x97061,x97062),x97063),x97064))+P22(f312(f312(f312(x97061,f351(x97061,x97064,x97063,x97062)),f352(x97061,x97064,x97063,x97062)),f312(f312(f89(a1),f353(x97061,x97064,x97063,x97062)),f87(a1))))+~P22(f312(f300(f859(f860(a1,f856(f853(a308))),f859(a1,a1)),a297),f312(f312(f239(f860(a1,f856(f853(a308))),f859(a1,a1)),x97062),f312(f312(f239(a1,a1),x97063),x97064))))
% 173.53/173.43 [9813]~P13(x98132,x98134,x98133)+E(x98131,f189(f860(x98132,a845)))+~P22(f312(f70(x98132),x98131))+P22(f312(f312(f314(x98132),f312(x98133,x98131)),x98131))+~P22(f312(f312(f314(x98132),f312(f312(x98134,f383(x98131,x98133,x98134,x98132)),f384(x98131,x98133,x98134,x98132))),f312(f312(f289(x98132),f383(x98131,x98133,x98134,x98132)),f312(f312(f289(x98132),f384(x98131,x98133,x98134,x98132)),f189(f860(x98132,a845))))))
% 173.53/173.43 [8459]~P31(x84591)+~P49(x84591,x84591,x84594)+~E(x84592,f109(x84591,x84594))+P22(f312(f312(f227(x84591),x84592),x84593))+~P22(f312(f312(f227(x84591),f312(x84594,f312(f312(f115(x84591),x84592),x84593))),x84593))
% 173.53/173.43 [9741]~P105(x97412)+~P63(x97411)+~P22(f312(f312(f227(f860(x97411,x97412)),x97413),x97414))+P22(f312(f312(f228(f860(x97411,x97412)),x97413),x97414))+~P22(f312(f66(x97411),f312(f312(f8(a845,a845,x97411),a307),f312(f312(f18(x97411,x97412,a845),f312(f312(f8(x97412,f860(x97412,a845),x97411),a309),x97413)),x97414))))
% 173.53/173.43 [9340]~P54(x93401,x93401,x93404)+P22(f312(f312(f314(f859(x93401,x93401)),f312(f312(f239(x93401,x93401),x93402),x93403)),f287(x93401,x93404)))+P22(f312(f312(f314(f859(x93401,x93401)),f312(f312(f239(x93401,x93401),x93403),x93402)),f287(x93401,x93404)))+~P22(f312(f312(f314(f859(x93401,x93401)),f312(f312(f239(x93401,x93401),x93405),x93402)),f287(x93401,x93404)))+~P22(f312(f312(f314(f859(x93401,x93401)),f312(f312(f239(x93401,x93401),x93405),x93403)),f287(x93401,x93404)))
% 173.53/173.43 [5544]E(x55441,f2(a852))+~E(f312(f53(x55442),x55445),x55441)+E(f312(f53(x55442),x55443),f312(a126,x55441))+~E(x55443,f312(f312(f289(x55442),x55444),x55445))+P22(f312(f312(f314(x55442),x55444),x55445))
% 173.53/173.43 [5666]~P65(x56662)+E(x56661,f2(x56662))+E(x56663,f2(x56662))+~E(f312(f312(f268(x56662),x56664),x56663),f312(f312(f268(x56662),x56665),x56661))+E(f312(f312(f90(x56662),x56664),x56661),f312(f312(f90(x56662),x56665),x56663))
% 173.53/173.43 [5667]~P65(x56672)+E(x56671,f2(x56672))+E(x56673,f2(x56672))+~E(f312(f312(f90(x56672),x56674),x56673),f312(f312(f90(x56672),x56675),x56671))+E(f312(f312(f268(x56672),x56674),x56671),f312(f312(f268(x56672),x56675),x56673))
% 173.53/173.43 [5727]~E(f312(f53(x57271),x57275),x57273)+~E(x57275,f189(f860(x57271,a845)))+E(f312(f53(x57271),x57272),f312(a126,x57273))+~E(x57272,f312(f312(f289(x57271),x57274),x57275))+P22(f312(f312(f314(x57271),x57274),x57275))
% 173.53/173.43 [5952]~P107(x59522)+~E(f312(x59523,x59525),f2(x59522))+E(f312(f312(f9(x59521,x59522),x59523),x59524),f2(x59522))+~P22(f312(f70(x59521),x59524))+~P22(f312(f312(f314(x59521),x59525),x59524))
% 173.53/173.43 [6313]~P103(x63133)+E(x63131,x63132)+~E(f312(f282(x63133,x63134),x63131),f312(f282(x63133,x63135),x63132))+~P22(f312(f312(f228(x63133),x63135),x63132))+~P22(f312(f312(f228(x63133),x63134),x63131))
% 173.53/173.43 [6314]~P103(x63143)+E(x63141,x63142)+~E(f312(f282(x63143,x63141),x63144),f312(f282(x63143,x63142),x63145))+~P22(f312(f312(f228(x63143),x63142),x63145))+~P22(f312(f312(f228(x63143),x63141),x63144))
% 173.53/173.43 [6473]~P105(x64731)+~P49(x64735,x64731,x64732)+~P105(x64735)+P22(f312(f312(f227(x64731),f312(x64732,x64733)),f312(x64732,x64734)))+~P22(f312(f312(f227(x64735),x64733),x64734))
% 173.53/173.43 [7357]~P103(x73571)+~P33(x73571,f312(f312(f129(x73571),x73574),x73575))+~P22(f312(f312(f314(x73571),x73573),f312(f168(x73571),x73575)))+~P22(f312(f312(f314(x73571),x73572),f312(f168(x73571),x73574)))+P22(f312(f312(f227(x73571),x73572),x73573))
% 173.53/173.43 [8470]~P105(x84701)+~P22(f312(f312(f228(f860(x84701,a845)),f283(x84701,x84705,x84702)),f283(x84701,x84704,x84703)))+~P22(f312(f312(f227(x84701),x84705),x84702))+P22(f312(f312(f228(x84701),x84702),x84703))+P22(f312(f312(f228(x84701),x84704),x84705))
% 173.53/173.43 [9458]~P49(f860(x94584,a845),f860(x94584,a845),x94585)+P22(f312(x94581,x94582))+~E(x94583,f109(f860(x94584,a845),x94585))+~P22(f312(x94581,f559(x94581,x94582,x94585,x94584,x94583)))+~P22(f312(f312(f314(x94584),x94582),x94583))
% 173.53/173.43 [9856]~P12(x98562,x98565,x98563)+E(x98561,f189(f860(x98562,a845)))+~E(f312(f312(x98565,f312(x98564,f548(x98561,x98564,x98563,x98565,x98562))),f312(x98564,f549(x98561,x98564,x98563,x98565,x98562))),f312(x98564,f312(f312(x98565,f548(x98561,x98564,x98563,x98565,x98562)),f549(x98561,x98564,x98563,x98565,x98562))))+E(f312(x98563,f312(f290(x98562,x98562,x98564),x98561)),f312(x98564,f312(x98563,x98561)))+~P22(f312(f70(x98562),x98561))
% 173.53/173.43 [6308]~P13(x63082,x63085,x63083)+E(x63081,f189(f860(x63082,a845)))+~P22(f312(f70(x63082),x63081))+E(f312(x63083,f312(f312(f289(x63082),x63084),x63081)),f312(f312(x63085,x63084),f312(x63083,x63081)))+P22(f312(f312(f314(x63082),x63084),x63081))
% 173.53/173.43 [7127]~P12(x71272,x71273,x71274)+E(f312(f312(x71273,f312(x71274,x71271)),f312(x71274,x71275)),f312(x71274,x71275))+E(x71271,f189(f860(x71272,a845)))+~P22(f312(f70(x71272),x71275))+~P22(f312(f312(f227(f860(x71272,a845)),x71271),x71275))
% 173.53/173.43 [7492]~P13(x74924,x74925,x74921)+E(f312(x74921,x74922),x74923)+~P22(f312(f70(x74924),x74922))+~E(f312(f312(f21(f860(x74924,a845)),x74922),f312(f312(f289(x74924),x74923),f189(f860(x74924,a845)))),f189(f860(x74924,a845)))+~P22(f312(f312(f314(x74924),x74923),x74922))
% 173.53/173.43 [7577]E(x75771,x75772)+~E(f312(f190(f853(x75773)),x75772),f312(f190(f853(x75774)),x75775))+~E(f312(f190(f853(x75773)),x75771),f312(f190(f853(x75774)),x75775))+~E(f312(f173(x75774,x75773),f312(f312(f177(x75774,x75773),x75775),x75771)),f312(f173(x75774,x75773),f312(f312(f177(x75774,x75773),x75775),x75772)))+~P22(f312(f133(x75774),x75775))
% 173.53/173.43 [8438]E(x84381,x84382)+~P3(x84383,x84384,x84385)+E(f312(f312(f115(f860(x84383,a845)),x84381),x84382),f189(f860(x84383,a845)))+~P22(f312(f312(f314(f860(x84383,a845)),x84382),f312(f312(f69(x84383),x84384),x84385)))+~P22(f312(f312(f314(f860(x84383,a845)),x84381),f312(f312(f69(x84383),x84384),x84385)))
% 173.53/173.43 [9222]~P72(x92222)+~E(f312(x92223,f443(x92223,x92224,x92225,x92221,x92222)),f87(x92222))+E(f312(f312(f9(x92221,x92222),x92223),x92224),f312(f312(f9(x92221,x92222),x92223),x92225))+~P22(f312(f70(x92221),x92225))+~P22(f312(f312(f227(f860(x92221,a845)),x92224),x92225))
% 173.53/173.43 [9223]~P72(x92232)+~E(f312(x92233,f446(x92233,x92234,x92235,x92231,x92232)),f87(x92232))+E(f312(f312(f9(x92231,x92232),x92233),x92234),f312(f312(f9(x92231,x92232),x92233),x92235))+~P22(f312(f70(x92231),x92235))+~P22(f312(f312(f227(f860(x92231,a845)),x92234),x92235))
% 173.53/173.43 [9224]~P26(x92242)+~E(f312(x92243,f508(x92243,x92244,x92245,x92241,x92242)),f2(x92242))+E(f312(f312(f6(x92241,x92242),x92243),x92244),f312(f312(f6(x92241,x92242),x92243),x92245))+~P22(f312(f70(x92241),x92245))+~P22(f312(f312(f227(f860(x92241,a845)),x92244),x92245))
% 173.53/173.43 [9225]~P26(x92252)+~E(f312(x92253,f509(x92253,x92254,x92255,x92251,x92252)),f2(x92252))+E(f312(f312(f6(x92251,x92252),x92253),x92254),f312(f312(f6(x92251,x92252),x92253),x92255))+~P22(f312(f70(x92251),x92255))+~P22(f312(f312(f227(f860(x92251,a845)),x92254),x92255))
% 173.53/173.43 [9633]~P49(f860(x96331,a845),f860(x96331,a845),f312(f312(f8(f860(x96331,a845),f860(x96331,a845),f860(x96331,a845)),f233(x96331)),x96334))+~P22(f312(f312(x96334,f312(f312(f124(f860(x96331,a845)),x96335),x96333)),f563(x96335,x96332,x96334,x96331,x96333)))+~E(x96333,f110(f860(x96331,a845),f312(f312(f8(f860(x96331,a845),f860(x96331,a845),f860(x96331,a845)),f233(x96331)),x96334)))+P22(f312(f312(f314(x96331),x96332),x96333))+~P22(f312(f312(f314(x96331),x96332),x96335))
% 173.53/173.43 [9635]~P49(f860(x96351,a845),f860(x96351,a845),f312(f312(f8(f860(x96351,a845),f860(x96351,a845),f860(x96351,a845)),f233(x96351)),x96355))+~E(x96353,f110(f860(x96351,a845),f312(f312(f8(f860(x96351,a845),f860(x96351,a845),f860(x96351,a845)),f233(x96351)),x96355)))+~P22(f312(f312(f314(x96351),x96352),x96354))+P22(f312(f312(f314(x96351),f563(x96354,x96352,x96355,x96351,x96353)),x96354))+P22(f312(f312(f314(x96351),x96352),x96353))
% 173.53/173.43 [9688]~P84(x96881)+~P22(f312(f70(x96882),x96885))+~P22(f312(f312(f227(x96881),f2(x96881)),f312(x96883,f488(x96883,x96884,x96885,x96882,x96881))))+P22(f312(f312(f227(x96881),f312(f312(f6(x96882,x96881),x96883),x96884)),f312(f312(f6(x96882,x96881),x96883),x96885)))+~P22(f312(f312(f227(f860(x96882,a845)),x96884),x96885))
% 173.53/173.43 [7227]E(x72271,f2(a852))+P22(f312(x72272,x72273))+~E(x72274,f312(f312(f89(a852),f312(f312(f90(a852),x72271),x72273)),x72275))+~P22(f312(x72272,f312(f47(a852,x72274),x72271)))+~P22(f312(f312(f228(a852),x72275),x72271))
% 173.53/173.43 [7432]E(x74321,f2(a852))+P22(f312(x74322,x74323))+~P22(f312(x74322,f54(a852,x74324,x74321)))+~E(x74324,f312(f312(f89(a852),f312(f312(f90(a852),x74321),x74325)),x74323))+~P22(f312(f312(f228(a852),x74323),x74321))
% 173.53/173.43 [7726]~P65(x77263)+E(f312(x77261,x77262),f2(x77263))+~P22(f312(f70(x77264),x77265))+E(f312(f312(f9(x77264,x77263),x77261),f312(f312(f21(f860(x77264,a845)),x77265),f312(f312(f289(x77264),x77262),f189(f860(x77264,a845))))),f312(f312(f9(x77264,x77263),x77261),x77265))+P22(f312(f312(f314(x77264),x77262),x77265))
% 173.53/173.43 [8125]~P72(x81251)+~P22(f312(f70(x81252),x81255))+~P22(f312(f70(x81252),x81254))+~E(f312(f312(f115(f860(x81252,a845)),x81254),x81255),f189(f860(x81252,a845)))+E(f312(f312(f90(x81251),f312(f312(f9(x81252,x81251),x81253),x81254)),f312(f312(f9(x81252,x81251),x81253),x81255)),f312(f312(f9(x81252,x81251),x81253),f312(f312(f124(f860(x81252,a845)),x81254),x81255)))
% 173.53/173.43 [8126]~P26(x81261)+~P22(f312(f70(x81262),x81265))+~P22(f312(f70(x81262),x81264))+~E(f312(f312(f115(f860(x81262,a845)),x81264),x81265),f189(f860(x81262,a845)))+E(f312(f312(f89(x81261),f312(f312(f6(x81262,x81261),x81263),x81264)),f312(f312(f6(x81262,x81261),x81263),x81265)),f312(f312(f6(x81262,x81261),x81263),f312(f312(f124(f860(x81262,a845)),x81264),x81265)))
% 173.53/173.43 [8220]~P65(x82203)+E(f312(x82201,x82202),f2(x82203))+~P22(f312(f70(x82204),x82205))+E(f312(f312(f9(x82204,x82203),x82201),f312(f312(f21(f860(x82204,a845)),x82205),f312(f312(f289(x82204),x82202),f189(f860(x82204,a845))))),f312(f312(f268(x82203),f312(f312(f9(x82204,x82203),x82201),x82205)),f312(x82201,x82202)))+~P22(f312(f312(f314(x82204),x82202),x82205))
% 173.53/173.43 [8941]~P3(x89411,x89415,x89414)+~E(f312(f312(f69(x89411),f312(f312(f289(x89411),x89412),f189(f860(x89411,a845)))),x89414),f312(f312(f69(x89411),f312(f312(f289(x89411),x89413),f189(f860(x89411,a845)))),x89414))+~P22(f312(f312(f314(x89411),x89413),x89415))+~P22(f312(f312(f314(x89411),x89412),x89415))+P22(f312(f312(f314(f859(x89411,x89411)),f312(f312(f239(x89411,x89411),x89412),x89413)),x89414))
% 173.53/173.43 [8960]~P3(x89601,x89605,x89603)+E(f312(f312(f69(x89601),f312(f312(f289(x89601),x89602),f189(f860(x89601,a845)))),x89603),f312(f312(f69(x89601),f312(f312(f289(x89601),x89604),f189(f860(x89601,a845)))),x89603))+~P22(f312(f312(f314(x89601),x89604),x89605))+~P22(f312(f312(f314(x89601),x89602),x89605))+~P22(f312(f312(f314(f859(x89601,x89601)),f312(f312(f239(x89601,x89601),x89602),x89604)),x89603))
% 173.53/173.43 [9249]~P72(x92491)+~P22(f312(f70(x92492),x92495))+~P22(f312(f70(x92492),x92494))+~E(f312(f312(f115(f860(x92492,a845)),x92494),x92495),f189(f860(x92492,a845)))+E(f312(f312(f90(x92491),f312(f312(f312(f74(x92491,x92492,f90(x92491)),x92493),f87(x92491)),x92494)),f312(f312(f312(f74(x92491,x92492,f90(x92491)),x92493),f87(x92491)),x92495)),f312(f312(f312(f74(x92491,x92492,f90(x92491)),x92493),f87(x92491)),f312(f312(f124(f860(x92492,a845)),x92494),x92495)))
% 173.53/173.43 [9257]~P72(x92571)+~E(f312(x92573,f401(x92573,x92575,x92574,x92572,x92571)),f87(x92571))+~P22(f312(f70(x92572),x92574))+~P22(f312(f70(x92572),x92575))+E(f312(f312(f90(x92571),f312(f312(f9(x92572,x92571),x92573),x92574)),f312(f312(f9(x92572,x92571),x92573),x92575)),f312(f312(f9(x92572,x92571),x92573),f312(f312(f124(f860(x92572,a845)),x92574),x92575)))
% 173.53/173.43 [9258]~P72(x92581)+~E(f312(x92583,f402(x92583,x92585,x92584,x92582,x92581)),f87(x92581))+~P22(f312(f70(x92582),x92584))+~P22(f312(f70(x92582),x92585))+E(f312(f312(f90(x92581),f312(f312(f9(x92582,x92581),x92583),x92584)),f312(f312(f9(x92582,x92581),x92583),x92585)),f312(f312(f9(x92582,x92581),x92583),f312(f312(f124(f860(x92582,a845)),x92584),x92585)))
% 173.53/173.43 [9259]~P26(x92591)+~E(f312(x92593,f486(x92593,x92595,x92594,x92592,x92591)),f2(x92591))+~P22(f312(f70(x92592),x92594))+~P22(f312(f70(x92592),x92595))+E(f312(f312(f89(x92591),f312(f312(f6(x92592,x92591),x92593),x92594)),f312(f312(f6(x92592,x92591),x92593),x92595)),f312(f312(f6(x92592,x92591),x92593),f312(f312(f124(f860(x92592,a845)),x92594),x92595)))
% 173.53/173.43 [9260]~P26(x92601)+~E(f312(x92603,f498(x92603,x92605,x92604,x92602,x92601)),f2(x92601))+~P22(f312(f70(x92602),x92604))+~P22(f312(f70(x92602),x92605))+E(f312(f312(f89(x92601),f312(f312(f6(x92602,x92601),x92603),x92604)),f312(f312(f6(x92602,x92601),x92603),x92605)),f312(f312(f6(x92602,x92601),x92603),f312(f312(f124(f860(x92602,a845)),x92604),x92605)))
% 173.53/173.43 [9466]~P72(x94661)+~E(f312(x94663,f427(x94663,x94665,x94664,x94662,x94661)),f87(x94661))+~P22(f312(f70(x94662),x94664))+~P22(f312(f70(x94662),x94665))+E(f312(f312(f90(x94661),f312(f312(f312(f74(x94661,x94662,f90(x94661)),x94663),f87(x94661)),x94664)),f312(f312(f312(f74(x94661,x94662,f90(x94661)),x94663),f87(x94661)),x94665)),f312(f312(f312(f74(x94661,x94662,f90(x94661)),x94663),f87(x94661)),f312(f312(f124(f860(x94662,a845)),x94664),x94665)))
% 173.53/173.43 [9568]~P72(x95682)+E(f312(f312(f9(x95681,x95682),x95683),x95684),f312(f312(f9(x95681,x95682),x95683),x95685))+~P22(f312(f70(x95681),x95685))+~P22(f312(f312(f227(f860(x95681,a845)),x95684),x95685))+P22(f312(f312(f314(x95681),f443(x95683,x95684,x95685,x95681,x95682)),f312(f312(f21(f860(x95681,a845)),x95685),x95684)))
% 173.53/173.43 [9569]~P72(x95692)+E(f312(f312(f9(x95691,x95692),x95693),x95694),f312(f312(f9(x95691,x95692),x95693),x95695))+~P22(f312(f70(x95691),x95695))+~P22(f312(f312(f227(f860(x95691,a845)),x95694),x95695))+P22(f312(f312(f314(x95691),f446(x95693,x95694,x95695,x95691,x95692)),f312(f312(f21(f860(x95691,a845)),x95695),x95694)))
% 173.53/173.43 [9570]~P26(x95702)+E(f312(f312(f6(x95701,x95702),x95703),x95704),f312(f312(f6(x95701,x95702),x95703),x95705))+~P22(f312(f70(x95701),x95705))+~P22(f312(f312(f227(f860(x95701,a845)),x95704),x95705))+P22(f312(f312(f314(x95701),f508(x95703,x95704,x95705,x95701,x95702)),f312(f312(f21(f860(x95701,a845)),x95705),x95704)))
% 173.53/173.43 [9571]~P26(x95712)+E(f312(f312(f6(x95711,x95712),x95713),x95714),f312(f312(f6(x95711,x95712),x95713),x95715))+~P22(f312(f70(x95711),x95715))+~P22(f312(f312(f227(f860(x95711,a845)),x95714),x95715))+P22(f312(f312(f314(x95711),f509(x95713,x95714,x95715,x95711,x95712)),f312(f312(f21(f860(x95711,a845)),x95715),x95714)))
% 173.53/173.43 [9587]~P72(x95871)+~P22(f312(f70(x95872),x95874))+~P22(f312(f70(x95872),x95875))+E(f312(f312(f90(x95871),f312(f312(f9(x95872,x95871),x95873),x95874)),f312(f312(f9(x95872,x95871),x95873),x95875)),f312(f312(f9(x95872,x95871),x95873),f312(f312(f124(f860(x95872,a845)),x95874),x95875)))+P22(f312(f312(f314(x95872),f401(x95873,x95875,x95874,x95872,x95871)),f312(f312(f115(f860(x95872,a845)),x95874),x95875)))
% 173.53/173.43 [9588]~P72(x95881)+~P22(f312(f70(x95882),x95884))+~P22(f312(f70(x95882),x95885))+E(f312(f312(f90(x95881),f312(f312(f9(x95882,x95881),x95883),x95884)),f312(f312(f9(x95882,x95881),x95883),x95885)),f312(f312(f9(x95882,x95881),x95883),f312(f312(f124(f860(x95882,a845)),x95884),x95885)))+P22(f312(f312(f314(x95882),f402(x95883,x95885,x95884,x95882,x95881)),f312(f312(f115(f860(x95882,a845)),x95884),x95885)))
% 173.53/173.43 [9589]~P26(x95891)+~P22(f312(f70(x95892),x95894))+~P22(f312(f70(x95892),x95895))+E(f312(f312(f89(x95891),f312(f312(f6(x95892,x95891),x95893),x95894)),f312(f312(f6(x95892,x95891),x95893),x95895)),f312(f312(f6(x95892,x95891),x95893),f312(f312(f124(f860(x95892,a845)),x95894),x95895)))+P22(f312(f312(f314(x95892),f486(x95893,x95895,x95894,x95892,x95891)),f312(f312(f115(f860(x95892,a845)),x95894),x95895)))
% 173.53/173.43 [9590]~P26(x95901)+~P22(f312(f70(x95902),x95904))+~P22(f312(f70(x95902),x95905))+E(f312(f312(f89(x95901),f312(f312(f6(x95902,x95901),x95903),x95904)),f312(f312(f6(x95902,x95901),x95903),x95905)),f312(f312(f6(x95902,x95901),x95903),f312(f312(f124(f860(x95902,a845)),x95904),x95905)))+P22(f312(f312(f314(x95902),f498(x95903,x95905,x95904,x95902,x95901)),f312(f312(f115(f860(x95902,a845)),x95904),x95905)))
% 173.53/173.43 [9593]~P49(f860(x95933,a845),f860(x95933,a845),x95934)+P22(f312(x95931,x95932))+~E(x95935,f109(f860(x95933,a845),x95934))+~P22(f312(f312(f314(x95933),x95932),x95935))+P22(f312(f312(f314(x95933),f559(x95931,x95932,x95934,x95933,x95935)),f312(x95934,f312(f312(f115(f860(x95933,a845)),x95935),f312(f233(x95933),x95931)))))
% 173.53/173.43 [9598]~P84(x95985)+~P22(f312(f70(x95981),x95984))+P22(f312(f312(f227(x95985),f312(f312(f6(x95981,x95985),x95982),x95983)),f312(f312(f6(x95981,x95985),x95982),x95984)))+~P22(f312(f312(f227(f860(x95981,a845)),x95983),x95984))+P22(f312(f312(f314(x95981),f488(x95982,x95983,x95984,x95981,x95985)),f312(f312(f21(f860(x95981,a845)),x95984),x95983)))
% 173.53/173.43 [9652]~P72(x96521)+~P22(f312(f70(x96522),x96524))+~P22(f312(f70(x96522),x96525))+E(f312(f312(f90(x96521),f312(f312(f312(f74(x96521,x96522,f90(x96521)),x96523),f87(x96521)),x96524)),f312(f312(f312(f74(x96521,x96522,f90(x96521)),x96523),f87(x96521)),x96525)),f312(f312(f312(f74(x96521,x96522,f90(x96521)),x96523),f87(x96521)),f312(f312(f124(f860(x96522,a845)),x96524),x96525)))+P22(f312(f312(f314(x96522),f427(x96523,x96525,x96524,x96522,x96521)),f312(f312(f115(f860(x96522,a845)),x96524),x96525)))
% 173.53/173.43 [8629]~P13(x86291,x86294,x86295)+~P22(f312(f70(x86291),x86292))+E(f312(f312(f21(f860(x86291,a845)),x86292),f312(f312(f289(x86291),x86293),f189(f860(x86291,a845)))),f189(f860(x86291,a845)))+~P22(f312(f312(f314(x86291),x86293),x86292))+E(f312(f312(x86294,x86293),f312(x86295,f312(f312(f21(f860(x86291,a845)),x86292),f312(f312(f289(x86291),x86293),f189(f860(x86291,a845)))))),f312(x86295,x86292))
% 173.53/173.43 [8702]~P13(x87021,x87024,x87025)+~P22(f312(f70(x87021),x87023))+~P22(f312(f70(x87021),x87022))+E(f312(f312(f115(f860(x87021,a845)),x87022),x87023),f189(f860(x87021,a845)))+E(f312(f312(x87024,f312(x87025,f312(f312(f124(f860(x87021,a845)),x87022),x87023))),f312(x87025,f312(f312(f115(f860(x87021,a845)),x87022),x87023))),f312(f312(x87024,f312(x87025,x87022)),f312(x87025,x87023)))
% 173.53/173.43 [8888]~P49(f860(x88881,a845),f860(x88881,a845),x88884)+~E(x88883,f110(f860(x88881,a845),x88884))+P22(f312(f312(f314(x88881),x88882),x88883))+~P22(f312(f312(f314(x88881),x88882),x88885))+~P22(f312(f312(f227(f860(x88881,a845)),x88885),f312(x88884,f312(f312(f124(f860(x88881,a845)),x88885),x88883))))
% 173.53/173.43 [9262]~P22(f312(f312(f227(a1),x92624),f2(a1)))+~P22(f312(f312(f228(a1),x92623),x92625))+P22(f312(f312(f227(a1),x92621),x92622))+~P22(f312(f312(f228(a1),x92623),x92624))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92623),x92622)),x92625)),f312(f312(f89(a1),f312(f312(f90(a1),x92623),x92621)),x92624)))
% 173.53/173.43 [9264]~P22(f312(f312(f227(a1),f2(a1)),x92645))+P22(f312(f312(f227(a1),x92641),x92642))+~P22(f312(f312(f228(a1),x92643),x92644))+~P22(f312(f312(f228(a1),x92645),x92644))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92644),x92641)),x92645)),f312(f312(f89(a1),f312(f312(f90(a1),x92644),x92642)),x92643)))
% 173.53/173.43 [9374]~P65(x93745)+E(f312(x93741,f421(x93741,x93742,x93743,x93744,x93745)),f2(x93745))+~P22(f312(f70(x93744),x93743))+~P22(f312(f70(x93744),x93742))+E(f312(f312(f268(x93745),f312(f312(f90(x93745),f312(f312(f9(x93744,x93745),x93741),x93743)),f312(f312(f9(x93744,x93745),x93741),x93742))),f312(f312(f9(x93744,x93745),x93741),f312(f312(f115(f860(x93744,a845)),x93743),x93742))),f312(f312(f9(x93744,x93745),x93741),f312(f312(f124(f860(x93744,a845)),x93743),x93742)))
% 173.53/173.43 [9647]~P65(x96471)+~P22(f312(f70(x96472),x96474))+~P22(f312(f70(x96472),x96475))+E(f312(f312(f268(x96471),f312(f312(f90(x96471),f312(f312(f9(x96472,x96471),x96473),x96474)),f312(f312(f9(x96472,x96471),x96473),x96475))),f312(f312(f9(x96472,x96471),x96473),f312(f312(f115(f860(x96472,a845)),x96474),x96475))),f312(f312(f9(x96472,x96471),x96473),f312(f312(f124(f860(x96472,a845)),x96474),x96475)))+P22(f312(f312(f314(x96472),f421(x96473,x96475,x96474,x96472,x96471)),f312(f312(f115(f860(x96472,a845)),x96474),x96475)))
% 173.53/173.43 [8978]E(f312(f312(f129(x89781),x89782),x89783),f312(f312(f129(x89781),x89784),x89785))+~E(f312(f312(f169(x89781),f312(f190(f853(x89781)),x89784)),x89782),x89784)+~E(f312(f312(f169(x89781),f312(f190(f853(x89781)),x89782)),x89784),x89782)+~E(x89785,f312(f312(f129(x89781),f312(f312(f134(x89781),f312(f190(f853(x89781)),x89784)),x89782)),x89783))+~E(f312(f312(f129(x89781),f312(f312(f134(x89781),f312(f190(f853(x89781)),x89782)),x89784)),x89785),x89783)
% 173.53/173.43 [9372]~P103(x93722)+E(f312(f312(f145(x93721,x93722,x93723),x93724),f166(x93721,x93724,x93725)),x93725)+~P33(x93722,f312(f312(f150(x93721,x93722),x93723),x93725))+~P22(f312(f312(f314(x93721),x93724),f312(f168(x93721),x93725)))+~E(f312(f137(x93721),f312(f132(x93721,f312(f312(f8(x93722,a845,x93721),f312(a309,f312(x93723,x93724))),x93723)),x93725)),x93724)
% 173.53/173.43 [9703]~P68(x97031)+~P22(f312(f75(x97031,x97031,f90(x97031),x97032,x97033),x97035))+~P22(f312(f312(f314(x97031),x97034),x97033))+P22(f312(f312(f314(x97031),x97032),x97033))+P22(f312(f75(x97031,x97031,f90(x97031),x97034,f312(f312(f289(x97031),x97032),f312(f312(f21(f860(x97031,a845)),x97033),f312(f312(f289(x97031),x97034),f189(f860(x97031,a845)))))),x97035))
% 173.53/173.43 [10049]~P49(f860(x100491,a845),f860(x100491,a845),x100494)+~E(x100493,f110(f860(x100491,a845),x100494))+P22(f312(f312(f314(x100491),x100492),x100493))+~P22(f312(f312(f314(x100491),x100492),x100495))+~P22(f312(f312(f227(f860(x100491,a845)),x100495),f312(x100494,f109(f860(x100491,a845),f312(f312(f7(f860(x100491,a845),f860(x100491,a845),f860(x100491,a845)),f312(f312(f8(f860(x100491,a845),f860(f860(x100491,a845),f860(x100491,a845)),f860(x100491,a845)),f124(f860(x100491,a845))),f312(f312(f7(f860(x100491,a845),f860(x100491,a845),f860(x100491,a845)),f312(f312(f8(f860(x100491,a845),f860(f860(x100491,a845),f860(x100491,a845)),f860(x100491,a845)),f124(f860(x100491,a845))),x100494)),x100495))),x100493)))))
% 173.53/173.43 [7132]E(x71321,x71322)+~P19(x71324,x71325,x71323,x71326)+~E(f312(x71323,x71321),f312(x71323,x71322))+~P22(f312(f312(f314(x71324),x71322),x71326))+~P22(f312(f312(f314(x71324),x71321),x71326))
% 173.53/173.43 [6402]~P136(x64024)+E(x64021,x64022)+~E(x64025,x64026)+E(x64023,f2(x64024))+~E(f312(f312(f89(x64024),x64025),f312(f312(f90(x64024),x64023),x64021)),f312(f312(f89(x64024),x64026),f312(f312(f90(x64024),x64023),x64022)))
% 173.53/173.43 [7413]~P103(x74131)+~P31(x74131)+~P22(f312(f312(f228(x74131),x74132),f312(x74135,x74136)))+~P22(f312(f312(f314(x74133),x74136),x74134))+P22(f312(f312(f228(x74131),x74132),f312(f312(f50(x74133,x74131),x74134),x74135)))
% 173.53/173.43 [8094]~P103(x80941)+~P31(x80941)+~P22(f312(f312(f228(x80941),f312(x80944,x80946)),x80945))+~P22(f312(f312(f314(x80942),x80946),x80943))+P22(f312(f312(f228(x80941),f312(f312(f51(x80942,x80941),x80943),x80944)),x80945))
% 173.53/173.43 [8362]~P14(x83622,x83625,x83626,x83621)+~P22(f312(f70(x83622),x83624))+~P22(f312(f70(x83622),x83623))+~E(f312(f312(f115(f860(x83622,a845)),x83623),x83624),f189(f860(x83622,a845)))+E(f312(x83621,f312(f312(f124(f860(x83622,a845)),x83623),x83624)),f312(f82(x83625,x83625,x83625,f312(x83621,x83623)),f312(x83621,x83624)))
% 173.53/173.43 [8673]E(x86731,x86732)+~P56(x86734,x86735,x86736,x86733,x86737)+~E(f312(x86733,x86731),f312(x86733,x86732))+~P22(f312(f312(f314(x86735),x86732),x86737))+~P22(f312(f312(f314(x86735),x86731),x86737))
% 173.53/173.43 [9960]~P22(f312(x99602,x99604))+~E(x99605,f312(f132(x99601,x99602),x99607))+E(f312(f132(x99601,x99602),x99603),f312(f312(f147(x99601),x99604),x99605))+~E(x99603,f312(f312(f129(x99601),x99606),f312(f312(f147(x99601),x99604),x99607)))+P22(f312(x99602,f731(x99605,x99604,x99603,x99602,x99601,x99606,x99607)))
% 173.53/173.43 [9961]~P22(f312(x99614,x99612))+~E(x99613,f312(f132(x99611,x99614),x99617))+E(f312(f312(f147(x99611),x99612),x99613),f312(f132(x99611,x99614),x99615))+~E(x99615,f312(f312(f129(x99611),x99616),f312(f312(f147(x99611),x99612),x99617)))+P22(f312(x99614,f733(x99615,x99614,x99613,x99612,x99611,x99616,x99617)))
% 173.53/173.43 [9994]~P22(f312(x99942,x99944))+~E(x99945,f312(f132(x99941,x99942),x99947))+E(f312(f132(x99941,x99942),x99943),f312(f312(f147(x99941),x99944),x99945))+~E(x99943,f312(f312(f129(x99941),x99946),f312(f312(f147(x99941),x99944),x99947)))+P22(f312(f312(f314(x99941),f731(x99945,x99944,x99943,x99942,x99941,x99946,x99947)),f312(f168(x99941),x99946)))
% 173.53/173.43 [9995]~P22(f312(x99954,x99952))+~E(x99953,f312(f132(x99951,x99954),x99957))+E(f312(f312(f147(x99951),x99952),x99953),f312(f132(x99951,x99954),x99955))+~E(x99955,f312(f312(f129(x99951),x99956),f312(f312(f147(x99951),x99952),x99957)))+P22(f312(f312(f314(x99951),f733(x99955,x99954,x99953,x99952,x99951,x99956,x99957)),f312(f168(x99951),x99956)))
% 173.53/173.43 [9998]~P3(x99981,x99987,x99986)+~P9(x99981,f860(x99985,a845),x99986,x99984)+P22(f312(f312(f314(x99981),f422(x99982,x99983,x99984,x99985,x99986,x99987,x99981)),x99987))+~P22(f312(f312(f314(f860(x99981,a845)),x99983),f312(f312(f69(x99981),x99987),x99986)))+P22(f312(f312(f314(f860(x99985,a845)),f312(f312(f50(x99981,f860(x99985,a845)),x99983),x99984)),x99982))
% 173.53/173.43 [10045]~P3(x100452,x100456,x100457)+~P9(x100452,f860(x100451,a845),x100457,x100454)+~P22(f312(f312(f314(f860(x100452,a845)),x100453),f312(f312(f69(x100452),x100456),x100457)))+~P22(f312(f312(f314(f860(x100451,a845)),f312(x100454,f422(x100455,x100453,x100454,x100451,x100457,x100456,x100452))),x100455))+P22(f312(f312(f314(f860(x100451,a845)),f312(f312(f50(x100452,f860(x100451,a845)),x100453),x100454)),x100455))
% 173.53/173.43 [8266]~P72(x82662)+~P19(x82661,x82665,x82668,x82664)+~E(x82663,f312(f82(x82665,x82662,x82661,x82666),x82668))+~E(x82667,f312(f290(x82661,x82665,x82668),x82664))+E(f312(f312(f9(x82661,x82662),x82663),x82664),f312(f312(f9(x82665,x82662),x82666),x82667))
% 173.53/173.43 [10048]~P72(x100482)+~P19(x100485,x100481,x100488,x100487)+~E(f312(x100486,f445(x100483,x100486,x100484,x100487,x100488,x100481,x100485,x100482)),f312(f312(f82(x100481,x100482,x100485,x100483),x100488),f445(x100483,x100486,x100484,x100487,x100488,x100481,x100485,x100482)))+~E(x100484,f312(f290(x100485,x100481,x100488),x100487))+E(f312(f312(f9(x100481,x100482),x100483),x100484),f312(f312(f9(x100485,x100482),x100486),x100487))
% 173.53/173.43 [10052]~P72(x100522)+~P19(x100521,x100525,x100528,x100524)+~E(x100527,f312(f290(x100521,x100525,x100528),x100524))+E(f312(f312(f9(x100521,x100522),x100523),x100524),f312(f312(f9(x100525,x100522),x100526),x100527))+P22(f312(f312(f314(x100521),f445(x100526,x100523,x100527,x100524,x100528,x100525,x100521,x100522)),x100524))
% 173.53/173.43 [10053]~P26(x100532)+~P19(x100531,x100535,x100538,x100534)+~E(x100537,f312(f290(x100531,x100535,x100538),x100534))+E(f312(f312(f6(x100531,x100532),x100533),x100534),f312(f312(f6(x100535,x100532),x100536),x100537))+P22(f312(f312(f314(x100531),f752(x100536,x100533,x100537,x100534,x100538,x100535,x100531,x100532)),x100534))
% 173.53/173.43 [10061]~P26(x100612)+~P19(x100615,x100611,x100618,x100617)+~E(x100614,f312(f290(x100615,x100611,x100618),x100617))+~E(f312(x100616,f752(x100613,x100616,x100614,x100617,x100618,x100611,x100615,x100612)),f312(x100613,f312(x100618,f752(x100613,x100616,x100614,x100617,x100618,x100611,x100615,x100612))))+E(f312(f312(f6(x100611,x100612),x100613),x100614),f312(f312(f6(x100615,x100612),x100616),x100617))
% 173.53/173.43 [9429]~E(f312(f190(f853(x94292)),x94295),f312(f190(f853(x94291)),x94293))+~E(f312(f190(f853(x94292)),x94294),f312(f190(f853(x94291)),x94293))+~E(f312(f312(f312(f81(x94291,f856(x94292)),f312(f173(x94291,x94292),f312(f312(f177(x94291,x94292),x94293),x94294))),x94296),f312(f219(x94292),x94297)),f312(f312(f312(f81(x94291,f856(x94292)),f312(f173(x94291,x94292),f312(f312(f177(x94291,x94292),x94293),x94295))),x94296),f312(f219(x94292),x94298)))+E(f312(f173(x94291,x94292),f312(f312(f177(x94291,x94292),x94293),x94294)),f312(f173(x94291,x94292),f312(f312(f177(x94291,x94292),x94293),x94295)))+P22(f312(f312(f314(x94291),x94296),f312(f168(x94291),x94293)))
% 173.53/173.43 [9537]~P17(x95376,x95372,x95375,x95377,x95378,x95371)+~P22(f312(f70(x95372),x95374))+~P22(f312(f70(x95372),x95373))+~E(f312(f312(f115(f860(x95372,a845)),x95373),x95374),f189(f860(x95372,a845)))+E(f312(x95371,f312(f312(f124(f860(x95372,a845)),x95373),x95374)),f312(f312(x95375,f312(x95371,x95373)),f312(x95371,x95374)))
% 173.53/173.43 [9946]~P17(x99468,x99462,x99465,x99467,x99466,x99461)+~E(f312(x99466,f552(x99464,x99463,x99461,x99466,x99467,x99465,x99462)),x99467)+~P22(f312(f70(x99462),x99463))+~P22(f312(f70(x99462),x99464))+E(f312(x99461,f312(f312(f124(f860(x99462,a845)),x99463),x99464)),f312(f312(x99465,f312(x99461,x99463)),f312(x99461,x99464)))
% 173.53/173.43 [10005]~P17(x100058,x100052,x100055,x100057,x100056,x100051)+~P22(f312(f70(x100052),x100053))+~P22(f312(f70(x100052),x100054))+E(f312(x100051,f312(f312(f124(f860(x100052,a845)),x100053),x100054)),f312(f312(x100055,f312(x100051,x100053)),f312(x100051,x100054)))+P22(f312(f312(f314(x100052),f552(x100054,x100053,x100051,x100056,x100057,x100055,x100052)),f312(f312(f115(f860(x100052,a845)),x100053),x100054)))
% 173.53/173.43 [9691]~P3(x96914,x96918,x96915)+~P3(x96911,x96919,x96913)+~P10(x96911,x96914,f860(x96912,a845),x96913,x96915,x96917)+P9(x96911,f860(x96912,a845),x96913,f312(f312(f8(f860(x96914,f860(x96912,a845)),f860(x96912,a845),x96911),f312(f50(x96914,f860(x96912,a845)),f312(f264(x96914,x96914,x96915),f312(f312(f289(x96914),x96916),f189(f860(x96914,a845)))))),x96917))+~P22(f312(f312(f314(x96914),x96916),x96918))
% 173.53/173.43 [5345]~P103(x53453)+~P33(x53453,x53451)+E(x53451,f687(x53452,x53453))+~E(f312(f168(x53453),x53451),x53452)+~P22(f312(f70(x53453),x53452))+~P22(f312(f133(x53453),x53451))
% 173.53/173.43 [4973]~P137(x49732)+~P126(x49732)+~P127(x49732)+~P109(x49732)+E(x49731,f2(x49732))+~E(f312(f312(f240(x49732),x49731),x49733),f2(x49732))
% 173.53/173.43 [4974]~P137(x49742)+~P126(x49742)+~P127(x49742)+~P109(x49742)+~E(x49741,f2(a852))+~E(f312(f312(f240(x49742),x49743),x49741),f2(x49742))
% 173.53/173.43 [6383]~P84(x63831)+~E(x63833,f2(x63831))+~E(x63832,f2(x63831))+E(f312(f312(f89(x63831),x63832),x63833),f2(x63831))+~P22(f312(f312(f227(x63831),f2(x63831)),x63833))+~P22(f312(f312(f227(x63831),f2(x63831)),x63832))
% 173.53/173.43 [8733]~E(f312(f246(a852,a852),x87333),f2(a852))+~E(x87331,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x87333)),x87332)),f312(f248(a852,a852),x87333)))+P22(f312(f56(x87331,x87332),x87333))+~P22(f312(f312(f227(a852),f312(f248(a852,a852),x87333)),f2(a852)))+P22(f312(f312(f228(a852),f2(a852)),x87332))+~P22(f312(f312(f228(a852),x87332),f312(f248(a852,a852),x87333)))
% 173.53/173.43 [8741]E(x87411,f2(a852))+~E(x87412,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x87413)),x87411)),f312(f248(a852,a852),x87413)))+P22(f312(f56(x87412,x87411),x87413))+~P22(f312(f312(f228(a852),f2(a852)),x87411))+~P22(f312(f312(f227(a852),f2(a852)),f312(f248(a852,a852),x87413)))+~P22(f312(f312(f228(a852),f312(f248(a852,a852),x87413)),x87411))
% 173.53/173.43 [8758]~E(f312(f246(a852,a852),x87583),f2(a852))+~E(x87581,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x87583)),x87582)),f312(f248(a852,a852),x87583)))+P22(f312(f56(x87581,x87582),x87583))+~P22(f312(f312(f228(a852),f2(a852)),x87582))+~P22(f312(f312(f227(a852),f2(a852)),f312(f248(a852,a852),x87583)))+~P22(f312(f312(f228(a852),f312(f248(a852,a852),x87583)),x87582))
% 173.53/173.43 [6754]~P87(x67542)+E(x67541,f189(f860(x67542,a845)))+E(x67543,f189(f860(x67542,a845)))+~P22(f312(f70(x67542),x67541))+~P22(f312(f70(x67542),x67543))+E(f11(x67542,f312(f312(f124(f860(x67542,a845)),x67543),x67541)),f312(f312(f115(x67542),f11(x67542,x67543)),f11(x67542,x67541)))
% 173.53/173.43 [6755]~P87(x67552)+E(x67551,f189(f860(x67552,a845)))+E(x67553,f189(f860(x67552,a845)))+~P22(f312(f70(x67552),x67551))+~P22(f312(f70(x67552),x67553))+E(f10(x67552,f312(f312(f124(f860(x67552,a845)),x67553),x67551)),f312(f312(f124(x67552),f10(x67552,x67553)),f10(x67552,x67551)))
% 173.53/173.43 [6756]~P103(x67562)+E(x67561,f189(f860(x67562,a845)))+E(x67563,f189(f860(x67562,a845)))+~P22(f312(f70(x67562),x67561))+~P22(f312(f70(x67562),x67563))+E(f14(x67562,f312(f312(f124(f860(x67562,a845)),x67563),x67561)),f312(f312(f226(x67562),f14(x67562,x67563)),f14(x67562,x67561)))
% 173.53/173.43 [6757]~P103(x67572)+E(x67571,f189(f860(x67572,a845)))+E(x67573,f189(f860(x67572,a845)))+~P22(f312(f70(x67572),x67571))+~P22(f312(f70(x67572),x67573))+E(f15(x67572,f312(f312(f124(f860(x67572,a845)),x67573),x67571)),f312(f312(f225(x67572),f15(x67572,x67573)),f15(x67572,x67571)))
% 173.53/173.43 [7388]~P93(x73882)+E(x73881,f189(f860(x73882,a845)))+E(x73883,f189(f860(x73882,a845)))+~P22(f312(f70(x73882),x73881))+~P22(f312(f70(x73882),x73883))+E(f312(f312(f90(x73882),f312(f72(x73882,f90(x73882)),x73883)),f312(f72(x73882,f90(x73882)),x73881)),f312(f72(x73882,f90(x73882)),f312(f312(f124(f860(x73882,a845)),x73883),x73881)))
% 173.53/173.43 [7545]~P103(x75452)+E(x75451,f189(f860(x75452,a845)))+E(x75453,f189(f860(x75452,a845)))+~P22(f312(f70(x75452),x75451))+~P22(f312(f70(x75452),x75453))+E(f312(f312(f226(x75452),f12(x75452,f226(x75452),x75453)),f12(x75452,f226(x75452),x75451)),f12(x75452,f226(x75452),f312(f312(f124(f860(x75452,a845)),x75453),x75451)))
% 173.53/173.43 [7546]~P103(x75462)+E(x75461,f189(f860(x75462,a845)))+E(x75463,f189(f860(x75462,a845)))+~P22(f312(f70(x75462),x75461))+~P22(f312(f70(x75462),x75463))+E(f312(f312(f225(x75462),f13(x75462,f225(x75462),x75463)),f13(x75462,f225(x75462),x75461)),f13(x75462,f225(x75462),f312(f312(f124(f860(x75462,a845)),x75463),x75461)))
% 173.53/173.43 [8582]~P22(f312(x85821,x85823))+P22(f312(x85821,f478(x85821,x85822)))+P22(f312(x85821,f470(x85821,x85822)))+~P22(f312(f312(f228(a1),f2(a1)),x85822))+~P22(f312(f312(f314(a1),x85823),f283(a1,f87(a1),x85822)))+P22(f312(x85821,f312(f312(f21(a1),f470(x85821,x85822)),f312(f312(f90(a1),f476(x85821,x85822)),x85822))))
% 173.53/173.43 [8878]~P22(f312(x88781,x88783))+~P22(f312(x88781,f470(x88781,x88782)))+P22(f312(x88781,f478(x88781,x88782)))+~P22(f312(f312(f228(a1),f2(a1)),x88782))+~P22(f312(f312(f314(a1),x88783),f283(a1,f87(a1),x88782)))+~P22(f312(x88781,f312(f312(f21(a1),f470(x88781,x88782)),f312(f312(f90(a1),f476(x88781,x88782)),x88782))))
% 173.53/173.43 [10085]~P96(x100852)+E(x100851,f189(f860(x100852,a845)))+E(x100853,f189(f860(x100852,a845)))+~P22(f312(f70(x100852),x100851))+~P22(f312(f70(x100852),x100853))+E(f11(x100852,f312(f233(x100852),f312(f312(f8(f860(x100852,a845),a845,x100852),f96(x100852)),f312(f312(f8(f860(x100852,f860(x100852,a845)),f860(x100852,a845),x100852),f312(f8(f860(x100852,a845),a845,x100852),f96(x100852))),f312(f312(f7(x100852,f860(x100852,f860(x100852,a845)),f860(x100852,f860(x100852,a845))),f312(f312(f8(f860(x100852,f860(f860(x100852,a845),f860(x100852,a845))),f860(f860(x100852,f860(x100852,a845)),f860(x100852,f860(x100852,a845))),x100852),f18(x100852,f860(x100852,a845),f860(x100852,a845))),f312(f312(f8(f860(x100852,f860(x100852,f860(a845,a845))),f860(x100852,f860(f860(x100852,a845),f860(x100852,a845))),x100852),f312(f8(f860(x100852,f860(a845,a845)),f860(f860(x100852,a845),f860(x100852,a845)),x100852),f18(x100852,a845,a845))),f312(f312(f8(f860(x100852,f860(x100852,a845)),f860(x100852,f860(x100852,f860(a845,a845))),x100852),f312(f8(f860(x100852,a845),f860(x100852,f860(a845,a845)),x100852),f312(f8(a845,f860(a845,a845),x100852),a310))),f312(f312(f7(x100852,f860(x100852,f860(x100852,x100852)),f860(x100852,f860(x100852,a845))),f312(f312(f8(f860(f860(x100852,x100852),f860(x100852,a845)),f860(f860(x100852,f860(x100852,x100852)),f860(x100852,f860(x100852,a845))),x100852),f8(f860(x100852,x100852),f860(x100852,a845),x100852)),f312(f312(f8(f860(x100852,a845),f860(f860(x100852,x100852),f860(x100852,a845)),x100852),f8(x100852,a845,x100852)),a309))),f124(x100852)))))),f312(f312(f7(x100852,f860(x100852,a845),f860(x100852,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x100852,a845),f860(x100852,a845)),x100852),f8(a845,a845,x100852)),f312(f312(f8(a845,f860(a845,a845),x100852),a310),f312(f312(f7(x100852,f860(x100852,a845),a845),f314(x100852)),x100853)))),f312(f312(f7(x100852,f860(x100852,a845),a845),f314(x100852)),x100851))))))),f312(f312(f124(x100852),f11(x100852,x100853)),f11(x100852,x100851)))
% 173.53/173.43 [10086]~P96(x100862)+E(x100861,f189(f860(x100862,a845)))+E(x100863,f189(f860(x100862,a845)))+~P22(f312(f70(x100862),x100861))+~P22(f312(f70(x100862),x100863))+E(f10(x100862,f312(f233(x100862),f312(f312(f8(f860(x100862,a845),a845,x100862),f96(x100862)),f312(f312(f8(f860(x100862,f860(x100862,a845)),f860(x100862,a845),x100862),f312(f8(f860(x100862,a845),a845,x100862),f96(x100862))),f312(f312(f7(x100862,f860(x100862,f860(x100862,a845)),f860(x100862,f860(x100862,a845))),f312(f312(f8(f860(x100862,f860(f860(x100862,a845),f860(x100862,a845))),f860(f860(x100862,f860(x100862,a845)),f860(x100862,f860(x100862,a845))),x100862),f18(x100862,f860(x100862,a845),f860(x100862,a845))),f312(f312(f8(f860(x100862,f860(x100862,f860(a845,a845))),f860(x100862,f860(f860(x100862,a845),f860(x100862,a845))),x100862),f312(f8(f860(x100862,f860(a845,a845)),f860(f860(x100862,a845),f860(x100862,a845)),x100862),f18(x100862,a845,a845))),f312(f312(f8(f860(x100862,f860(x100862,a845)),f860(x100862,f860(x100862,f860(a845,a845))),x100862),f312(f8(f860(x100862,a845),f860(x100862,f860(a845,a845)),x100862),f312(f8(a845,f860(a845,a845),x100862),a310))),f312(f312(f7(x100862,f860(x100862,f860(x100862,x100862)),f860(x100862,f860(x100862,a845))),f312(f312(f8(f860(f860(x100862,x100862),f860(x100862,a845)),f860(f860(x100862,f860(x100862,x100862)),f860(x100862,f860(x100862,a845))),x100862),f8(f860(x100862,x100862),f860(x100862,a845),x100862)),f312(f312(f8(f860(x100862,a845),f860(f860(x100862,x100862),f860(x100862,a845)),x100862),f8(x100862,a845,x100862)),a309))),f115(x100862)))))),f312(f312(f7(x100862,f860(x100862,a845),f860(x100862,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x100862,a845),f860(x100862,a845)),x100862),f8(a845,a845,x100862)),f312(f312(f8(a845,f860(a845,a845),x100862),a310),f312(f312(f7(x100862,f860(x100862,a845),a845),f314(x100862)),x100863)))),f312(f312(f7(x100862,f860(x100862,a845),a845),f314(x100862)),x100861))))))),f312(f312(f115(x100862),f10(x100862,x100863)),f10(x100862,x100861)))
% 173.53/173.43 [10087]~P103(x100872)+E(x100871,f189(f860(x100872,a845)))+E(x100873,f189(f860(x100872,a845)))+~P22(f312(f70(x100872),x100871))+~P22(f312(f70(x100872),x100873))+E(f12(x100872,f226(x100872),f312(f233(x100872),f312(f312(f8(f860(x100872,a845),a845,x100872),f96(x100872)),f312(f312(f8(f860(x100872,f860(x100872,a845)),f860(x100872,a845),x100872),f312(f8(f860(x100872,a845),a845,x100872),f96(x100872))),f312(f312(f7(x100872,f860(x100872,f860(x100872,a845)),f860(x100872,f860(x100872,a845))),f312(f312(f8(f860(x100872,f860(f860(x100872,a845),f860(x100872,a845))),f860(f860(x100872,f860(x100872,a845)),f860(x100872,f860(x100872,a845))),x100872),f18(x100872,f860(x100872,a845),f860(x100872,a845))),f312(f312(f8(f860(x100872,f860(x100872,f860(a845,a845))),f860(x100872,f860(f860(x100872,a845),f860(x100872,a845))),x100872),f312(f8(f860(x100872,f860(a845,a845)),f860(f860(x100872,a845),f860(x100872,a845)),x100872),f18(x100872,a845,a845))),f312(f312(f8(f860(x100872,f860(x100872,a845)),f860(x100872,f860(x100872,f860(a845,a845))),x100872),f312(f8(f860(x100872,a845),f860(x100872,f860(a845,a845)),x100872),f312(f8(a845,f860(a845,a845),x100872),a310))),f312(f312(f7(x100872,f860(x100872,f860(x100872,x100872)),f860(x100872,f860(x100872,a845))),f312(f312(f8(f860(f860(x100872,x100872),f860(x100872,a845)),f860(f860(x100872,f860(x100872,x100872)),f860(x100872,f860(x100872,a845))),x100872),f8(f860(x100872,x100872),f860(x100872,a845),x100872)),f312(f312(f8(f860(x100872,a845),f860(f860(x100872,x100872),f860(x100872,a845)),x100872),f8(x100872,a845,x100872)),a309))),f225(x100872)))))),f312(f312(f7(x100872,f860(x100872,a845),f860(x100872,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x100872,a845),f860(x100872,a845)),x100872),f8(a845,a845,x100872)),f312(f312(f8(a845,f860(a845,a845),x100872),a310),f312(f312(f7(x100872,f860(x100872,a845),a845),f314(x100872)),x100873)))),f312(f312(f7(x100872,f860(x100872,a845),a845),f314(x100872)),x100871))))))),f312(f312(f225(x100872),f12(x100872,f226(x100872),x100873)),f12(x100872,f226(x100872),x100871)))
% 173.53/173.43 [10088]~P103(x100882)+E(x100881,f189(f860(x100882,a845)))+E(x100883,f189(f860(x100882,a845)))+~P22(f312(f70(x100882),x100881))+~P22(f312(f70(x100882),x100883))+E(f13(x100882,f225(x100882),f312(f233(x100882),f312(f312(f8(f860(x100882,a845),a845,x100882),f96(x100882)),f312(f312(f8(f860(x100882,f860(x100882,a845)),f860(x100882,a845),x100882),f312(f8(f860(x100882,a845),a845,x100882),f96(x100882))),f312(f312(f7(x100882,f860(x100882,f860(x100882,a845)),f860(x100882,f860(x100882,a845))),f312(f312(f8(f860(x100882,f860(f860(x100882,a845),f860(x100882,a845))),f860(f860(x100882,f860(x100882,a845)),f860(x100882,f860(x100882,a845))),x100882),f18(x100882,f860(x100882,a845),f860(x100882,a845))),f312(f312(f8(f860(x100882,f860(x100882,f860(a845,a845))),f860(x100882,f860(f860(x100882,a845),f860(x100882,a845))),x100882),f312(f8(f860(x100882,f860(a845,a845)),f860(f860(x100882,a845),f860(x100882,a845)),x100882),f18(x100882,a845,a845))),f312(f312(f8(f860(x100882,f860(x100882,a845)),f860(x100882,f860(x100882,f860(a845,a845))),x100882),f312(f8(f860(x100882,a845),f860(x100882,f860(a845,a845)),x100882),f312(f8(a845,f860(a845,a845),x100882),a310))),f312(f312(f7(x100882,f860(x100882,f860(x100882,x100882)),f860(x100882,f860(x100882,a845))),f312(f312(f8(f860(f860(x100882,x100882),f860(x100882,a845)),f860(f860(x100882,f860(x100882,x100882)),f860(x100882,f860(x100882,a845))),x100882),f8(f860(x100882,x100882),f860(x100882,a845),x100882)),f312(f312(f8(f860(x100882,a845),f860(f860(x100882,x100882),f860(x100882,a845)),x100882),f8(x100882,a845,x100882)),a309))),f226(x100882)))))),f312(f312(f7(x100882,f860(x100882,a845),f860(x100882,a845)),f312(f312(f8(f860(a845,a845),f860(f860(x100882,a845),f860(x100882,a845)),x100882),f8(a845,a845,x100882)),f312(f312(f8(a845,f860(a845,a845),x100882),a310),f312(f312(f7(x100882,f860(x100882,a845),a845),f314(x100882)),x100883)))),f312(f312(f7(x100882,f860(x100882,a845),a845),f314(x100882)),x100881))))))),f312(f312(f226(x100882),f13(x100882,f225(x100882),x100883)),f13(x100882,f225(x100882),x100881)))
% 173.53/173.43 [7087]~P117(x70873)+E(x70871,x70872)+~E(f312(f312(f240(x70873),x70871),x70874),f312(f312(f240(x70873),x70872),x70874))+~P22(f312(f312(f227(x70873),f2(x70873)),x70872))+~P22(f312(f312(f227(x70873),f2(x70873)),x70871))+~P22(f312(f312(f228(a852),f2(a852)),x70874))
% 173.53/173.43 [9012]~P22(f312(x90122,x90123))+~P22(f312(x90121,x90124))+E(f231(a852,x90121),f312(a126,f231(a852,x90122)))+P22(f312(x90122,f750(x90123,x90122,x90124,x90121)))+P22(f312(x90121,f2(a852)))+P22(f312(x90121,f312(a126,f750(x90123,x90122,x90124,x90121))))
% 173.53/173.43 [9266]~P22(f312(x92662,x92663))+~P22(f312(x92661,x92664))+E(f231(a852,x92661),f312(a126,f231(a852,x92662)))+~P22(f312(x92662,f750(x92663,x92662,x92664,x92661)))+P22(f312(x92661,f2(a852)))+~P22(f312(x92661,f312(a126,f750(x92663,x92662,x92664,x92661))))
% 173.53/173.43 [7347]~P103(x73472)+E(x73471,f189(f860(x73472,a845)))+~P22(f312(f70(x73472),x73471))+~P22(f312(f312(f314(x73472),x73474),x73471))+P22(f312(f312(f228(x73472),x73473),x73474))+~P22(f312(f312(f228(x73472),x73473),f312(f72(x73472,f225(x73472)),x73471)))
% 173.53/173.43 [7348]~P99(x73482)+E(x73481,f189(f860(x73482,a845)))+~P22(f312(f70(x73482),x73481))+~P22(f312(f312(f314(x73482),x73484),x73481))+P22(f312(f312(f227(x73482),x73483),x73484))+~P22(f312(f312(f227(x73482),x73483),f312(f72(x73482,f115(x73482)),x73481)))
% 173.53/173.43 [7349]~P103(x73492)+E(x73491,f189(f860(x73492,a845)))+~P22(f312(f70(x73492),x73491))+~P22(f312(f312(f314(x73492),x73494),x73491))+P22(f312(f312(f227(x73492),x73493),x73494))+~P22(f312(f312(f227(x73492),x73493),f312(f72(x73492,f225(x73492)),x73491)))
% 173.53/173.43 [7226]E(x72261,f2(a1))+E(f312(f47(a1,x72262),x72261),x72263)+~P22(f312(f312(f227(a1),x72264),f2(a1)))+~E(x72262,f312(f312(f89(a1),f312(f312(f90(a1),x72261),x72263)),x72264))+P22(f312(f312(f228(a1),f2(a1)),x72261))+~P22(f312(f312(f228(a1),x72261),x72264))
% 173.53/173.43 [7265]E(f54(a1,x72652,x72651),x72653)+E(x72651,f2(a1))+~P22(f312(f312(f227(a1),x72653),f2(a1)))+~E(x72652,f312(f312(f89(a1),f312(f312(f90(a1),x72651),x72654)),x72653))+P22(f312(f312(f228(a1),f2(a1)),x72651))+~P22(f312(f312(f228(a1),x72651),x72653))
% 173.53/173.43 [7375]E(x73751,f2(a1))+E(f312(f47(a1,x73752),x73751),x73753)+~E(x73752,f312(f312(f89(a1),f312(f312(f90(a1),x73751),x73753)),x73754))+~P22(f312(f312(f228(a1),f2(a1)),x73751))+~P22(f312(f312(f227(a1),f2(a1)),x73754))+~P22(f312(f312(f228(a1),x73754),x73751))
% 173.53/173.43 [7409]E(f54(a1,x74092,x74091),x74093)+E(x74091,f2(a1))+~E(x74092,f312(f312(f89(a1),f312(f312(f90(a1),x74091),x74094)),x74093))+~P22(f312(f312(f228(a1),f2(a1)),x74091))+~P22(f312(f312(f227(a1),f2(a1)),x74093))+~P22(f312(f312(f228(a1),x74093),x74091))
% 173.53/173.43 [7548]~P103(x75482)+E(x75481,f189(f860(x75482,a845)))+~P22(f312(f70(x75482),x75481))+~P22(f312(f312(f228(x75482),x75484),x75483))+~P22(f312(f312(f314(x75482),x75484),x75481))+P22(f312(f312(f228(x75482),f312(f72(x75482,f225(x75482)),x75481)),x75483))
% 173.53/173.43 [7549]~P103(x75492)+E(x75491,f189(f860(x75492,a845)))+~P22(f312(f70(x75492),x75491))+~P22(f312(f312(f227(x75492),x75494),x75493))+~P22(f312(f312(f314(x75492),x75494),x75491))+P22(f312(f312(f227(x75492),f312(f72(x75492,f225(x75492)),x75491)),x75493))
% 173.53/173.43 [8119]~P22(f312(f312(f227(a1),x81194),f2(a1)))+~E(x81191,f312(f312(f89(a1),f312(f312(f90(a1),x81192),x81193)),x81194))+~P22(f312(f312(f227(a1),f2(a1)),x81194))+~P22(f312(f312(f228(a1),x81194),x81192))+~P22(f312(f312(f228(a1),x81192),x81194))+P22(f312(f57(x81191,x81192),f312(f312(f239(a1,a1),x81193),x81194)))
% 173.53/173.43 [9068]~P63(x90683)+~P63(x90684)+E(x90681,x90682)+~E(f312(f190(f853(x90683)),x90682),f312(f190(f853(x90684)),f64(x90684)))+~E(f312(f190(f853(x90683)),x90681),f312(f190(f853(x90684)),f64(x90684)))+~E(f312(f82(f856(x90683),x90683,x90684,f223(x90683)),f312(f173(x90684,x90683),f312(f312(f177(x90684,x90683),f64(x90684)),x90681))),f312(f82(f856(x90683),x90683,x90684,f223(x90683)),f312(f173(x90684,x90683),f312(f312(f177(x90684,x90683),f64(x90684)),x90682))))
% 173.53/173.43 [8287]~P105(x82871)+P22(f312(f312(f228(f860(x82871,a845)),f283(x82871,x82872,x82873)),f283(x82871,x82874,x82875)))+~P22(f312(f312(f228(x82871),x82873),x82875))+~P22(f312(f312(f227(x82871),x82874),x82872))+~P22(f312(f312(f227(x82871),x82874),x82875))+~P22(f312(f312(f227(x82871),x82873),x82875))
% 173.53/173.43 [8288]~P105(x82881)+P22(f312(f312(f228(f860(x82881,a845)),f283(x82881,x82882,x82883)),f283(x82881,x82884,x82885)))+~P22(f312(f312(f228(x82881),x82884),x82882))+~P22(f312(f312(f227(x82881),x82883),x82885))+~P22(f312(f312(f227(x82881),x82884),x82885))+~P22(f312(f312(f227(x82881),x82884),x82882))
% 173.53/173.43 [9134]P58(x91342,x91343,x91344,x91341)+E(x91341,f189(f860(x91342,a845)))+~P22(f312(f70(x91342),x91344))+~P22(f312(f70(x91342),x91341))+~P22(f312(f312(x91343,f511(x91341,x91344,x91343,x91342)),x91345))+~P22(f312(f312(f314(x91342),x91345),x91341))
% 173.53/173.43 [9281]~E(x92813,x92815)+~P26(x92811)+~P72(x92811)+~P43(x92813)+E(f312(f312(f9(a1,x92811),x92812),x92813),f312(f312(f9(a1,x92811),x92814),x92815))+P22(f312(f312(f227(a1),f2(a1)),f512(x92812,x92814,x92813,x92815,x92811)))
% 173.53/173.43 [9282]~E(x92823,x92825)+~P26(x92821)+~P72(x92821)+~P43(x92823)+E(f312(f312(f6(a1,x92821),x92822),x92823),f312(f312(f6(a1,x92821),x92824),x92825))+P22(f312(f312(f227(a1),f2(a1)),f513(x92822,x92824,x92823,x92825,x92821)))
% 173.53/173.43 [9449]~E(x94495,x94493)+~P26(x94491)+~P72(x94491)+~P43(x94495)+~E(f312(x94492,f512(x94494,x94492,x94495,x94493,x94491)),f312(x94494,f512(x94494,x94492,x94495,x94493,x94491)))+E(f312(f312(f9(a1,x94491),x94492),x94493),f312(f312(f9(a1,x94491),x94494),x94495))
% 173.53/173.43 [9450]~E(x94505,x94503)+~P26(x94501)+~P72(x94501)+~P43(x94505)+~E(f312(x94502,f513(x94504,x94502,x94505,x94503,x94501)),f312(x94504,f513(x94504,x94502,x94505,x94503,x94501)))+E(f312(f312(f6(a1,x94501),x94502),x94503),f312(f312(f6(a1,x94501),x94504),x94505))
% 173.53/173.43 [9534]~P76(x95343)+E(f312(x95341,x95342),f2(x95343))+~E(f312(f312(f6(x95344,x95343),x95341),x95345),f2(x95343))+~P22(f312(f70(x95344),x95345))+P22(f312(f312(f314(x95344),f500(x95342,x95341,x95345,x95344,x95343)),x95345))+~P22(f312(f312(f314(x95344),x95342),x95345))
% 173.53/173.43 [9668]~P76(x96683)+E(f312(x96681,x96682),f2(x96683))+~E(f312(f312(f6(x96684,x96683),x96681),x96685),f2(x96683))+~P22(f312(f70(x96684),x96685))+~P22(f312(f312(f314(x96684),x96682),x96685))+~P22(f312(f312(f227(x96683),f2(x96683)),f312(x96681,f500(x96682,x96681,x96685,x96684,x96683))))
% 173.53/173.43 [8202]~P122(x82021)+~P22(f312(f312(f227(x82021),f2(x82021)),x82023))+~P22(f312(f312(f228(x82021),x82023),x82025))+~P22(f312(f312(f228(x82021),x82022),x82024))+~P22(f312(f312(f228(x82021),f2(x82021)),x82024))+P22(f312(f312(f228(x82021),f312(f312(f90(x82021),x82022),x82023)),f312(f312(f90(x82021),x82024),x82025)))
% 173.53/173.43 [8203]~P122(x82031)+~P22(f312(f312(f227(x82031),f2(x82031)),x82033))+~P22(f312(f312(f227(x82031),f2(x82031)),x82032))+~P22(f312(f312(f228(x82031),x82033),x82035))+~P22(f312(f312(f228(x82031),x82032),x82034))+P22(f312(f312(f228(x82031),f312(f312(f90(x82031),x82032),x82033)),f312(f312(f90(x82031),x82034),x82035)))
% 173.53/173.43 [8204]~P122(x82041)+~P22(f312(f312(f227(x82041),x82042),x82044))+~P22(f312(f312(f227(x82041),f2(x82041)),x82043))+~P22(f312(f312(f228(x82041),x82043),x82045))+~P22(f312(f312(f228(x82041),f2(x82041)),x82042))+P22(f312(f312(f228(x82041),f312(f312(f90(x82041),x82042),x82043)),f312(f312(f90(x82041),x82044),x82045)))
% 173.53/173.43 [8205]~P122(x82051)+~P22(f312(f312(f227(x82051),x82053),x82055))+~P22(f312(f312(f227(x82051),f2(x82051)),x82052))+~P22(f312(f312(f228(x82051),x82052),x82054))+~P22(f312(f312(f228(x82051),f2(x82051)),x82053))+P22(f312(f312(f228(x82051),f312(f312(f90(x82051),x82052),x82053)),f312(f312(f90(x82051),x82054),x82055)))
% 173.53/173.43 [8206]~P67(x82061)+~P22(f312(f312(f227(x82061),x82062),x82064))+~P22(f312(f312(f228(x82061),x82065),x82063))+~P22(f312(f312(f228(x82061),f2(x82061)),x82065))+~P22(f312(f312(f228(x82061),f2(x82061)),x82062))+P22(f312(f312(f228(x82061),f312(f312(f268(x82061),x82062),x82063)),f312(f312(f268(x82061),x82064),x82065)))
% 173.53/173.43 [8207]~P67(x82071)+~P22(f312(f312(f227(x82071),x82075),x82073))+~P22(f312(f312(f227(x82071),f2(x82071)),x82072))+~P22(f312(f312(f228(x82071),x82072),x82074))+~P22(f312(f312(f228(x82071),f2(x82071)),x82075))+P22(f312(f312(f228(x82071),f312(f312(f268(x82071),x82072),x82073)),f312(f312(f268(x82071),x82074),x82075)))
% 173.53/173.43 [8208]~P130(x82081)+~P22(f312(f312(f227(x82081),x82083),x82085))+~P22(f312(f312(f227(x82081),x82082),x82084))+~P22(f312(f312(f227(x82081),f2(x82081)),x82083))+~P22(f312(f312(f227(x82081),f2(x82081)),x82084))+P22(f312(f312(f227(x82081),f312(f312(f90(x82081),x82082),x82083)),f312(f312(f90(x82081),x82084),x82085)))
% 173.53/173.43 [8209]~P130(x82091)+~P22(f312(f312(f227(x82091),x82093),x82095))+~P22(f312(f312(f227(x82091),x82092),x82094))+~P22(f312(f312(f227(x82091),f2(x82091)),x82093))+~P22(f312(f312(f227(x82091),f2(x82091)),x82092))+P22(f312(f312(f227(x82091),f312(f312(f90(x82091),x82092),x82093)),f312(f312(f90(x82091),x82094),x82095)))
% 173.53/173.43 [8210]~P67(x82101)+~P22(f312(f312(f228(x82101),f2(x82101)),x82105))+~P22(f312(f312(f227(x82101),x82105),x82103))+~P22(f312(f312(f227(x82101),x82102),x82104))+~P22(f312(f312(f227(x82101),f2(x82101)),x82102))+P22(f312(f312(f227(x82101),f312(f312(f268(x82101),x82102),x82103)),f312(f312(f268(x82101),x82104),x82105)))
% 173.53/173.43 [9572]~P26(x95725)+~P80(x95725)+E(x95721,f189(f860(x95722,a845)))+~P22(f312(f70(x95722),x95721))+P22(f312(f312(f314(x95722),f510(x95723,x95724,x95721,x95722,x95725)),x95721))+P22(f312(f312(f228(x95725),f312(f312(f6(x95722,x95725),x95724),x95721)),f312(f312(f6(x95722,x95725),x95723),x95721)))
% 173.53/173.43 [9689]~P26(x96891)+~P82(x96891)+~P22(f312(f70(x96892),x96895))+~P22(f312(f312(f227(x96891),f2(x96891)),f312(x96893,f501(x96893,x96894,x96895,x96892,x96891))))+P22(f312(f312(f227(x96891),f312(f312(f6(x96892,x96891),x96893),x96894)),f312(f312(f6(x96892,x96891),x96893),x96895)))+~P22(f312(f312(f227(f860(x96892,a845)),x96894),x96895))
% 173.53/173.43 [9861]~P26(x98613)+~P80(x98613)+E(x98611,f189(f860(x98612,a845)))+~P22(f312(f70(x98612),x98611))+~P22(f312(f312(f228(x98613),f312(x98614,f510(x98615,x98614,x98611,x98612,x98613))),f312(x98615,f510(x98615,x98614,x98611,x98612,x98613))))+P22(f312(f312(f228(x98613),f312(f312(f6(x98612,x98613),x98614),x98611)),f312(f312(f6(x98612,x98613),x98615),x98611)))
% 173.53/173.43 [6944]~P12(x69442,x69445,x69444)+E(x69441,f189(f860(x69442,a845)))+E(x69443,f189(f860(x69442,a845)))+~P22(f312(f70(x69442),x69441))+~P22(f312(f70(x69442),x69443))+E(f312(x69444,f312(f312(f124(f860(x69442,a845)),x69443),x69441)),f312(f312(x69445,f312(x69444,x69443)),f312(x69444,x69441)))
% 173.53/173.43 [7517]~P140(x75171,x75174,x75173)+P22(f312(x75171,x75172))+~P22(f312(f312(f228(a1),x75174),f2(a1)))+~P22(f312(f312(f227(a1),x75175),f2(a1)))+~E(x75173,f312(f312(f89(a1),f312(f312(f90(a1),x75174),x75172)),x75175))+~P22(f312(f312(f228(a1),x75174),x75175))
% 173.53/173.43 [7518]~P139(x75181,x75184,x75183)+P22(f312(x75181,x75182))+~P22(f312(f312(f228(a1),x75184),f2(a1)))+~P22(f312(f312(f227(a1),x75182),f2(a1)))+~E(x75183,f312(f312(f89(a1),f312(f312(f90(a1),x75184),x75185)),x75182))+~P22(f312(f312(f228(a1),x75184),x75182))
% 173.53/173.43 [7558]~P140(x75581,x75584,x75583)+P22(f312(x75581,x75582))+~E(x75583,f312(f312(f89(a1),f312(f312(f90(a1),x75584),x75582)),x75585))+~P22(f312(f312(f228(a1),f2(a1)),x75584))+~P22(f312(f312(f227(a1),f2(a1)),x75585))+~P22(f312(f312(f228(a1),x75585),x75584))
% 173.53/173.43 [7559]~P139(x75591,x75594,x75593)+P22(f312(x75591,x75592))+~E(x75593,f312(f312(f89(a1),f312(f312(f90(a1),x75594),x75595)),x75592))+~P22(f312(f312(f228(a1),f2(a1)),x75594))+~P22(f312(f312(f227(a1),f2(a1)),x75592))+~P22(f312(f312(f228(a1),x75592),x75594))
% 173.53/173.43 [8436]P22(f312(f312(x84361,x84362),x84363))+~P22(f312(f312(x84361,f312(f47(a1,x84364),x84365)),f54(a1,x84364,x84365)))+~P22(f312(f312(f228(a1),x84365),f2(a1)))+~P22(f312(f312(f227(a1),x84363),f2(a1)))+~E(x84364,f312(f312(f89(a1),f312(f312(f90(a1),x84365),x84362)),x84363))+~P22(f312(f312(f228(a1),x84365),x84363))
% 173.53/173.43 [8456]P22(f312(f312(x84561,x84562),x84563))+~P22(f312(f312(x84561,f312(f47(a1,x84564),x84565)),f54(a1,x84564,x84565)))+~E(x84564,f312(f312(f89(a1),f312(f312(f90(a1),x84565),x84562)),x84563))+~P22(f312(f312(f228(a1),f2(a1)),x84565))+~P22(f312(f312(f227(a1),f2(a1)),x84563))+~P22(f312(f312(f228(a1),x84563),x84565))
% 173.53/173.43 [8748]E(x87481,x87482)+~P55(x87483,x87485,x87484)+~P22(f312(f312(f314(x87483),x87482),x87485))+~P22(f312(f312(f314(x87483),x87481),x87485))+P22(f312(f312(f314(f859(x87483,x87483)),f312(f312(f239(x87483,x87483),x87481),x87482)),x87484))+P22(f312(f312(f314(f859(x87483,x87483)),f312(f312(f239(x87483,x87483),x87482),x87481)),x87484))
% 173.53/173.43 [9552]~P105(x95521)+~P105(x95522)+~P49(x95522,x95521,x95523)+~P22(f312(f312(f227(x95522),x95525),f830(x95524,x95523,x95522,x95521,x95525)))+E(f231(x95521,f312(f312(f7(x95521,f860(x95521,a845),a845),f314(x95521)),f312(f290(x95522,x95521,x95523),x95524))),f312(x95523,f231(x95522,f312(f312(f7(x95522,f860(x95522,a845),a845),f314(x95522)),x95524))))+~P22(f312(f312(f314(x95522),x95525),x95524))
% 173.53/173.43 [9599]~P26(x95995)+~P82(x95995)+~P22(f312(f70(x95991),x95994))+P22(f312(f312(f227(x95995),f312(f312(f6(x95991,x95995),x95992),x95993)),f312(f312(f6(x95991,x95995),x95992),x95994)))+~P22(f312(f312(f227(f860(x95991,a845)),x95993),x95994))+P22(f312(f312(f314(x95991),f501(x95992,x95993,x95994,x95991,x95995)),f312(f312(f21(f860(x95991,a845)),x95994),x95993)))
% 173.53/173.43 [9616]~P105(x96161)+~P105(x96162)+~P49(x96162,x96161,x96163)+E(f231(x96161,f312(f312(f7(x96161,f860(x96161,a845),a845),f314(x96161)),f312(f290(x96162,x96161,x96163),x96164))),f312(x96163,f231(x96162,f312(f312(f7(x96162,f860(x96162,a845),a845),f314(x96162)),x96164))))+~P22(f312(f312(f314(x96162),x96165),x96164))+P22(f312(f312(f314(x96162),f830(x96164,x96163,x96162,x96161,x96165)),x96164))
% 173.53/173.43 [9695]E(x96951,f189(f860(x96952,a845)))+~P22(f312(f70(x96952),x96953))+~P22(f312(f70(x96952),x96951))+P22(f312(f312(f314(f859(f860(x96952,a845),f860(x96952,a845))),f312(f312(f239(f860(x96952,a845),f860(x96952,a845)),x96953),x96951)),f303(x96952,x96954)))+~P22(f312(f312(f314(x96952),x96955),x96951))+~P22(f312(f312(f314(f859(x96952,x96952)),f312(f312(f239(x96952,x96952),f516(x96954,x96951,x96953,x96952)),x96955)),x96954))
% 173.53/173.43 [9696]E(x96961,f189(f860(x96962,a845)))+~P22(f312(f70(x96962),x96963))+~P22(f312(f70(x96962),x96961))+P22(f312(f312(f314(f859(f860(x96962,a845),f860(x96962,a845))),f312(f312(f239(f860(x96962,a845),f860(x96962,a845)),x96963),x96961)),f303(x96962,x96964)))+~P22(f312(f312(f314(x96962),x96965),x96961))+~P22(f312(f312(f314(f859(x96962,x96962)),f312(f312(f239(x96962,x96962),f740(x96964,x96961,x96963,x96962)),x96965)),x96964))
% 173.53/173.43 [9866]~P76(x98661)+~E(f312(f312(f6(x98665,x98661),x98662),x98666),x98664)+~P22(f312(f70(x98665),x98666))+P22(f312(f312(f314(x98665),f504(x98663,x98664,x98662,x98666,x98665,x98661)),x98666))+P22(f312(f312(f227(x98661),f312(x98662,x98663)),x98664))+~P22(f312(f312(f314(x98665),x98663),x98666))
% 173.53/173.43 [9917]~P76(x99171)+~E(f312(f312(f6(x99175,x99171),x99172),x99176),x99174)+~P22(f312(f70(x99175),x99176))+~P22(f312(f312(f314(x99175),x99173),x99176))+~P22(f312(f312(f227(x99171),f2(x99171)),f312(x99172,f504(x99173,x99174,x99172,x99176,x99175,x99171))))+P22(f312(f312(f227(x99171),f312(x99172,x99173)),x99174))
% 173.53/173.43 [10031]~E(x100315,x100318)+~E(x100314,x100317)+~P26(x100312)+~P104(x100311)+E(f312(f312(f6(x100311,x100312),x100313),f312(f282(x100311,x100314),x100315)),f312(f312(f6(x100311,x100312),x100316),f312(f282(x100311,x100317),x100318)))+P22(f312(f312(f227(x100311),x100314),f751(x100313,x100316,x100315,x100318,x100314,x100317,x100311,x100312)))
% 173.53/173.43 [10047]~E(x100477,x100474)+~E(x100478,x100475)+~P26(x100472)+~P104(x100471)+~E(f312(x100473,f751(x100476,x100473,x100478,x100475,x100477,x100474,x100471,x100472)),f312(x100476,f751(x100476,x100473,x100478,x100475,x100477,x100474,x100471,x100472)))+E(f312(f312(f6(x100471,x100472),x100473),f312(f282(x100471,x100474),x100475)),f312(f312(f6(x100471,x100472),x100476),f312(f282(x100471,x100477),x100478)))
% 173.53/173.43 [10051]~E(x100514,x100517)+~E(x100515,x100518)+~P26(x100512)+~P104(x100511)+E(f312(f312(f6(x100511,x100512),x100513),f312(f282(x100511,x100514),x100515)),f312(f312(f6(x100511,x100512),x100516),f312(f282(x100511,x100517),x100518)))+P22(f312(f312(f228(x100511),f751(x100513,x100516,x100515,x100518,x100514,x100517,x100511,x100512)),x100515))
% 173.53/173.43 [9701]~P3(x97015,x97019,x97016)+~P3(x97011,x970110,x97013)+~P10(x97011,x97015,f860(x97012,a845),x97013,x97016,x97018)+~P22(f312(f312(f314(x97015),x97017),x97019))+~P22(f312(f312(f314(x97011),x97014),x970110))+E(f312(f312(f50(x97011,f860(x97012,a845)),f312(f264(x97011,x97011,x97013),f312(f312(f289(x97011),x97014),f189(f860(x97011,a845))))),f312(f312(f8(f860(x97015,f860(x97012,a845)),f860(x97012,a845),x97011),f312(f50(x97015,f860(x97012,a845)),f312(f264(x97015,x97015,x97016),f312(f312(f289(x97015),x97017),f189(f860(x97015,a845)))))),x97018)),f312(f312(x97018,x97014),x97017))
% 173.53/173.43 [5513]~P103(x55133)+~P33(x55133,x55132)+~P33(x55133,x55131)+E(x55131,x55132)+~E(f312(f168(x55133),x55131),f312(f168(x55133),x55132))+~P22(f312(f133(x55133),x55132))+~P22(f312(f133(x55133),x55131))
% 173.53/173.43 [4861]~P137(x48612)+~P126(x48612)+~P127(x48612)+~P109(x48612)+~E(x48613,f2(x48612))+E(x48611,f2(a852))+E(f312(f312(f240(x48612),x48613),x48611),f2(x48612))
% 173.53/173.43 [9011]E(x90111,f2(a852))+~E(x90112,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x90113)),x90111)),f312(f248(a852,a852),x90113)))+P22(f312(f56(x90112,x90111),x90113))+~P22(f312(f312(f227(a852),f312(f248(a852,a852),x90113)),f2(a852)))+~P22(f312(f312(f227(a852),f2(a852)),f312(f248(a852,a852),x90113)))+~P22(f312(f312(f228(a852),x90111),f312(f248(a852,a852),x90113)))+~P22(f312(f312(f228(a852),f312(f248(a852,a852),x90113)),x90111))
% 173.53/173.43 [9021]~E(f312(f246(a852,a852),x90213),f2(a852))+~E(x90211,f312(f312(f89(a852),f312(f312(f90(a852),f312(f246(a852,a852),x90213)),x90212)),f312(f248(a852,a852),x90213)))+P22(f312(f56(x90211,x90212),x90213))+~P22(f312(f312(f227(a852),f312(f248(a852,a852),x90213)),f2(a852)))+~P22(f312(f312(f227(a852),f2(a852)),f312(f248(a852,a852),x90213)))+~P22(f312(f312(f228(a852),x90212),f312(f248(a852,a852),x90213)))+~P22(f312(f312(f228(a852),f312(f248(a852,a852),x90213)),x90212))
% 173.53/173.43 [7865]~P68(x78652)+E(x78651,f189(f860(x78652,a845)))+E(x78653,f189(f860(x78652,a845)))+~P22(f312(f70(x78652),x78651))+~P22(f312(f70(x78652),x78653))+~E(f312(f312(f115(f860(x78652,a845)),x78653),x78651),f189(f860(x78652,a845)))+E(f312(f312(f90(x78652),f312(f72(x78652,f90(x78652)),x78653)),f312(f72(x78652,f90(x78652)),x78651)),f312(f72(x78652,f90(x78652)),f312(f312(f124(f860(x78652,a845)),x78653),x78651)))
% 173.53/173.43 [7644]E(x76441,f2(a1))+E(f312(f47(a1,x76442),x76441),x76443)+~P22(f312(f312(f227(a1),x76444),f2(a1)))+~E(x76442,f312(f312(f89(a1),f312(f312(f90(a1),x76441),x76443)),x76444))+~P22(f312(f312(f227(a1),f2(a1)),x76444))+~P22(f312(f312(f228(a1),x76444),x76441))+~P22(f312(f312(f228(a1),x76441),x76444))
% 173.53/173.43 [7662]E(f54(a1,x76622,x76621),x76623)+E(x76621,f2(a1))+~P22(f312(f312(f227(a1),x76623),f2(a1)))+~E(x76622,f312(f312(f89(a1),f312(f312(f90(a1),x76621),x76624)),x76623))+~P22(f312(f312(f227(a1),f2(a1)),x76623))+~P22(f312(f312(f228(a1),x76623),x76621))+~P22(f312(f312(f228(a1),x76621),x76623))
% 173.53/173.43 [7566]~P13(x75662,x75665,x75664)+E(x75661,f189(f860(x75662,a845)))+E(x75663,f189(f860(x75662,a845)))+~P22(f312(f70(x75662),x75661))+~P22(f312(f70(x75662),x75663))+~E(f312(f312(f115(f860(x75662,a845)),x75663),x75661),f189(f860(x75662,a845)))+E(f312(x75664,f312(f312(f124(f860(x75662,a845)),x75663),x75661)),f312(f312(x75665,f312(x75664,x75663)),f312(x75664,x75661)))
% 173.53/173.43 [9253]~P19(x92533,x92531,x92535,x92534)+~P19(x92531,x92533,x92536,x92532)+E(f312(f53(x92531),x92532),f312(f53(x92533),x92534))+~P22(f312(f70(x92533),x92534))+~P22(f312(f70(x92531),x92532))+~P22(f312(f312(f227(f860(x92533,a845)),f312(f290(x92531,x92533,x92536),x92532)),x92534))+~P22(f312(f312(f227(f860(x92531,a845)),f312(f290(x92533,x92531,x92535),x92534)),x92532))
% 173.53/173.43 [9201]~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92015),x92011)),x92016)),f2(a1)))+~E(f312(f312(f89(a1),f312(f312(f90(a1),x92013),x92012)),x92014),f312(f312(f89(a1),f312(f312(f90(a1),x92015),x92011)),x92016))+~P22(f312(f312(f228(a1),f2(a1)),x92015))+~P22(f312(f312(f227(a1),f2(a1)),x92016))+~P22(f312(f312(f228(a1),x92014),x92013))+~P22(f312(f312(f227(a1),x92015),x92013))+P22(f312(f312(f227(a1),x92011),x92012))
% 173.53/173.43 [8965]~E(f312(f312(f89(a1),f312(f312(f90(a1),x89653),x89651)),x89654),f312(f312(f89(a1),f312(f312(f90(a1),x89655),x89652)),x89656))+~P22(f312(f312(f228(a1),f2(a1)),x89655))+~P22(f312(f312(f227(a1),f2(a1)),x89654))+~P22(f312(f312(f228(a1),x89656),x89655))+~P22(f312(f312(f227(a1),x89655),x89653))+P22(f312(f312(f227(a1),x89651),x89652))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x89655),x89652)),x89656)))
% 173.53/173.43 [9141]~P124(x91411)+~E(f312(f312(f89(x91411),x91412),x91414),f87(x91411))+~P22(f312(f312(f227(x91411),f2(x91411)),x91414))+~P22(f312(f312(f227(x91411),f2(x91411)),x91412))+~P22(f312(f312(f228(x91411),x91415),x91416))+~P22(f312(f312(f228(x91411),x91413),x91416))+P22(f312(f312(f228(x91411),f312(f312(f89(x91411),f312(f312(f90(x91411),x91412),x91413)),f312(f312(f90(x91411),x91414),x91415))),x91416))
% 173.53/173.43 [9142]~P125(x91421)+~E(f312(f312(f89(x91421),x91422),x91424),f87(x91421))+~P22(f312(f312(f227(x91421),x91425),x91426))+~P22(f312(f312(f227(x91421),x91423),x91426))+~P22(f312(f312(f227(x91421),f2(x91421)),x91424))+~P22(f312(f312(f227(x91421),f2(x91421)),x91422))+P22(f312(f312(f227(x91421),f312(f312(f89(x91421),f312(f312(f90(x91421),x91422),x91423)),f312(f312(f90(x91421),x91424),x91425))),x91426))
% 173.53/173.43 [9963]~P3(x99637,x99636,x99635)+E(x99631,x99632)+~P9(x99637,f860(x99634,a845),x99635,x99633)+E(f312(x99633,f415(x99631,x99632,x99633,x99634,x99635,x99636,x99637)),f312(x99633,f416(x99631,x99632,x99633,x99634,x99635,x99636,x99637)))+~E(f312(f312(f50(x99637,f860(x99634,a845)),x99631),x99633),f312(f312(f50(x99637,f860(x99634,a845)),x99632),x99633))+~P22(f312(f312(f314(f860(x99637,a845)),x99632),f312(f312(f69(x99637),x99636),x99635)))+~P22(f312(f312(f314(f860(x99637,a845)),x99631),f312(f312(f69(x99637),x99636),x99635)))
% 173.53/173.43 [9996]~P3(x99963,x99967,x99966)+E(x99961,x99962)+~P9(x99963,f860(x99965,a845),x99966,x99964)+~E(f312(f312(f50(x99963,f860(x99965,a845)),x99961),x99964),f312(f312(f50(x99963,f860(x99965,a845)),x99962),x99964))+P22(f312(f312(f314(x99963),f416(x99961,x99962,x99964,x99965,x99966,x99967,x99963)),x99967))+~P22(f312(f312(f314(f860(x99963,a845)),x99962),f312(f312(f69(x99963),x99967),x99966)))+~P22(f312(f312(f314(f860(x99963,a845)),x99961),f312(f312(f69(x99963),x99967),x99966)))
% 173.53/173.43 [9997]~P3(x99973,x99977,x99976)+E(x99971,x99972)+~P9(x99973,f860(x99975,a845),x99976,x99974)+~E(f312(f312(f50(x99973,f860(x99975,a845)),x99971),x99974),f312(f312(f50(x99973,f860(x99975,a845)),x99972),x99974))+P22(f312(f312(f314(x99973),f415(x99971,x99972,x99974,x99975,x99976,x99977,x99973)),x99977))+~P22(f312(f312(f314(f860(x99973,a845)),x99972),f312(f312(f69(x99973),x99977),x99976)))+~P22(f312(f312(f314(f860(x99973,a845)),x99971),f312(f312(f69(x99973),x99977),x99976)))
% 173.53/173.43 [10069]E(x100691,x100692)+~P3(x100693,x100696,x100697)+~P9(x100693,f860(x100694,a845),x100697,x100695)+~E(f312(f312(f50(x100693,f860(x100694,a845)),x100691),x100695),f312(f312(f50(x100693,f860(x100694,a845)),x100692),x100695))+~P22(f312(f312(f314(f859(x100693,x100693)),f312(f312(f239(x100693,x100693),f416(x100691,x100692,x100695,x100694,x100697,x100696,x100693)),f415(x100691,x100692,x100695,x100694,x100697,x100696,x100693))),x100697))+~P22(f312(f312(f314(f860(x100693,a845)),x100692),f312(f312(f69(x100693),x100696),x100697)))+~P22(f312(f312(f314(f860(x100693,a845)),x100691),f312(f312(f69(x100693),x100696),x100697)))
% 173.53/173.43 [8964]~P3(x89641,x89647,x89644)+~E(x89645,x89646)+~P22(f312(f312(f314(x89641),x89643),x89646))+~P22(f312(f312(f314(x89641),x89642),x89645))+~P22(f312(f312(f314(f860(x89641,a845)),x89646),f312(f312(f69(x89641),x89647),x89644)))+~P22(f312(f312(f314(f860(x89641,a845)),x89645),f312(f312(f69(x89641),x89647),x89644)))+P22(f312(f312(f314(f859(x89641,x89641)),f312(f312(f239(x89641,x89641),x89642),x89643)),x89644))
% 173.53/173.43 [9096]E(x90961,x90962)+~P3(x90963,x90964,x90965)+~P22(f312(f312(f314(x90963),x90966),x90962))+~P22(f312(f312(f314(x90963),x90967),x90961))+~P22(f312(f312(f314(f860(x90963,a845)),x90962),f312(f312(f69(x90963),x90964),x90965)))+~P22(f312(f312(f314(f860(x90963,a845)),x90961),f312(f312(f69(x90963),x90964),x90965)))+~P22(f312(f312(f314(f859(x90963,x90963)),f312(f312(f239(x90963,x90963),x90967),x90966)),x90965))
% 173.53/173.43 [10092]~P3(x100929,x100928,x100927)+~P3(x100921,x1009211,x1009210)+~P10(x100921,x100929,f860(x100926,a845),x1009210,x100927,x100925)+P22(f312(f312(f314(x100921),f417(x100922,x100923,x100924,x100925,x100926,x100927,x100928,x100929,x1009210,x1009211,x100921)),x1009211))+~P22(f312(f312(f314(f860(x100929,a845)),x100923),f312(f312(f69(x100929),x100928),x100927)))+~P22(f312(f312(f314(f860(x100921,a845)),x100924),f312(f312(f69(x100921),x1009211),x1009210)))+P22(f312(f312(f314(f860(x100926,a845)),f312(f312(f50(x100921,f860(x100926,a845)),x100924),f312(f312(f8(f860(x100929,f860(x100926,a845)),f860(x100926,a845),x100921),f312(f50(x100929,f860(x100926,a845)),x100923)),x100925))),x100922))
% 173.53/173.43 [10093]~P3(x1009311,x1009310,x100939)+~P3(x100931,x100938,x100937)+~P10(x1009311,x100931,f860(x100936,a845),x100939,x100937,x100935)+P22(f312(f312(f314(x100931),f423(x100932,x100933,x100934,x100935,x100936,x100937,x100938,x100931,x100939,x1009310,x1009311)),x100938))+~P22(f312(f312(f314(f860(x1009311,a845)),x100934),f312(f312(f69(x1009311),x1009310),x100939)))+~P22(f312(f312(f314(f860(x100931,a845)),x100933),f312(f312(f69(x100931),x100938),x100937)))+P22(f312(f312(f314(f860(x100936,a845)),f312(f312(f50(x1009311,f860(x100936,a845)),x100934),f312(f312(f8(f860(x100931,f860(x100936,a845)),f860(x100936,a845),x1009311),f312(f50(x100931,f860(x100936,a845)),x100933)),x100935))),x100932))
% 173.53/173.43 [10096]~P3(x100962,x100968,x100969)+~P3(x100964,x1009610,x1009611)+~P10(x100962,x100964,f860(x100961,a845),x100969,x1009611,x100966)+~P22(f312(f312(f314(f860(x100962,a845)),x100963),f312(f312(f69(x100962),x100968),x100969)))+~P22(f312(f312(f314(f860(x100964,a845)),x100965),f312(f312(f69(x100964),x1009610),x1009611)))+~P22(f312(f312(f314(f860(x100961,a845)),f312(f312(x100966,f417(x100967,x100965,x100963,x100966,x100961,x1009611,x1009610,x100964,x100969,x100968,x100962)),f423(x100967,x100965,x100963,x100966,x100961,x1009611,x1009610,x100964,x100969,x100968,x100962))),x100967))+P22(f312(f312(f314(f860(x100961,a845)),f312(f312(f50(x100962,f860(x100961,a845)),x100963),f312(f312(f8(f860(x100964,f860(x100961,a845)),f860(x100961,a845),x100962),f312(f50(x100964,f860(x100961,a845)),x100965)),x100966))),x100967))
% 173.53/173.43 [8998]E(x89981,x89982)+~P103(x89984)+~P19(x89983,x89984,x89985,f312(f312(f124(f860(x89983,a845)),f312(f168(x89983),x89981)),f312(f168(x89983),x89982)))+~E(f312(f168(x89983),x89981),f312(f168(x89983),x89982))+~P33(x89984,f312(f312(f150(x89983,x89984),x89985),x89982))+~P33(x89984,f312(f312(f150(x89983,x89984),x89985),x89981))+~P22(f312(f133(x89984),f312(f312(f150(x89983,x89984),x89985),x89982)))+~P22(f312(f133(x89984),f312(f312(f150(x89983,x89984),x89985),x89981)))
% 173.53/173.43 %EqnAxiom
% 173.53/173.43 [1]E(x11,x11)
% 173.53/173.43 [2]E(x22,x21)+~E(x21,x22)
% 173.53/173.43 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 173.53/173.43 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 173.53/173.43 [5]~E(x51,x52)+E(f114(x51),f114(x52))
% 173.53/173.43 [6]~E(x61,x62)+E(f21(x61),f21(x62))
% 173.53/173.43 [7]~E(x71,x72)+E(f189(x71),f189(x72))
% 173.53/173.43 [8]~E(x81,x82)+E(f312(x81,x83),f312(x82,x83))
% 173.53/173.43 [9]~E(x91,x92)+E(f312(x93,x91),f312(x93,x92))
% 173.53/173.43 [10]~E(x101,x102)+E(f34(x101),f34(x102))
% 173.53/173.43 [11]~E(x111,x112)+E(f8(x111,x113,x114),f8(x112,x113,x114))
% 173.53/173.43 [12]~E(x121,x122)+E(f8(x123,x121,x124),f8(x123,x122,x124))
% 173.53/173.43 [13]~E(x131,x132)+E(f8(x133,x134,x131),f8(x133,x134,x132))
% 173.53/173.43 [14]~E(x141,x142)+E(f93(x141),f93(x142))
% 173.53/173.43 [15]~E(x151,x152)+E(f860(x151,x153),f860(x152,x153))
% 173.53/173.43 [16]~E(x161,x162)+E(f860(x163,x161),f860(x163,x162))
% 173.53/173.43 [17]~E(x171,x172)+E(f225(x171),f225(x172))
% 173.53/173.43 [18]~E(x181,x182)+E(f423(x181,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812),f423(x182,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812))
% 173.53/173.43 [19]~E(x191,x192)+E(f423(x193,x191,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f423(x193,x192,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912))
% 173.53/173.43 [20]~E(x201,x202)+E(f423(x203,x204,x201,x205,x206,x207,x208,x209,x2010,x2011,x2012),f423(x203,x204,x202,x205,x206,x207,x208,x209,x2010,x2011,x2012))
% 173.53/173.43 [21]~E(x211,x212)+E(f423(x213,x214,x215,x211,x216,x217,x218,x219,x2110,x2111,x2112),f423(x213,x214,x215,x212,x216,x217,x218,x219,x2110,x2111,x2112))
% 173.53/173.43 [22]~E(x221,x222)+E(f423(x223,x224,x225,x226,x221,x227,x228,x229,x2210,x2211,x2212),f423(x223,x224,x225,x226,x222,x227,x228,x229,x2210,x2211,x2212))
% 173.53/173.43 [23]~E(x231,x232)+E(f423(x233,x234,x235,x236,x237,x231,x238,x239,x2310,x2311,x2312),f423(x233,x234,x235,x236,x237,x232,x238,x239,x2310,x2311,x2312))
% 173.53/173.43 [24]~E(x241,x242)+E(f423(x243,x244,x245,x246,x247,x248,x241,x249,x2410,x2411,x2412),f423(x243,x244,x245,x246,x247,x248,x242,x249,x2410,x2411,x2412))
% 173.53/173.43 [25]~E(x251,x252)+E(f423(x253,x254,x255,x256,x257,x258,x259,x251,x2510,x2511,x2512),f423(x253,x254,x255,x256,x257,x258,x259,x252,x2510,x2511,x2512))
% 173.53/173.43 [26]~E(x261,x262)+E(f423(x263,x264,x265,x266,x267,x268,x269,x2610,x261,x2611,x2612),f423(x263,x264,x265,x266,x267,x268,x269,x2610,x262,x2611,x2612))
% 173.53/173.43 [27]~E(x271,x272)+E(f423(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x271,x2712),f423(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x272,x2712))
% 173.53/173.43 [28]~E(x281,x282)+E(f423(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x281),f423(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x282))
% 173.53/173.43 [29]~E(x291,x292)+E(f115(x291),f115(x292))
% 173.53/173.43 [30]~E(x301,x302)+E(f228(x301),f228(x302))
% 173.53/173.43 [31]~E(x311,x312)+E(f124(x311),f124(x312))
% 173.53/173.43 [32]~E(x321,x322)+E(f226(x321),f226(x322))
% 173.53/173.43 [33]~E(x331,x332)+E(f116(x331),f116(x332))
% 173.53/173.43 [34]~E(x341,x342)+E(f39(x341),f39(x342))
% 173.53/173.43 [35]~E(x351,x352)+E(f268(x351),f268(x352))
% 173.53/173.43 [36]~E(x361,x362)+E(f87(x361),f87(x362))
% 173.53/173.43 [37]~E(x371,x372)+E(f417(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f417(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 173.53/173.43 [38]~E(x381,x382)+E(f417(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f417(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 173.53/173.43 [39]~E(x391,x392)+E(f417(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f417(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 173.53/173.43 [40]~E(x401,x402)+E(f417(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f417(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 173.53/173.43 [41]~E(x411,x412)+E(f417(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f417(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 173.53/173.43 [42]~E(x421,x422)+E(f417(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f417(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 173.53/173.43 [43]~E(x431,x432)+E(f417(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f417(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 173.53/173.43 [44]~E(x441,x442)+E(f417(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f417(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 173.53/173.43 [45]~E(x451,x452)+E(f417(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f417(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 173.53/173.43 [46]~E(x461,x462)+E(f417(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f417(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 173.53/173.43 [47]~E(x471,x472)+E(f417(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f417(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 173.53/173.43 [48]~E(x481,x482)+E(f125(x481),f125(x482))
% 173.53/173.43 [49]~E(x491,x492)+E(f314(x491),f314(x492))
% 173.53/173.43 [50]~E(x501,x502)+E(f195(x501),f195(x502))
% 173.53/173.43 [51]~E(x511,x512)+E(f4(x511),f4(x512))
% 173.53/173.43 [52]~E(x521,x522)+E(f147(x521),f147(x522))
% 173.53/173.43 [53]~E(x531,x532)+E(f851(x531),f851(x532))
% 173.53/173.43 [54]~E(x541,x542)+E(f856(x541),f856(x542))
% 173.53/173.43 [55]~E(x551,x552)+E(f853(x551),f853(x552))
% 173.53/173.43 [56]~E(x561,x562)+E(f854(x561),f854(x562))
% 173.53/173.43 [57]~E(x571,x572)+E(f40(x571),f40(x572))
% 173.53/173.43 [58]~E(x581,x582)+E(f42(x581),f42(x582))
% 173.53/173.43 [59]~E(x591,x592)+E(f859(x591,x593),f859(x592,x593))
% 173.53/173.43 [60]~E(x601,x602)+E(f859(x603,x601),f859(x603,x602))
% 173.53/173.43 [61]~E(x611,x612)+E(f41(x611),f41(x612))
% 173.53/173.43 [62]~E(x621,x622)+E(f227(x621),f227(x622))
% 173.53/173.43 [63]~E(x631,x632)+E(f13(x631,x633,x634),f13(x632,x633,x634))
% 173.53/173.43 [64]~E(x641,x642)+E(f13(x643,x641,x644),f13(x643,x642,x644))
% 173.53/173.43 [65]~E(x651,x652)+E(f13(x653,x654,x651),f13(x653,x654,x652))
% 173.53/173.43 [66]~E(x661,x662)+E(f88(x661),f88(x662))
% 173.53/173.43 [67]~E(x671,x672)+E(f117(x671),f117(x672))
% 173.53/173.43 [68]~E(x681,x682)+E(f190(x681),f190(x682))
% 173.53/173.43 [69]~E(x691,x692)+E(f7(x691,x693,x694),f7(x692,x693,x694))
% 173.53/173.43 [70]~E(x701,x702)+E(f7(x703,x701,x704),f7(x703,x702,x704))
% 173.53/173.43 [71]~E(x711,x712)+E(f7(x713,x714,x711),f7(x713,x714,x712))
% 173.53/173.43 [72]~E(x721,x722)+E(f89(x721),f89(x722))
% 173.53/173.43 [73]~E(x731,x732)+E(f18(x731,x733,x734),f18(x732,x733,x734))
% 173.53/173.43 [74]~E(x741,x742)+E(f18(x743,x741,x744),f18(x743,x742,x744))
% 173.53/173.43 [75]~E(x751,x752)+E(f18(x753,x754,x751),f18(x753,x754,x752))
% 173.53/173.43 [76]~E(x761,x762)+E(f69(x761),f69(x762))
% 173.53/173.43 [77]~E(x771,x772)+E(f35(x771,x773),f35(x772,x773))
% 173.53/173.43 [78]~E(x781,x782)+E(f35(x783,x781),f35(x783,x782))
% 173.53/173.43 [79]~E(x791,x792)+E(f6(x791,x793),f6(x792,x793))
% 173.53/173.43 [80]~E(x801,x802)+E(f6(x803,x801),f6(x803,x802))
% 173.53/173.43 [81]~E(x811,x812)+E(f90(x811),f90(x812))
% 173.53/173.43 [82]~E(x821,x822)+E(f127(x821),f127(x822))
% 173.53/173.43 [83]~E(x831,x832)+E(f235(x831),f235(x832))
% 173.53/173.43 [84]~E(x841,x842)+E(f239(x841,x843),f239(x842,x843))
% 173.53/173.43 [85]~E(x851,x852)+E(f239(x853,x851),f239(x853,x852))
% 173.53/173.43 [86]~E(x861,x862)+E(f289(x861),f289(x862))
% 173.53/173.43 [87]~E(x871,x872)+E(f284(x871,x873,x874),f284(x872,x873,x874))
% 173.53/173.43 [88]~E(x881,x882)+E(f284(x883,x881,x884),f284(x883,x882,x884))
% 173.53/173.43 [89]~E(x891,x892)+E(f284(x893,x894,x891),f284(x893,x894,x892))
% 173.53/173.43 [90]~E(x901,x902)+E(f9(x901,x903),f9(x902,x903))
% 173.53/173.43 [91]~E(x911,x912)+E(f9(x913,x911),f9(x913,x912))
% 173.53/173.43 [92]~E(x921,x922)+E(f269(x921,x923),f269(x922,x923))
% 173.53/173.43 [93]~E(x931,x932)+E(f269(x933,x931),f269(x933,x932))
% 173.53/173.43 [94]~E(x941,x942)+E(f54(x941,x943,x944),f54(x942,x943,x944))
% 173.53/173.43 [95]~E(x951,x952)+E(f54(x953,x951,x954),f54(x953,x952,x954))
% 173.53/173.43 [96]~E(x961,x962)+E(f54(x963,x964,x961),f54(x963,x964,x962))
% 173.53/173.43 [97]~E(x971,x972)+E(f290(x971,x973,x974),f290(x972,x973,x974))
% 173.53/173.43 [98]~E(x981,x982)+E(f290(x983,x981,x984),f290(x983,x982,x984))
% 173.53/173.43 [99]~E(x991,x992)+E(f290(x993,x994,x991),f290(x993,x994,x992))
% 173.53/173.43 [100]~E(x1001,x1002)+E(f16(x1001,x1003),f16(x1002,x1003))
% 173.53/173.43 [101]~E(x1011,x1012)+E(f16(x1013,x1011),f16(x1013,x1012))
% 173.53/173.43 [102]~E(x1021,x1022)+E(f70(x1021),f70(x1022))
% 173.53/173.43 [103]~E(x1031,x1032)+E(f168(x1031),f168(x1032))
% 173.53/173.43 [104]~E(x1041,x1042)+E(f47(x1041,x1043),f47(x1042,x1043))
% 173.53/173.43 [105]~E(x1051,x1052)+E(f47(x1053,x1051),f47(x1053,x1052))
% 173.53/173.43 [106]~E(x1061,x1062)+E(f50(x1061,x1063),f50(x1062,x1063))
% 173.53/173.43 [107]~E(x1071,x1072)+E(f50(x1073,x1071),f50(x1073,x1072))
% 173.53/173.43 [108]~E(x1081,x1082)+E(f657(x1081,x1083),f657(x1082,x1083))
% 173.53/173.43 [109]~E(x1091,x1092)+E(f657(x1093,x1091),f657(x1093,x1092))
% 173.53/173.43 [110]~E(x1101,x1102)+E(f100(x1101),f100(x1102))
% 173.53/173.43 [111]~E(x1111,x1112)+E(f153(x1111,x1113),f153(x1112,x1113))
% 173.53/173.43 [112]~E(x1121,x1122)+E(f153(x1123,x1121),f153(x1123,x1122))
% 173.53/173.43 [113]~E(x1131,x1132)+E(f818(x1131),f818(x1132))
% 173.53/173.43 [114]~E(x1141,x1142)+E(f108(x1141),f108(x1142))
% 173.53/173.43 [115]~E(x1151,x1152)+E(f233(x1151),f233(x1152))
% 173.53/173.43 [116]~E(x1161,x1162)+E(f150(x1161,x1163),f150(x1162,x1163))
% 173.53/173.43 [117]~E(x1171,x1172)+E(f150(x1173,x1171),f150(x1173,x1172))
% 173.53/173.43 [118]~E(x1181,x1182)+E(f137(x1181),f137(x1182))
% 173.53/173.43 [119]~E(x1191,x1192)+E(f84(x1191),f84(x1192))
% 173.53/173.43 [120]~E(x1201,x1202)+E(f161(x1201),f161(x1202))
% 173.53/173.43 [121]~E(x1211,x1212)+E(f249(x1211,x1213,x1214),f249(x1212,x1213,x1214))
% 173.53/173.43 [122]~E(x1221,x1222)+E(f249(x1223,x1221,x1224),f249(x1223,x1222,x1224))
% 173.53/173.43 [123]~E(x1231,x1232)+E(f249(x1233,x1234,x1231),f249(x1233,x1234,x1232))
% 173.53/173.43 [124]~E(x1241,x1242)+E(f53(x1241),f53(x1242))
% 173.53/173.43 [125]~E(x1251,x1252)+E(f267(x1251,x1253,x1254),f267(x1252,x1253,x1254))
% 173.53/173.43 [126]~E(x1261,x1262)+E(f267(x1263,x1261,x1264),f267(x1263,x1262,x1264))
% 173.53/173.43 [127]~E(x1271,x1272)+E(f267(x1273,x1274,x1271),f267(x1273,x1274,x1272))
% 173.53/173.43 [128]~E(x1281,x1282)+E(f238(x1281,x1283),f238(x1282,x1283))
% 173.53/173.43 [129]~E(x1291,x1292)+E(f238(x1293,x1291),f238(x1293,x1292))
% 173.53/173.43 [130]~E(x1301,x1302)+E(f157(x1301,x1303),f157(x1302,x1303))
% 173.53/173.43 [131]~E(x1311,x1312)+E(f157(x1313,x1311),f157(x1313,x1312))
% 173.53/173.43 [132]~E(x1321,x1322)+E(f82(x1321,x1323,x1324,x1325),f82(x1322,x1323,x1324,x1325))
% 173.53/173.43 [133]~E(x1331,x1332)+E(f82(x1333,x1331,x1334,x1335),f82(x1333,x1332,x1334,x1335))
% 173.53/173.43 [134]~E(x1341,x1342)+E(f82(x1343,x1344,x1341,x1345),f82(x1343,x1344,x1342,x1345))
% 173.53/173.43 [135]~E(x1351,x1352)+E(f82(x1353,x1354,x1355,x1351),f82(x1353,x1354,x1355,x1352))
% 173.53/173.43 [136]~E(x1361,x1362)+E(f413(x1361,x1363,x1364,x1365),f413(x1362,x1363,x1364,x1365))
% 173.53/173.43 [137]~E(x1371,x1372)+E(f413(x1373,x1371,x1374,x1375),f413(x1373,x1372,x1374,x1375))
% 173.53/173.43 [138]~E(x1381,x1382)+E(f413(x1383,x1384,x1381,x1385),f413(x1383,x1384,x1382,x1385))
% 173.53/173.43 [139]~E(x1391,x1392)+E(f413(x1393,x1394,x1395,x1391),f413(x1393,x1394,x1395,x1392))
% 173.53/173.43 [140]~E(x1401,x1402)+E(f244(x1401,x1403,x1404),f244(x1402,x1403,x1404))
% 173.53/173.43 [141]~E(x1411,x1412)+E(f244(x1413,x1411,x1414),f244(x1413,x1412,x1414))
% 173.53/173.43 [142]~E(x1421,x1422)+E(f244(x1423,x1424,x1421),f244(x1423,x1424,x1422))
% 173.53/173.43 [143]~E(x1431,x1432)+E(f356(x1431,x1433,x1434),f356(x1432,x1433,x1434))
% 173.53/173.43 [144]~E(x1441,x1442)+E(f356(x1443,x1441,x1444),f356(x1443,x1442,x1444))
% 173.53/173.43 [145]~E(x1451,x1452)+E(f356(x1453,x1454,x1451),f356(x1453,x1454,x1452))
% 173.53/173.43 [146]~E(x1461,x1462)+E(f109(x1461,x1463),f109(x1462,x1463))
% 173.53/173.43 [147]~E(x1471,x1472)+E(f109(x1473,x1471),f109(x1473,x1472))
% 173.53/173.43 [148]~E(x1481,x1482)+E(f110(x1481,x1483),f110(x1482,x1483))
% 173.53/173.43 [149]~E(x1491,x1492)+E(f110(x1493,x1491),f110(x1493,x1492))
% 173.53/173.43 [150]~E(x1501,x1502)+E(f119(x1501),f119(x1502))
% 173.53/173.43 [151]~E(x1511,x1512)+E(f120(x1511),f120(x1512))
% 173.53/173.43 [152]~E(x1521,x1522)+E(f313(x1521),f313(x1522))
% 173.53/173.43 [153]~E(x1531,x1532)+E(f141(x1531,x1533),f141(x1532,x1533))
% 173.53/173.43 [154]~E(x1541,x1542)+E(f141(x1543,x1541),f141(x1543,x1542))
% 173.53/173.43 [155]~E(x1551,x1552)+E(f192(x1551),f192(x1552))
% 173.53/173.43 [156]~E(x1561,x1562)+E(f465(x1561,x1563,x1564),f465(x1562,x1563,x1564))
% 173.53/173.43 [157]~E(x1571,x1572)+E(f465(x1573,x1571,x1574),f465(x1573,x1572,x1574))
% 173.53/173.43 [158]~E(x1581,x1582)+E(f465(x1583,x1584,x1581),f465(x1583,x1584,x1582))
% 173.53/173.43 [159]~E(x1591,x1592)+E(f51(x1591,x1593),f51(x1592,x1593))
% 173.53/173.43 [160]~E(x1601,x1602)+E(f51(x1603,x1601),f51(x1603,x1602))
% 173.53/173.43 [161]~E(x1611,x1612)+E(f162(x1611),f162(x1612))
% 173.53/173.43 [162]~E(x1621,x1622)+E(f5(x1621),f5(x1622))
% 173.53/173.43 [163]~E(x1631,x1632)+E(f48(x1631,x1633),f48(x1632,x1633))
% 173.53/173.43 [164]~E(x1641,x1642)+E(f48(x1643,x1641),f48(x1643,x1642))
% 173.53/173.43 [165]~E(x1651,x1652)+E(f236(x1651,x1653),f236(x1652,x1653))
% 173.53/173.43 [166]~E(x1661,x1662)+E(f236(x1663,x1661),f236(x1663,x1662))
% 173.53/173.43 [167]~E(x1671,x1672)+E(f700(x1671,x1673),f700(x1672,x1673))
% 173.53/173.43 [168]~E(x1681,x1682)+E(f700(x1683,x1681),f700(x1683,x1682))
% 173.53/173.43 [169]~E(x1691,x1692)+E(f408(x1691,x1693,x1694,x1695,x1696),f408(x1692,x1693,x1694,x1695,x1696))
% 173.53/173.43 [170]~E(x1701,x1702)+E(f408(x1703,x1701,x1704,x1705,x1706),f408(x1703,x1702,x1704,x1705,x1706))
% 173.53/173.43 [171]~E(x1711,x1712)+E(f408(x1713,x1714,x1711,x1715,x1716),f408(x1713,x1714,x1712,x1715,x1716))
% 173.53/173.43 [172]~E(x1721,x1722)+E(f408(x1723,x1724,x1725,x1721,x1726),f408(x1723,x1724,x1725,x1722,x1726))
% 173.53/173.43 [173]~E(x1731,x1732)+E(f408(x1733,x1734,x1735,x1736,x1731),f408(x1733,x1734,x1735,x1736,x1732))
% 173.53/173.43 [174]~E(x1741,x1742)+E(f354(x1741,x1743,x1744),f354(x1742,x1743,x1744))
% 173.53/173.43 [175]~E(x1751,x1752)+E(f354(x1753,x1751,x1754),f354(x1753,x1752,x1754))
% 173.53/173.43 [176]~E(x1761,x1762)+E(f354(x1763,x1764,x1761),f354(x1763,x1764,x1762))
% 173.53/173.43 [177]~E(x1771,x1772)+E(f56(x1771,x1773),f56(x1772,x1773))
% 173.53/173.43 [178]~E(x1781,x1782)+E(f56(x1783,x1781),f56(x1783,x1782))
% 173.53/173.43 [179]~E(x1791,x1792)+E(f135(x1791,x1793),f135(x1792,x1793))
% 173.53/173.43 [180]~E(x1801,x1802)+E(f135(x1803,x1801),f135(x1803,x1802))
% 173.53/173.43 [181]~E(x1811,x1812)+E(f287(x1811,x1813),f287(x1812,x1813))
% 173.53/173.43 [182]~E(x1821,x1822)+E(f287(x1823,x1821),f287(x1823,x1822))
% 173.53/173.43 [183]~E(x1831,x1832)+E(f796(x1831,x1833,x1834),f796(x1832,x1833,x1834))
% 173.53/173.43 [184]~E(x1841,x1842)+E(f796(x1843,x1841,x1844),f796(x1843,x1842,x1844))
% 173.53/173.43 [185]~E(x1851,x1852)+E(f796(x1853,x1854,x1851),f796(x1853,x1854,x1852))
% 173.53/173.43 [186]~E(x1861,x1862)+E(f264(x1861,x1863,x1864),f264(x1862,x1863,x1864))
% 173.53/173.43 [187]~E(x1871,x1872)+E(f264(x1873,x1871,x1874),f264(x1873,x1872,x1874))
% 173.53/173.43 [188]~E(x1881,x1882)+E(f264(x1883,x1884,x1881),f264(x1883,x1884,x1882))
% 173.53/173.43 [189]~E(x1891,x1892)+E(f248(x1891,x1893),f248(x1892,x1893))
% 173.53/173.43 [190]~E(x1901,x1902)+E(f248(x1903,x1901),f248(x1903,x1902))
% 173.53/173.43 [191]~E(x1911,x1912)+E(f629(x1911,x1913,x1914),f629(x1912,x1913,x1914))
% 173.53/173.43 [192]~E(x1921,x1922)+E(f629(x1923,x1921,x1924),f629(x1923,x1922,x1924))
% 173.53/173.43 [193]~E(x1931,x1932)+E(f629(x1933,x1934,x1931),f629(x1933,x1934,x1932))
% 173.53/173.43 [194]~E(x1941,x1942)+E(f240(x1941),f240(x1942))
% 173.53/173.43 [195]~E(x1951,x1952)+E(f656(x1951,x1953,x1954),f656(x1952,x1953,x1954))
% 173.53/173.43 [196]~E(x1961,x1962)+E(f656(x1963,x1961,x1964),f656(x1963,x1962,x1964))
% 173.53/173.43 [197]~E(x1971,x1972)+E(f656(x1973,x1974,x1971),f656(x1973,x1974,x1972))
% 173.53/173.43 [198]~E(x1981,x1982)+E(f282(x1981,x1983),f282(x1982,x1983))
% 173.53/173.43 [199]~E(x1991,x1992)+E(f282(x1993,x1991),f282(x1993,x1992))
% 173.53/173.43 [200]~E(x2001,x2002)+E(f64(x2001),f64(x2002))
% 173.53/173.43 [201]~E(x2011,x2012)+E(f410(x2011,x2013,x2014,x2015,x2016,x2017,x2018,x2019),f410(x2012,x2013,x2014,x2015,x2016,x2017,x2018,x2019))
% 173.53/173.43 [202]~E(x2021,x2022)+E(f410(x2023,x2021,x2024,x2025,x2026,x2027,x2028,x2029),f410(x2023,x2022,x2024,x2025,x2026,x2027,x2028,x2029))
% 173.53/173.43 [203]~E(x2031,x2032)+E(f410(x2033,x2034,x2031,x2035,x2036,x2037,x2038,x2039),f410(x2033,x2034,x2032,x2035,x2036,x2037,x2038,x2039))
% 173.53/173.43 [204]~E(x2041,x2042)+E(f410(x2043,x2044,x2045,x2041,x2046,x2047,x2048,x2049),f410(x2043,x2044,x2045,x2042,x2046,x2047,x2048,x2049))
% 173.53/173.43 [205]~E(x2051,x2052)+E(f410(x2053,x2054,x2055,x2056,x2051,x2057,x2058,x2059),f410(x2053,x2054,x2055,x2056,x2052,x2057,x2058,x2059))
% 173.53/173.43 [206]~E(x2061,x2062)+E(f410(x2063,x2064,x2065,x2066,x2067,x2061,x2068,x2069),f410(x2063,x2064,x2065,x2066,x2067,x2062,x2068,x2069))
% 173.53/173.43 [207]~E(x2071,x2072)+E(f410(x2073,x2074,x2075,x2076,x2077,x2078,x2071,x2079),f410(x2073,x2074,x2075,x2076,x2077,x2078,x2072,x2079))
% 173.53/173.43 [208]~E(x2081,x2082)+E(f410(x2083,x2084,x2085,x2086,x2087,x2088,x2089,x2081),f410(x2083,x2084,x2085,x2086,x2087,x2088,x2089,x2082))
% 173.53/173.43 [209]~E(x2091,x2092)+E(f644(x2091,x2093,x2094),f644(x2092,x2093,x2094))
% 173.53/173.43 [210]~E(x2101,x2102)+E(f644(x2103,x2101,x2104),f644(x2103,x2102,x2104))
% 173.53/173.43 [211]~E(x2111,x2112)+E(f644(x2113,x2114,x2111),f644(x2113,x2114,x2112))
% 173.53/173.43 [212]~E(x2121,x2122)+E(f788(x2121,x2123,x2124),f788(x2122,x2123,x2124))
% 173.53/173.43 [213]~E(x2131,x2132)+E(f788(x2133,x2131,x2134),f788(x2133,x2132,x2134))
% 173.53/173.43 [214]~E(x2141,x2142)+E(f788(x2143,x2144,x2141),f788(x2143,x2144,x2142))
% 173.53/173.43 [215]~E(x2151,x2152)+E(f91(x2151,x2153),f91(x2152,x2153))
% 173.53/173.43 [216]~E(x2161,x2162)+E(f91(x2163,x2161),f91(x2163,x2162))
% 173.53/173.43 [217]~E(x2171,x2172)+E(f421(x2171,x2173,x2174,x2175,x2176),f421(x2172,x2173,x2174,x2175,x2176))
% 173.53/173.43 [218]~E(x2181,x2182)+E(f421(x2183,x2181,x2184,x2185,x2186),f421(x2183,x2182,x2184,x2185,x2186))
% 173.53/173.43 [219]~E(x2191,x2192)+E(f421(x2193,x2194,x2191,x2195,x2196),f421(x2193,x2194,x2192,x2195,x2196))
% 173.53/173.43 [220]~E(x2201,x2202)+E(f421(x2203,x2204,x2205,x2201,x2206),f421(x2203,x2204,x2205,x2202,x2206))
% 173.53/173.43 [221]~E(x2211,x2212)+E(f421(x2213,x2214,x2215,x2216,x2211),f421(x2213,x2214,x2215,x2216,x2212))
% 173.53/173.43 [222]~E(x2221,x2222)+E(f778(x2221,x2223,x2224,x2225),f778(x2222,x2223,x2224,x2225))
% 173.53/173.43 [223]~E(x2231,x2232)+E(f778(x2233,x2231,x2234,x2235),f778(x2233,x2232,x2234,x2235))
% 173.53/173.43 [224]~E(x2241,x2242)+E(f778(x2243,x2244,x2241,x2245),f778(x2243,x2244,x2242,x2245))
% 173.53/173.43 [225]~E(x2251,x2252)+E(f778(x2253,x2254,x2255,x2251),f778(x2253,x2254,x2255,x2252))
% 173.53/173.43 [226]~E(x2261,x2262)+E(f144(x2261,x2263,x2264,x2265),f144(x2262,x2263,x2264,x2265))
% 173.53/173.43 [227]~E(x2271,x2272)+E(f144(x2273,x2271,x2274,x2275),f144(x2273,x2272,x2274,x2275))
% 173.53/173.43 [228]~E(x2281,x2282)+E(f144(x2283,x2284,x2281,x2285),f144(x2283,x2284,x2282,x2285))
% 173.53/173.43 [229]~E(x2291,x2292)+E(f144(x2293,x2294,x2295,x2291),f144(x2293,x2294,x2295,x2292))
% 173.53/173.43 [230]~E(x2301,x2302)+E(f164(x2301),f164(x2302))
% 173.53/173.43 [231]~E(x2311,x2312)+E(f720(x2311,x2313,x2314,x2315),f720(x2312,x2313,x2314,x2315))
% 173.53/173.43 [232]~E(x2321,x2322)+E(f720(x2323,x2321,x2324,x2325),f720(x2323,x2322,x2324,x2325))
% 173.53/173.43 [233]~E(x2331,x2332)+E(f720(x2333,x2334,x2331,x2335),f720(x2333,x2334,x2332,x2335))
% 173.53/173.43 [234]~E(x2341,x2342)+E(f720(x2343,x2344,x2345,x2341),f720(x2343,x2344,x2345,x2342))
% 173.53/173.43 [235]~E(x2351,x2352)+E(f132(x2351,x2353),f132(x2352,x2353))
% 173.53/173.43 [236]~E(x2361,x2362)+E(f132(x2363,x2361),f132(x2363,x2362))
% 173.53/173.43 [237]~E(x2371,x2372)+E(f291(x2371,x2373,x2374),f291(x2372,x2373,x2374))
% 173.53/173.43 [238]~E(x2381,x2382)+E(f291(x2383,x2381,x2384),f291(x2383,x2382,x2384))
% 173.53/173.43 [239]~E(x2391,x2392)+E(f291(x2393,x2394,x2391),f291(x2393,x2394,x2392))
% 173.53/173.43 [240]~E(x2401,x2402)+E(f219(x2401),f219(x2402))
% 173.53/173.43 [241]~E(x2411,x2412)+E(f266(x2411,x2413),f266(x2412,x2413))
% 173.53/173.43 [242]~E(x2421,x2422)+E(f266(x2423,x2421),f266(x2423,x2422))
% 173.53/173.43 [243]~E(x2431,x2432)+E(f57(x2431,x2433),f57(x2432,x2433))
% 173.53/173.43 [244]~E(x2441,x2442)+E(f57(x2443,x2441),f57(x2443,x2442))
% 173.53/173.43 [245]~E(x2451,x2452)+E(f129(x2451),f129(x2452))
% 173.53/173.43 [246]~E(x2461,x2462)+E(f288(x2461),f288(x2462))
% 173.53/173.43 [247]~E(x2471,x2472)+E(f154(x2471,x2473),f154(x2472,x2473))
% 173.53/173.43 [248]~E(x2481,x2482)+E(f154(x2483,x2481),f154(x2483,x2482))
% 173.53/173.43 [249]~E(x2491,x2492)+E(f33(x2491,x2493,x2494),f33(x2492,x2493,x2494))
% 173.53/173.43 [250]~E(x2501,x2502)+E(f33(x2503,x2501,x2504),f33(x2503,x2502,x2504))
% 173.53/173.43 [251]~E(x2511,x2512)+E(f33(x2513,x2514,x2511),f33(x2513,x2514,x2512))
% 173.53/173.43 [252]~E(x2521,x2522)+E(f822(x2521,x2523,x2524),f822(x2522,x2523,x2524))
% 173.53/173.43 [253]~E(x2531,x2532)+E(f822(x2533,x2531,x2534),f822(x2533,x2532,x2534))
% 173.53/173.43 [254]~E(x2541,x2542)+E(f822(x2543,x2544,x2541),f822(x2543,x2544,x2542))
% 173.53/173.43 [255]~E(x2551,x2552)+E(f263(x2551),f263(x2552))
% 173.53/173.43 [256]~E(x2561,x2562)+E(f128(x2561,x2563),f128(x2562,x2563))
% 173.53/173.43 [257]~E(x2571,x2572)+E(f128(x2573,x2571),f128(x2573,x2572))
% 173.53/173.43 [258]~E(x2581,x2582)+E(f152(x2581,x2583,x2584,x2585),f152(x2582,x2583,x2584,x2585))
% 173.53/173.43 [259]~E(x2591,x2592)+E(f152(x2593,x2591,x2594,x2595),f152(x2593,x2592,x2594,x2595))
% 173.53/173.43 [260]~E(x2601,x2602)+E(f152(x2603,x2604,x2601,x2605),f152(x2603,x2604,x2602,x2605))
% 173.53/173.43 [261]~E(x2611,x2612)+E(f152(x2613,x2614,x2615,x2611),f152(x2613,x2614,x2615,x2612))
% 173.53/173.43 [262]~E(x2621,x2622)+E(f692(x2621,x2623,x2624),f692(x2622,x2623,x2624))
% 173.53/173.43 [263]~E(x2631,x2632)+E(f692(x2633,x2631,x2634),f692(x2633,x2632,x2634))
% 173.53/173.43 [264]~E(x2641,x2642)+E(f692(x2643,x2644,x2641),f692(x2643,x2644,x2642))
% 173.53/173.43 [265]~E(x2651,x2652)+E(f148(x2651,x2653),f148(x2652,x2653))
% 173.53/173.43 [266]~E(x2661,x2662)+E(f148(x2663,x2661),f148(x2663,x2662))
% 173.53/173.43 [267]~E(x2671,x2672)+E(f428(x2671,x2673,x2674),f428(x2672,x2673,x2674))
% 173.53/173.43 [268]~E(x2681,x2682)+E(f428(x2683,x2681,x2684),f428(x2683,x2682,x2684))
% 173.53/173.43 [269]~E(x2691,x2692)+E(f428(x2693,x2694,x2691),f428(x2693,x2694,x2692))
% 173.53/173.43 [270]~E(x2701,x2702)+E(f172(x2701,x2703,x2704),f172(x2702,x2703,x2704))
% 173.53/173.43 [271]~E(x2711,x2712)+E(f172(x2713,x2711,x2714),f172(x2713,x2712,x2714))
% 173.53/173.43 [272]~E(x2721,x2722)+E(f172(x2723,x2724,x2721),f172(x2723,x2724,x2722))
% 173.53/173.43 [273]~E(x2731,x2732)+E(f138(x2731,x2733,x2734,x2735),f138(x2732,x2733,x2734,x2735))
% 173.53/173.43 [274]~E(x2741,x2742)+E(f138(x2743,x2741,x2744,x2745),f138(x2743,x2742,x2744,x2745))
% 173.53/173.43 [275]~E(x2751,x2752)+E(f138(x2753,x2754,x2751,x2755),f138(x2753,x2754,x2752,x2755))
% 173.53/173.43 [276]~E(x2761,x2762)+E(f138(x2763,x2764,x2765,x2761),f138(x2763,x2764,x2765,x2762))
% 173.53/173.43 [277]~E(x2771,x2772)+E(f246(x2771,x2773),f246(x2772,x2773))
% 173.53/173.43 [278]~E(x2781,x2782)+E(f246(x2783,x2781),f246(x2783,x2782))
% 173.53/173.43 [279]~E(x2791,x2792)+E(f300(x2791,x2793),f300(x2792,x2793))
% 173.53/173.43 [280]~E(x2801,x2802)+E(f300(x2803,x2801),f300(x2803,x2802))
% 173.53/173.43 [281]~E(x2811,x2812)+E(f96(x2811),f96(x2812))
% 173.53/173.43 [282]~E(x2821,x2822)+E(f36(x2821,x2823),f36(x2822,x2823))
% 173.53/173.43 [283]~E(x2831,x2832)+E(f36(x2833,x2831),f36(x2833,x2832))
% 173.53/173.43 [284]~E(x2841,x2842)+E(f169(x2841),f169(x2842))
% 173.53/173.43 [285]~E(x2851,x2852)+E(f134(x2851),f134(x2852))
% 173.53/173.43 [286]~E(x2861,x2862)+E(f301(x2861,x2863),f301(x2862,x2863))
% 173.53/173.43 [287]~E(x2871,x2872)+E(f301(x2873,x2871),f301(x2873,x2872))
% 173.53/173.43 [288]~E(x2881,x2882)+E(f175(x2881,x2883),f175(x2882,x2883))
% 173.53/173.43 [289]~E(x2891,x2892)+E(f175(x2893,x2891),f175(x2893,x2892))
% 173.53/173.43 [290]~E(x2901,x2902)+E(f283(x2901,x2903,x2904),f283(x2902,x2903,x2904))
% 173.53/173.43 [291]~E(x2911,x2912)+E(f283(x2913,x2911,x2914),f283(x2913,x2912,x2914))
% 173.53/173.43 [292]~E(x2921,x2922)+E(f283(x2923,x2924,x2921),f283(x2923,x2924,x2922))
% 173.53/173.43 [293]~E(x2931,x2932)+E(f258(x2931,x2933),f258(x2932,x2933))
% 173.53/173.43 [294]~E(x2941,x2942)+E(f258(x2943,x2941),f258(x2943,x2942))
% 173.53/173.43 [295]~E(x2951,x2952)+E(f177(x2951,x2953),f177(x2952,x2953))
% 173.53/173.43 [296]~E(x2961,x2962)+E(f177(x2963,x2961),f177(x2963,x2962))
% 173.53/173.43 [297]~E(x2971,x2972)+E(f858(x2971,x2973),f858(x2972,x2973))
% 173.53/173.43 [298]~E(x2981,x2982)+E(f858(x2983,x2981),f858(x2983,x2982))
% 173.53/173.43 [299]~E(x2991,x2992)+E(f857(x2991,x2993),f857(x2992,x2993))
% 173.53/173.43 [300]~E(x3001,x3002)+E(f857(x3003,x3001),f857(x3003,x3002))
% 173.53/173.43 [301]~E(x3011,x3012)+E(f165(x3011),f165(x3012))
% 173.53/173.43 [302]~E(x3021,x3022)+E(f14(x3021,x3023),f14(x3022,x3023))
% 173.53/173.43 [303]~E(x3031,x3032)+E(f14(x3033,x3031),f14(x3033,x3032))
% 173.53/173.43 [304]~E(x3041,x3042)+E(f426(x3041,x3043,x3044),f426(x3042,x3043,x3044))
% 173.53/173.43 [305]~E(x3051,x3052)+E(f426(x3053,x3051,x3054),f426(x3053,x3052,x3054))
% 173.53/173.43 [306]~E(x3061,x3062)+E(f426(x3063,x3064,x3061),f426(x3063,x3064,x3062))
% 173.53/173.43 [307]~E(x3071,x3072)+E(f323(x3071,x3073,x3074,x3075),f323(x3072,x3073,x3074,x3075))
% 173.53/173.43 [308]~E(x3081,x3082)+E(f323(x3083,x3081,x3084,x3085),f323(x3083,x3082,x3084,x3085))
% 173.53/173.43 [309]~E(x3091,x3092)+E(f323(x3093,x3094,x3091,x3095),f323(x3093,x3094,x3092,x3095))
% 173.53/173.43 [310]~E(x3101,x3102)+E(f323(x3103,x3104,x3105,x3101),f323(x3103,x3104,x3105,x3102))
% 173.53/173.43 [311]~E(x3111,x3112)+E(f293(x3111,x3113,x3114),f293(x3112,x3113,x3114))
% 173.53/173.43 [312]~E(x3121,x3122)+E(f293(x3123,x3121,x3124),f293(x3123,x3122,x3124))
% 173.53/173.43 [313]~E(x3131,x3132)+E(f293(x3133,x3134,x3131),f293(x3133,x3134,x3132))
% 173.53/173.43 [314]~E(x3141,x3142)+E(f167(x3141),f167(x3142))
% 173.53/173.43 [315]~E(x3151,x3152)+E(f792(x3151,x3153,x3154),f792(x3152,x3153,x3154))
% 173.53/173.43 [316]~E(x3161,x3162)+E(f792(x3163,x3161,x3164),f792(x3163,x3162,x3164))
% 173.53/173.43 [317]~E(x3171,x3172)+E(f792(x3173,x3174,x3171),f792(x3173,x3174,x3172))
% 173.53/173.43 [318]~E(x3181,x3182)+E(f265(x3181,x3183),f265(x3182,x3183))
% 173.53/173.43 [319]~E(x3191,x3192)+E(f265(x3193,x3191),f265(x3193,x3192))
% 173.53/173.43 [320]~E(x3201,x3202)+E(f382(x3201,x3203),f382(x3202,x3203))
% 173.53/173.43 [321]~E(x3211,x3212)+E(f382(x3213,x3211),f382(x3213,x3212))
% 173.53/173.43 [322]~E(x3221,x3222)+E(f173(x3221,x3223),f173(x3222,x3223))
% 173.53/173.43 [323]~E(x3231,x3232)+E(f173(x3233,x3231),f173(x3233,x3232))
% 173.53/173.43 [324]~E(x3241,x3242)+E(f58(x3241,x3243),f58(x3242,x3243))
% 173.53/173.43 [325]~E(x3251,x3252)+E(f58(x3253,x3251),f58(x3253,x3252))
% 173.53/173.43 [326]~E(x3261,x3262)+E(f32(x3261,x3263,x3264),f32(x3262,x3263,x3264))
% 173.53/173.43 [327]~E(x3271,x3272)+E(f32(x3273,x3271,x3274),f32(x3273,x3272,x3274))
% 173.53/173.43 [328]~E(x3281,x3282)+E(f32(x3283,x3284,x3281),f32(x3283,x3284,x3282))
% 173.53/173.43 [329]~E(x3291,x3292)+E(f170(x3291,x3293,x3294),f170(x3292,x3293,x3294))
% 173.53/173.43 [330]~E(x3301,x3302)+E(f170(x3303,x3301,x3304),f170(x3303,x3302,x3304))
% 173.53/173.43 [331]~E(x3311,x3312)+E(f170(x3313,x3314,x3311),f170(x3313,x3314,x3312))
% 173.53/173.43 [332]~E(x3321,x3322)+E(f74(x3321,x3323,x3324),f74(x3322,x3323,x3324))
% 173.53/173.43 [333]~E(x3331,x3332)+E(f74(x3333,x3331,x3334),f74(x3333,x3332,x3334))
% 173.53/173.43 [334]~E(x3341,x3342)+E(f74(x3343,x3344,x3341),f74(x3343,x3344,x3342))
% 173.53/173.43 [335]~E(x3351,x3352)+E(f507(x3351,x3353,x3354,x3355),f507(x3352,x3353,x3354,x3355))
% 173.53/173.43 [336]~E(x3361,x3362)+E(f507(x3363,x3361,x3364,x3365),f507(x3363,x3362,x3364,x3365))
% 173.53/173.43 [337]~E(x3371,x3372)+E(f507(x3373,x3374,x3371,x3375),f507(x3373,x3374,x3372,x3375))
% 173.53/173.43 [338]~E(x3381,x3382)+E(f507(x3383,x3384,x3385,x3381),f507(x3383,x3384,x3385,x3382))
% 173.53/173.43 [339]~E(x3391,x3392)+E(f327(x3391,x3393),f327(x3392,x3393))
% 173.53/173.43 [340]~E(x3401,x3402)+E(f327(x3403,x3401),f327(x3403,x3402))
% 173.53/173.43 [341]~E(x3411,x3412)+E(f72(x3411,x3413),f72(x3412,x3413))
% 173.53/173.43 [342]~E(x3421,x3422)+E(f72(x3423,x3421),f72(x3423,x3422))
% 173.53/173.43 [343]~E(x3431,x3432)+E(f28(x3431,x3433),f28(x3432,x3433))
% 173.53/173.43 [344]~E(x3441,x3442)+E(f28(x3443,x3441),f28(x3443,x3442))
% 173.53/173.43 [345]~E(x3451,x3452)+E(f247(x3451,x3453),f247(x3452,x3453))
% 173.53/173.43 [346]~E(x3461,x3462)+E(f247(x3463,x3461),f247(x3463,x3462))
% 173.53/173.43 [347]~E(x3471,x3472)+E(f431(x3471,x3473,x3474),f431(x3472,x3473,x3474))
% 173.53/173.43 [348]~E(x3481,x3482)+E(f431(x3483,x3481,x3484),f431(x3483,x3482,x3484))
% 173.53/173.43 [349]~E(x3491,x3492)+E(f431(x3493,x3494,x3491),f431(x3493,x3494,x3492))
% 173.53/173.43 [350]~E(x3501,x3502)+E(f473(x3501,x3503,x3504,x3505),f473(x3502,x3503,x3504,x3505))
% 173.53/173.43 [351]~E(x3511,x3512)+E(f473(x3513,x3511,x3514,x3515),f473(x3513,x3512,x3514,x3515))
% 173.53/173.43 [352]~E(x3521,x3522)+E(f473(x3523,x3524,x3521,x3525),f473(x3523,x3524,x3522,x3525))
% 173.53/173.43 [353]~E(x3531,x3532)+E(f473(x3533,x3534,x3535,x3531),f473(x3533,x3534,x3535,x3532))
% 173.53/173.43 [354]~E(x3541,x3542)+E(f133(x3541),f133(x3542))
% 173.53/173.43 [355]~E(x3551,x3552)+E(f182(x3551,x3553,x3554,x3555,x3556),f182(x3552,x3553,x3554,x3555,x3556))
% 173.53/173.43 [356]~E(x3561,x3562)+E(f182(x3563,x3561,x3564,x3565,x3566),f182(x3563,x3562,x3564,x3565,x3566))
% 173.53/173.43 [357]~E(x3571,x3572)+E(f182(x3573,x3574,x3571,x3575,x3576),f182(x3573,x3574,x3572,x3575,x3576))
% 173.53/173.43 [358]~E(x3581,x3582)+E(f182(x3583,x3584,x3585,x3581,x3586),f182(x3583,x3584,x3585,x3582,x3586))
% 173.53/173.43 [359]~E(x3591,x3592)+E(f182(x3593,x3594,x3595,x3596,x3591),f182(x3593,x3594,x3595,x3596,x3592))
% 173.53/173.43 [360]~E(x3601,x3602)+E(f303(x3601,x3603),f303(x3602,x3603))
% 173.53/173.43 [361]~E(x3611,x3612)+E(f303(x3613,x3611),f303(x3613,x3612))
% 173.53/173.43 [362]~E(x3621,x3622)+E(f791(x3621,x3623,x3624),f791(x3622,x3623,x3624))
% 173.53/173.43 [363]~E(x3631,x3632)+E(f791(x3633,x3631,x3634),f791(x3633,x3632,x3634))
% 173.53/173.43 [364]~E(x3641,x3642)+E(f791(x3643,x3644,x3641),f791(x3643,x3644,x3642))
% 173.53/173.43 [365]~E(x3651,x3652)+E(f305(x3651,x3653),f305(x3652,x3653))
% 173.53/173.43 [366]~E(x3661,x3662)+E(f305(x3663,x3661),f305(x3663,x3662))
% 173.53/173.43 [367]~E(x3671,x3672)+E(f470(x3671,x3673),f470(x3672,x3673))
% 173.53/173.43 [368]~E(x3681,x3682)+E(f470(x3683,x3681),f470(x3683,x3682))
% 173.53/173.43 [369]~E(x3691,x3692)+E(f250(x3691,x3693,x3694,x3695,x3696,x3697),f250(x3692,x3693,x3694,x3695,x3696,x3697))
% 173.53/173.43 [370]~E(x3701,x3702)+E(f250(x3703,x3701,x3704,x3705,x3706,x3707),f250(x3703,x3702,x3704,x3705,x3706,x3707))
% 173.53/173.43 [371]~E(x3711,x3712)+E(f250(x3713,x3714,x3711,x3715,x3716,x3717),f250(x3713,x3714,x3712,x3715,x3716,x3717))
% 173.53/173.43 [372]~E(x3721,x3722)+E(f250(x3723,x3724,x3725,x3721,x3726,x3727),f250(x3723,x3724,x3725,x3722,x3726,x3727))
% 173.53/173.43 [373]~E(x3731,x3732)+E(f250(x3733,x3734,x3735,x3736,x3731,x3737),f250(x3733,x3734,x3735,x3736,x3732,x3737))
% 173.53/173.43 [374]~E(x3741,x3742)+E(f250(x3743,x3744,x3745,x3746,x3747,x3741),f250(x3743,x3744,x3745,x3746,x3747,x3742))
% 173.53/173.43 [375]~E(x3751,x3752)+E(f184(x3751,x3753),f184(x3752,x3753))
% 173.53/173.43 [376]~E(x3761,x3762)+E(f184(x3763,x3761),f184(x3763,x3762))
% 173.53/173.43 [377]~E(x3771,x3772)+E(f75(x3771,x3773,x3774,x3775,x3776),f75(x3772,x3773,x3774,x3775,x3776))
% 173.53/173.43 [378]~E(x3781,x3782)+E(f75(x3783,x3781,x3784,x3785,x3786),f75(x3783,x3782,x3784,x3785,x3786))
% 173.53/173.43 [379]~E(x3791,x3792)+E(f75(x3793,x3794,x3791,x3795,x3796),f75(x3793,x3794,x3792,x3795,x3796))
% 173.53/173.43 [380]~E(x3801,x3802)+E(f75(x3803,x3804,x3805,x3801,x3806),f75(x3803,x3804,x3805,x3802,x3806))
% 173.53/173.43 [381]~E(x3811,x3812)+E(f75(x3813,x3814,x3815,x3816,x3811),f75(x3813,x3814,x3815,x3816,x3812))
% 173.53/173.43 [382]~E(x3821,x3822)+E(f805(x3821,x3823,x3824,x3825),f805(x3822,x3823,x3824,x3825))
% 173.53/173.43 [383]~E(x3831,x3832)+E(f805(x3833,x3831,x3834,x3835),f805(x3833,x3832,x3834,x3835))
% 173.53/173.43 [384]~E(x3841,x3842)+E(f805(x3843,x3844,x3841,x3845),f805(x3843,x3844,x3842,x3845))
% 173.53/173.43 [385]~E(x3851,x3852)+E(f805(x3853,x3854,x3855,x3851),f805(x3853,x3854,x3855,x3852))
% 173.53/173.43 [386]~E(x3861,x3862)+E(f245(x3861,x3863,x3864),f245(x3862,x3863,x3864))
% 173.53/173.43 [387]~E(x3871,x3872)+E(f245(x3873,x3871,x3874),f245(x3873,x3872,x3874))
% 173.53/173.43 [388]~E(x3881,x3882)+E(f245(x3883,x3884,x3881),f245(x3883,x3884,x3882))
% 173.53/173.43 [389]~E(x3891,x3892)+E(f563(x3891,x3893,x3894,x3895,x3896),f563(x3892,x3893,x3894,x3895,x3896))
% 173.53/173.43 [390]~E(x3901,x3902)+E(f563(x3903,x3901,x3904,x3905,x3906),f563(x3903,x3902,x3904,x3905,x3906))
% 173.53/173.43 [391]~E(x3911,x3912)+E(f563(x3913,x3914,x3911,x3915,x3916),f563(x3913,x3914,x3912,x3915,x3916))
% 173.53/173.43 [392]~E(x3921,x3922)+E(f563(x3923,x3924,x3925,x3921,x3926),f563(x3923,x3924,x3925,x3922,x3926))
% 173.53/173.43 [393]~E(x3931,x3932)+E(f563(x3933,x3934,x3935,x3936,x3931),f563(x3933,x3934,x3935,x3936,x3932))
% 173.53/173.43 [394]~E(x3941,x3942)+E(f143(x3941,x3943),f143(x3942,x3943))
% 173.53/173.43 [395]~E(x3951,x3952)+E(f143(x3953,x3951),f143(x3953,x3952))
% 173.53/173.43 [396]~E(x3961,x3962)+E(f11(x3961,x3963),f11(x3962,x3963))
% 173.53/173.43 [397]~E(x3971,x3972)+E(f11(x3973,x3971),f11(x3973,x3972))
% 173.53/173.43 [398]~E(x3981,x3982)+E(f498(x3981,x3983,x3984,x3985,x3986),f498(x3982,x3983,x3984,x3985,x3986))
% 173.53/173.43 [399]~E(x3991,x3992)+E(f498(x3993,x3991,x3994,x3995,x3996),f498(x3993,x3992,x3994,x3995,x3996))
% 173.53/173.43 [400]~E(x4001,x4002)+E(f498(x4003,x4004,x4001,x4005,x4006),f498(x4003,x4004,x4002,x4005,x4006))
% 173.53/173.43 [401]~E(x4011,x4012)+E(f498(x4013,x4014,x4015,x4011,x4016),f498(x4013,x4014,x4015,x4012,x4016))
% 173.53/173.43 [402]~E(x4021,x4022)+E(f498(x4023,x4024,x4025,x4026,x4021),f498(x4023,x4024,x4025,x4026,x4022))
% 173.53/173.43 [403]~E(x4031,x4032)+E(f280(x4031),f280(x4032))
% 173.53/173.43 [404]~E(x4041,x4042)+E(f81(x4041,x4043),f81(x4042,x4043))
% 173.53/173.43 [405]~E(x4051,x4052)+E(f81(x4053,x4051),f81(x4053,x4052))
% 173.53/173.43 [406]~E(x4061,x4062)+E(f608(x4061,x4063,x4064,x4065,x4066),f608(x4062,x4063,x4064,x4065,x4066))
% 173.53/173.43 [407]~E(x4071,x4072)+E(f608(x4073,x4071,x4074,x4075,x4076),f608(x4073,x4072,x4074,x4075,x4076))
% 173.53/173.43 [408]~E(x4081,x4082)+E(f608(x4083,x4084,x4081,x4085,x4086),f608(x4083,x4084,x4082,x4085,x4086))
% 173.53/173.43 [409]~E(x4091,x4092)+E(f608(x4093,x4094,x4095,x4091,x4096),f608(x4093,x4094,x4095,x4092,x4096))
% 173.53/173.43 [410]~E(x4101,x4102)+E(f608(x4103,x4104,x4105,x4106,x4101),f608(x4103,x4104,x4105,x4106,x4102))
% 173.53/173.43 [411]~E(x4111,x4112)+E(f625(x4111,x4113,x4114,x4115),f625(x4112,x4113,x4114,x4115))
% 173.53/173.43 [412]~E(x4121,x4122)+E(f625(x4123,x4121,x4124,x4125),f625(x4123,x4122,x4124,x4125))
% 173.53/173.43 [413]~E(x4131,x4132)+E(f625(x4133,x4134,x4131,x4135),f625(x4133,x4134,x4132,x4135))
% 173.53/173.43 [414]~E(x4141,x4142)+E(f625(x4143,x4144,x4145,x4141),f625(x4143,x4144,x4145,x4142))
% 173.53/173.43 [415]~E(x4151,x4152)+E(f159(x4151,x4153,x4154,x4155),f159(x4152,x4153,x4154,x4155))
% 173.53/173.43 [416]~E(x4161,x4162)+E(f159(x4163,x4161,x4164,x4165),f159(x4163,x4162,x4164,x4165))
% 173.53/173.43 [417]~E(x4171,x4172)+E(f159(x4173,x4174,x4171,x4175),f159(x4173,x4174,x4172,x4175))
% 173.53/173.43 [418]~E(x4181,x4182)+E(f159(x4183,x4184,x4185,x4181),f159(x4183,x4184,x4185,x4182))
% 173.53/173.43 [419]~E(x4191,x4192)+E(f185(x4191,x4193,x4194),f185(x4192,x4193,x4194))
% 173.53/173.43 [420]~E(x4201,x4202)+E(f185(x4203,x4201,x4204),f185(x4203,x4202,x4204))
% 173.53/173.43 [421]~E(x4211,x4212)+E(f185(x4213,x4214,x4211),f185(x4213,x4214,x4212))
% 173.53/173.43 [422]~E(x4221,x4222)+E(f94(x4221,x4223),f94(x4222,x4223))
% 173.53/173.43 [423]~E(x4231,x4232)+E(f94(x4233,x4231),f94(x4233,x4232))
% 173.53/173.43 [424]~E(x4241,x4242)+E(f449(x4241,x4243,x4244,x4245),f449(x4242,x4243,x4244,x4245))
% 173.53/173.43 [425]~E(x4251,x4252)+E(f449(x4253,x4251,x4254,x4255),f449(x4253,x4252,x4254,x4255))
% 173.53/173.43 [426]~E(x4261,x4262)+E(f449(x4263,x4264,x4261,x4265),f449(x4263,x4264,x4262,x4265))
% 173.53/173.43 [427]~E(x4271,x4272)+E(f449(x4273,x4274,x4275,x4271),f449(x4273,x4274,x4275,x4272))
% 173.53/173.43 [428]~E(x4281,x4282)+E(f99(x4281,x4283),f99(x4282,x4283))
% 173.53/173.43 [429]~E(x4291,x4292)+E(f99(x4293,x4291),f99(x4293,x4292))
% 173.53/173.43 [430]~E(x4301,x4302)+E(f174(x4301,x4303),f174(x4302,x4303))
% 173.53/173.43 [431]~E(x4311,x4312)+E(f174(x4313,x4311),f174(x4313,x4312))
% 173.53/173.43 [432]~E(x4321,x4322)+E(f149(x4321,x4323),f149(x4322,x4323))
% 173.53/173.43 [433]~E(x4331,x4332)+E(f149(x4333,x4331),f149(x4333,x4332))
% 173.53/173.43 [434]~E(x4341,x4342)+E(f171(x4341,x4343,x4344),f171(x4342,x4343,x4344))
% 173.53/173.43 [435]~E(x4351,x4352)+E(f171(x4353,x4351,x4354),f171(x4353,x4352,x4354))
% 173.53/173.43 [436]~E(x4361,x4362)+E(f171(x4363,x4364,x4361),f171(x4363,x4364,x4362))
% 173.53/173.43 [437]~E(x4371,x4372)+E(f511(x4371,x4373,x4374,x4375),f511(x4372,x4373,x4374,x4375))
% 173.53/173.43 [438]~E(x4381,x4382)+E(f511(x4383,x4381,x4384,x4385),f511(x4383,x4382,x4384,x4385))
% 173.53/173.43 [439]~E(x4391,x4392)+E(f511(x4393,x4394,x4391,x4395),f511(x4393,x4394,x4392,x4395))
% 173.53/173.43 [440]~E(x4401,x4402)+E(f511(x4403,x4404,x4405,x4401),f511(x4403,x4404,x4405,x4402))
% 173.53/173.43 [441]~E(x4411,x4412)+E(f52(x4411),f52(x4412))
% 173.53/173.43 [442]~E(x4421,x4422)+E(f49(x4421,x4423),f49(x4422,x4423))
% 173.53/173.43 [443]~E(x4431,x4432)+E(f49(x4433,x4431),f49(x4433,x4432))
% 173.53/173.43 [444]~E(x4441,x4442)+E(f199(x4441,x4443),f199(x4442,x4443))
% 173.53/173.43 [445]~E(x4451,x4452)+E(f199(x4453,x4451),f199(x4453,x4452))
% 173.53/173.43 [446]~E(x4461,x4462)+E(f66(x4461),f66(x4462))
% 173.53/173.43 [447]~E(x4471,x4472)+E(f572(x4471,x4473,x4474),f572(x4472,x4473,x4474))
% 173.53/173.43 [448]~E(x4481,x4482)+E(f572(x4483,x4481,x4484),f572(x4483,x4482,x4484))
% 173.53/173.43 [449]~E(x4491,x4492)+E(f572(x4493,x4494,x4491),f572(x4493,x4494,x4492))
% 173.53/173.43 [450]~E(x4501,x4502)+E(f394(x4501),f394(x4502))
% 173.53/173.43 [451]~E(x4511,x4512)+E(f62(x4511,x4513),f62(x4512,x4513))
% 173.53/173.43 [452]~E(x4521,x4522)+E(f62(x4523,x4521),f62(x4523,x4522))
% 173.53/173.43 [453]~E(x4531,x4532)+E(f353(x4531,x4533,x4534,x4535),f353(x4532,x4533,x4534,x4535))
% 173.53/173.43 [454]~E(x4541,x4542)+E(f353(x4543,x4541,x4544,x4545),f353(x4543,x4542,x4544,x4545))
% 173.53/173.43 [455]~E(x4551,x4552)+E(f353(x4553,x4554,x4551,x4555),f353(x4553,x4554,x4552,x4555))
% 173.53/173.43 [456]~E(x4561,x4562)+E(f353(x4563,x4564,x4565,x4561),f353(x4563,x4564,x4565,x4562))
% 173.53/173.43 [457]~E(x4571,x4572)+E(f785(x4571),f785(x4572))
% 173.53/173.43 [458]~E(x4581,x4582)+E(f12(x4581,x4583,x4584),f12(x4582,x4583,x4584))
% 173.53/173.43 [459]~E(x4591,x4592)+E(f12(x4593,x4591,x4594),f12(x4593,x4592,x4594))
% 173.53/173.43 [460]~E(x4601,x4602)+E(f12(x4603,x4604,x4601),f12(x4603,x4604,x4602))
% 173.53/173.43 [461]~E(x4611,x4612)+E(f537(x4611,x4613,x4614),f537(x4612,x4613,x4614))
% 173.53/173.43 [462]~E(x4621,x4622)+E(f537(x4623,x4621,x4624),f537(x4623,x4622,x4624))
% 173.53/173.43 [463]~E(x4631,x4632)+E(f537(x4633,x4634,x4631),f537(x4633,x4634,x4632))
% 173.53/173.43 [464]~E(x4641,x4642)+E(f396(x4641,x4643,x4644,x4645),f396(x4642,x4643,x4644,x4645))
% 173.53/173.43 [465]~E(x4651,x4652)+E(f396(x4653,x4651,x4654,x4655),f396(x4653,x4652,x4654,x4655))
% 173.53/173.43 [466]~E(x4661,x4662)+E(f396(x4663,x4664,x4661,x4665),f396(x4663,x4664,x4662,x4665))
% 173.53/173.43 [467]~E(x4671,x4672)+E(f396(x4673,x4674,x4675,x4671),f396(x4673,x4674,x4675,x4672))
% 173.53/173.43 [468]~E(x4681,x4682)+E(f299(x4681,x4683,x4684,x4685,x4686),f299(x4682,x4683,x4684,x4685,x4686))
% 173.53/173.43 [469]~E(x4691,x4692)+E(f299(x4693,x4691,x4694,x4695,x4696),f299(x4693,x4692,x4694,x4695,x4696))
% 173.53/173.43 [470]~E(x4701,x4702)+E(f299(x4703,x4704,x4701,x4705,x4706),f299(x4703,x4704,x4702,x4705,x4706))
% 173.53/173.43 [471]~E(x4711,x4712)+E(f299(x4713,x4714,x4715,x4711,x4716),f299(x4713,x4714,x4715,x4712,x4716))
% 173.53/173.43 [472]~E(x4721,x4722)+E(f299(x4723,x4724,x4725,x4726,x4721),f299(x4723,x4724,x4725,x4726,x4722))
% 173.53/173.43 [473]~E(x4731,x4732)+E(f209(x4731,x4733,x4734,x4735),f209(x4732,x4733,x4734,x4735))
% 173.53/173.43 [474]~E(x4741,x4742)+E(f209(x4743,x4741,x4744,x4745),f209(x4743,x4742,x4744,x4745))
% 173.53/173.43 [475]~E(x4751,x4752)+E(f209(x4753,x4754,x4751,x4755),f209(x4753,x4754,x4752,x4755))
% 173.53/173.43 [476]~E(x4761,x4762)+E(f209(x4763,x4764,x4765,x4761),f209(x4763,x4764,x4765,x4762))
% 173.53/173.43 [477]~E(x4771,x4772)+E(f386(x4771,x4773,x4774,x4775,x4776),f386(x4772,x4773,x4774,x4775,x4776))
% 173.53/173.43 [478]~E(x4781,x4782)+E(f386(x4783,x4781,x4784,x4785,x4786),f386(x4783,x4782,x4784,x4785,x4786))
% 173.53/173.43 [479]~E(x4791,x4792)+E(f386(x4793,x4794,x4791,x4795,x4796),f386(x4793,x4794,x4792,x4795,x4796))
% 173.53/173.43 [480]~E(x4801,x4802)+E(f386(x4803,x4804,x4805,x4801,x4806),f386(x4803,x4804,x4805,x4802,x4806))
% 173.53/173.43 [481]~E(x4811,x4812)+E(f386(x4813,x4814,x4815,x4816,x4811),f386(x4813,x4814,x4815,x4816,x4812))
% 173.53/173.43 [482]~E(x4821,x4822)+E(f694(x4821,x4823,x4824,x4825,x4826),f694(x4822,x4823,x4824,x4825,x4826))
% 173.53/173.43 [483]~E(x4831,x4832)+E(f694(x4833,x4831,x4834,x4835,x4836),f694(x4833,x4832,x4834,x4835,x4836))
% 173.53/173.43 [484]~E(x4841,x4842)+E(f694(x4843,x4844,x4841,x4845,x4846),f694(x4843,x4844,x4842,x4845,x4846))
% 173.53/173.43 [485]~E(x4851,x4852)+E(f694(x4853,x4854,x4855,x4851,x4856),f694(x4853,x4854,x4855,x4852,x4856))
% 173.53/173.43 [486]~E(x4861,x4862)+E(f694(x4863,x4864,x4865,x4866,x4861),f694(x4863,x4864,x4865,x4866,x4862))
% 173.53/173.43 [487]~E(x4871,x4872)+E(f95(x4871,x4873),f95(x4872,x4873))
% 173.53/173.43 [488]~E(x4881,x4882)+E(f95(x4883,x4881),f95(x4883,x4882))
% 173.53/173.43 [489]~E(x4891,x4892)+E(f701(x4891,x4893),f701(x4892,x4893))
% 173.53/173.43 [490]~E(x4901,x4902)+E(f701(x4903,x4901),f701(x4903,x4902))
% 173.53/173.43 [491]~E(x4911,x4912)+E(f638(x4911,x4913,x4914,x4915),f638(x4912,x4913,x4914,x4915))
% 173.53/173.43 [492]~E(x4921,x4922)+E(f638(x4923,x4921,x4924,x4925),f638(x4923,x4922,x4924,x4925))
% 173.53/173.43 [493]~E(x4931,x4932)+E(f638(x4933,x4934,x4931,x4935),f638(x4933,x4934,x4932,x4935))
% 173.53/173.43 [494]~E(x4941,x4942)+E(f638(x4943,x4944,x4945,x4941),f638(x4943,x4944,x4945,x4942))
% 173.53/173.43 [495]~E(x4951,x4952)+E(f156(x4951,x4953),f156(x4952,x4953))
% 173.53/173.43 [496]~E(x4961,x4962)+E(f156(x4963,x4961),f156(x4963,x4962))
% 173.53/173.43 [497]~E(x4971,x4972)+E(f256(x4971,x4973),f256(x4972,x4973))
% 173.53/173.43 [498]~E(x4981,x4982)+E(f256(x4983,x4981),f256(x4983,x4982))
% 173.53/173.43 [499]~E(x4991,x4992)+E(f551(x4991,x4993,x4994,x4995,x4996,x4997),f551(x4992,x4993,x4994,x4995,x4996,x4997))
% 173.53/173.43 [500]~E(x5001,x5002)+E(f551(x5003,x5001,x5004,x5005,x5006,x5007),f551(x5003,x5002,x5004,x5005,x5006,x5007))
% 173.53/173.43 [501]~E(x5011,x5012)+E(f551(x5013,x5014,x5011,x5015,x5016,x5017),f551(x5013,x5014,x5012,x5015,x5016,x5017))
% 173.53/173.43 [502]~E(x5021,x5022)+E(f551(x5023,x5024,x5025,x5021,x5026,x5027),f551(x5023,x5024,x5025,x5022,x5026,x5027))
% 173.53/173.43 [503]~E(x5031,x5032)+E(f551(x5033,x5034,x5035,x5036,x5031,x5037),f551(x5033,x5034,x5035,x5036,x5032,x5037))
% 173.53/173.43 [504]~E(x5041,x5042)+E(f551(x5043,x5044,x5045,x5046,x5047,x5041),f551(x5043,x5044,x5045,x5046,x5047,x5042))
% 173.53/173.43 [505]~E(x5051,x5052)+E(f558(x5051,x5053,x5054,x5055),f558(x5052,x5053,x5054,x5055))
% 173.53/173.43 [506]~E(x5061,x5062)+E(f558(x5063,x5061,x5064,x5065),f558(x5063,x5062,x5064,x5065))
% 173.53/173.43 [507]~E(x5071,x5072)+E(f558(x5073,x5074,x5071,x5075),f558(x5073,x5074,x5072,x5075))
% 173.53/173.43 [508]~E(x5081,x5082)+E(f558(x5083,x5084,x5085,x5081),f558(x5083,x5084,x5085,x5082))
% 173.53/173.43 [509]~E(x5091,x5092)+E(f155(x5091,x5093),f155(x5092,x5093))
% 173.53/173.43 [510]~E(x5101,x5102)+E(f155(x5103,x5101),f155(x5103,x5102))
% 173.53/173.43 [511]~E(x5111,x5112)+E(f146(x5111,x5113,x5114,x5115,x5116),f146(x5112,x5113,x5114,x5115,x5116))
% 173.53/173.43 [512]~E(x5121,x5122)+E(f146(x5123,x5121,x5124,x5125,x5126),f146(x5123,x5122,x5124,x5125,x5126))
% 173.53/173.43 [513]~E(x5131,x5132)+E(f146(x5133,x5134,x5131,x5135,x5136),f146(x5133,x5134,x5132,x5135,x5136))
% 173.53/173.43 [514]~E(x5141,x5142)+E(f146(x5143,x5144,x5145,x5141,x5146),f146(x5143,x5144,x5145,x5142,x5146))
% 173.53/173.43 [515]~E(x5151,x5152)+E(f146(x5153,x5154,x5155,x5156,x5151),f146(x5153,x5154,x5155,x5156,x5152))
% 173.53/173.43 [516]~E(x5161,x5162)+E(f793(x5161,x5163,x5164),f793(x5162,x5163,x5164))
% 173.53/173.43 [517]~E(x5171,x5172)+E(f793(x5173,x5171,x5174),f793(x5173,x5172,x5174))
% 173.53/173.43 [518]~E(x5181,x5182)+E(f793(x5183,x5184,x5181),f793(x5183,x5184,x5182))
% 173.53/173.43 [519]~E(x5191,x5192)+E(f10(x5191,x5193),f10(x5192,x5193))
% 173.53/173.43 [520]~E(x5201,x5202)+E(f10(x5203,x5201),f10(x5203,x5202))
% 173.53/173.43 [521]~E(x5211,x5212)+E(f180(x5211,x5213,x5214,x5215),f180(x5212,x5213,x5214,x5215))
% 173.53/173.43 [522]~E(x5221,x5222)+E(f180(x5223,x5221,x5224,x5225),f180(x5223,x5222,x5224,x5225))
% 173.53/173.43 [523]~E(x5231,x5232)+E(f180(x5233,x5234,x5231,x5235),f180(x5233,x5234,x5232,x5235))
% 173.53/173.43 [524]~E(x5241,x5242)+E(f180(x5243,x5244,x5245,x5241),f180(x5243,x5244,x5245,x5242))
% 173.53/173.43 [525]~E(x5251,x5252)+E(f476(x5251,x5253),f476(x5252,x5253))
% 173.53/173.43 [526]~E(x5261,x5262)+E(f476(x5263,x5261),f476(x5263,x5262))
% 173.53/173.43 [527]~E(x5271,x5272)+E(f490(x5271,x5273,x5274,x5275),f490(x5272,x5273,x5274,x5275))
% 173.53/173.43 [528]~E(x5281,x5282)+E(f490(x5283,x5281,x5284,x5285),f490(x5283,x5282,x5284,x5285))
% 173.53/173.43 [529]~E(x5291,x5292)+E(f490(x5293,x5294,x5291,x5295),f490(x5293,x5294,x5292,x5295))
% 173.53/173.43 [530]~E(x5301,x5302)+E(f490(x5303,x5304,x5305,x5301),f490(x5303,x5304,x5305,x5302))
% 173.53/173.43 [531]~E(x5311,x5312)+E(f812(x5311,x5313),f812(x5312,x5313))
% 173.53/173.43 [532]~E(x5321,x5322)+E(f812(x5323,x5321),f812(x5323,x5322))
% 173.53/173.43 [533]~E(x5331,x5332)+E(f286(x5331),f286(x5332))
% 173.53/173.43 [534]~E(x5341,x5342)+E(f145(x5341,x5343,x5344),f145(x5342,x5343,x5344))
% 173.53/173.43 [535]~E(x5351,x5352)+E(f145(x5353,x5351,x5354),f145(x5353,x5352,x5354))
% 173.53/173.43 [536]~E(x5361,x5362)+E(f145(x5363,x5364,x5361),f145(x5363,x5364,x5362))
% 173.53/173.43 [537]~E(x5371,x5372)+E(f318(x5371),f318(x5372))
% 173.53/173.43 [538]~E(x5381,x5382)+E(f626(x5381,x5383,x5384,x5385),f626(x5382,x5383,x5384,x5385))
% 173.53/173.43 [539]~E(x5391,x5392)+E(f626(x5393,x5391,x5394,x5395),f626(x5393,x5392,x5394,x5395))
% 173.53/173.43 [540]~E(x5401,x5402)+E(f626(x5403,x5404,x5401,x5405),f626(x5403,x5404,x5402,x5405))
% 173.53/173.43 [541]~E(x5411,x5412)+E(f626(x5413,x5414,x5415,x5411),f626(x5413,x5414,x5415,x5412))
% 173.53/173.43 [542]~E(x5421,x5422)+E(f609(x5421,x5423,x5424,x5425),f609(x5422,x5423,x5424,x5425))
% 173.53/173.43 [543]~E(x5431,x5432)+E(f609(x5433,x5431,x5434,x5435),f609(x5433,x5432,x5434,x5435))
% 173.53/173.43 [544]~E(x5441,x5442)+E(f609(x5443,x5444,x5441,x5445),f609(x5443,x5444,x5442,x5445))
% 173.53/173.43 [545]~E(x5451,x5452)+E(f609(x5453,x5454,x5455,x5451),f609(x5453,x5454,x5455,x5452))
% 173.53/173.43 [546]~E(x5461,x5462)+E(f320(x5461),f320(x5462))
% 173.53/173.43 [547]~E(x5471,x5472)+E(f592(x5471,x5473,x5474,x5475,x5476),f592(x5472,x5473,x5474,x5475,x5476))
% 173.53/173.43 [548]~E(x5481,x5482)+E(f592(x5483,x5481,x5484,x5485,x5486),f592(x5483,x5482,x5484,x5485,x5486))
% 173.53/173.43 [549]~E(x5491,x5492)+E(f592(x5493,x5494,x5491,x5495,x5496),f592(x5493,x5494,x5492,x5495,x5496))
% 173.53/173.43 [550]~E(x5501,x5502)+E(f592(x5503,x5504,x5505,x5501,x5506),f592(x5503,x5504,x5505,x5502,x5506))
% 173.53/173.43 [551]~E(x5511,x5512)+E(f592(x5513,x5514,x5515,x5516,x5511),f592(x5513,x5514,x5515,x5516,x5512))
% 173.53/173.43 [552]~E(x5521,x5522)+E(f234(x5521),f234(x5522))
% 173.53/173.43 [553]~E(x5531,x5532)+E(f779(x5531,x5533,x5534),f779(x5532,x5533,x5534))
% 173.53/173.43 [554]~E(x5541,x5542)+E(f779(x5543,x5541,x5544),f779(x5543,x5542,x5544))
% 173.53/173.43 [555]~E(x5551,x5552)+E(f779(x5553,x5554,x5551),f779(x5553,x5554,x5552))
% 173.53/173.43 [556]~E(x5561,x5562)+E(f676(x5561,x5563,x5564),f676(x5562,x5563,x5564))
% 173.53/173.43 [557]~E(x5571,x5572)+E(f676(x5573,x5571,x5574),f676(x5573,x5572,x5574))
% 173.53/173.43 [558]~E(x5581,x5582)+E(f676(x5583,x5584,x5581),f676(x5583,x5584,x5582))
% 173.53/173.43 [559]~E(x5591,x5592)+E(f627(x5591,x5593,x5594,x5595),f627(x5592,x5593,x5594,x5595))
% 173.53/173.43 [560]~E(x5601,x5602)+E(f627(x5603,x5601,x5604,x5605),f627(x5603,x5602,x5604,x5605))
% 173.53/173.43 [561]~E(x5611,x5612)+E(f627(x5613,x5614,x5611,x5615),f627(x5613,x5614,x5612,x5615))
% 173.53/173.43 [562]~E(x5621,x5622)+E(f627(x5623,x5624,x5625,x5621),f627(x5623,x5624,x5625,x5622))
% 173.53/173.43 [563]~E(x5631,x5632)+E(f585(x5631,x5633,x5634,x5635,x5636),f585(x5632,x5633,x5634,x5635,x5636))
% 173.53/173.43 [564]~E(x5641,x5642)+E(f585(x5643,x5641,x5644,x5645,x5646),f585(x5643,x5642,x5644,x5645,x5646))
% 173.53/173.43 [565]~E(x5651,x5652)+E(f585(x5653,x5654,x5651,x5655,x5656),f585(x5653,x5654,x5652,x5655,x5656))
% 173.53/173.43 [566]~E(x5661,x5662)+E(f585(x5663,x5664,x5665,x5661,x5666),f585(x5663,x5664,x5665,x5662,x5666))
% 173.53/173.43 [567]~E(x5671,x5672)+E(f585(x5673,x5674,x5675,x5676,x5671),f585(x5673,x5674,x5675,x5676,x5672))
% 173.53/173.43 [568]~E(x5681,x5682)+E(f279(x5681),f279(x5682))
% 173.53/173.43 [569]~E(x5691,x5692)+E(f221(x5691,x5693,x5694,x5695),f221(x5692,x5693,x5694,x5695))
% 173.53/173.43 [570]~E(x5701,x5702)+E(f221(x5703,x5701,x5704,x5705),f221(x5703,x5702,x5704,x5705))
% 173.53/173.43 [571]~E(x5711,x5712)+E(f221(x5713,x5714,x5711,x5715),f221(x5713,x5714,x5712,x5715))
% 173.53/173.43 [572]~E(x5721,x5722)+E(f221(x5723,x5724,x5725,x5721),f221(x5723,x5724,x5725,x5722))
% 173.53/173.43 [573]~E(x5731,x5732)+E(f187(x5731),f187(x5732))
% 173.53/173.43 [574]~E(x5741,x5742)+E(f502(x5741,x5743,x5744,x5745,x5746,x5747),f502(x5742,x5743,x5744,x5745,x5746,x5747))
% 173.53/173.43 [575]~E(x5751,x5752)+E(f502(x5753,x5751,x5754,x5755,x5756,x5757),f502(x5753,x5752,x5754,x5755,x5756,x5757))
% 173.53/173.43 [576]~E(x5761,x5762)+E(f502(x5763,x5764,x5761,x5765,x5766,x5767),f502(x5763,x5764,x5762,x5765,x5766,x5767))
% 173.53/173.43 [577]~E(x5771,x5772)+E(f502(x5773,x5774,x5775,x5771,x5776,x5777),f502(x5773,x5774,x5775,x5772,x5776,x5777))
% 173.53/173.43 [578]~E(x5781,x5782)+E(f502(x5783,x5784,x5785,x5786,x5781,x5787),f502(x5783,x5784,x5785,x5786,x5782,x5787))
% 173.53/173.43 [579]~E(x5791,x5792)+E(f502(x5793,x5794,x5795,x5796,x5797,x5791),f502(x5793,x5794,x5795,x5796,x5797,x5792))
% 173.53/173.43 [580]~E(x5801,x5802)+E(f86(x5801,x5803,x5804,x5805),f86(x5802,x5803,x5804,x5805))
% 173.53/173.43 [581]~E(x5811,x5812)+E(f86(x5813,x5811,x5814,x5815),f86(x5813,x5812,x5814,x5815))
% 173.53/173.43 [582]~E(x5821,x5822)+E(f86(x5823,x5824,x5821,x5825),f86(x5823,x5824,x5822,x5825))
% 173.53/173.43 [583]~E(x5831,x5832)+E(f86(x5833,x5834,x5835,x5831),f86(x5833,x5834,x5835,x5832))
% 173.53/173.43 [584]~E(x5841,x5842)+E(f357(x5841,x5843,x5844),f357(x5842,x5843,x5844))
% 173.53/173.43 [585]~E(x5851,x5852)+E(f357(x5853,x5851,x5854),f357(x5853,x5852,x5854))
% 173.53/173.43 [586]~E(x5861,x5862)+E(f357(x5863,x5864,x5861),f357(x5863,x5864,x5862))
% 173.53/173.43 [587]~E(x5871,x5872)+E(f777(x5871,x5873,x5874,x5875,x5876),f777(x5872,x5873,x5874,x5875,x5876))
% 173.53/173.43 [588]~E(x5881,x5882)+E(f777(x5883,x5881,x5884,x5885,x5886),f777(x5883,x5882,x5884,x5885,x5886))
% 173.53/173.43 [589]~E(x5891,x5892)+E(f777(x5893,x5894,x5891,x5895,x5896),f777(x5893,x5894,x5892,x5895,x5896))
% 173.53/173.43 [590]~E(x5901,x5902)+E(f777(x5903,x5904,x5905,x5901,x5906),f777(x5903,x5904,x5905,x5902,x5906))
% 173.53/173.43 [591]~E(x5911,x5912)+E(f777(x5913,x5914,x5915,x5916,x5911),f777(x5913,x5914,x5915,x5916,x5912))
% 173.53/173.43 [592]~E(x5921,x5922)+E(f179(x5921,x5923,x5924),f179(x5922,x5923,x5924))
% 173.53/173.43 [593]~E(x5931,x5932)+E(f179(x5933,x5931,x5934),f179(x5933,x5932,x5934))
% 173.53/173.43 [594]~E(x5941,x5942)+E(f179(x5943,x5944,x5941),f179(x5943,x5944,x5942))
% 173.53/173.43 [595]~E(x5951,x5952)+E(f285(x5951,x5953,x5954),f285(x5952,x5953,x5954))
% 173.53/173.43 [596]~E(x5961,x5962)+E(f285(x5963,x5961,x5964),f285(x5963,x5962,x5964))
% 173.53/173.43 [597]~E(x5971,x5972)+E(f285(x5973,x5974,x5971),f285(x5973,x5974,x5972))
% 173.53/173.43 [598]~E(x5981,x5982)+E(f67(x5981),f67(x5982))
% 173.53/173.43 [599]~E(x5991,x5992)+E(f31(x5991,x5993,x5994),f31(x5992,x5993,x5994))
% 173.53/173.43 [600]~E(x6001,x6002)+E(f31(x6003,x6001,x6004),f31(x6003,x6002,x6004))
% 173.53/173.43 [601]~E(x6011,x6012)+E(f31(x6013,x6014,x6011),f31(x6013,x6014,x6012))
% 173.53/173.43 [602]~E(x6021,x6022)+E(f740(x6021,x6023,x6024,x6025),f740(x6022,x6023,x6024,x6025))
% 173.53/173.43 [603]~E(x6031,x6032)+E(f740(x6033,x6031,x6034,x6035),f740(x6033,x6032,x6034,x6035))
% 173.53/173.43 [604]~E(x6041,x6042)+E(f740(x6043,x6044,x6041,x6045),f740(x6043,x6044,x6042,x6045))
% 173.53/173.43 [605]~E(x6051,x6052)+E(f740(x6053,x6054,x6055,x6051),f740(x6053,x6054,x6055,x6052))
% 173.53/173.43 [606]~E(x6061,x6062)+E(f254(x6061,x6063),f254(x6062,x6063))
% 173.53/173.43 [607]~E(x6071,x6072)+E(f254(x6073,x6071),f254(x6073,x6072))
% 173.53/173.43 [608]~E(x6081,x6082)+E(f586(x6081,x6083,x6084),f586(x6082,x6083,x6084))
% 173.53/173.43 [609]~E(x6091,x6092)+E(f586(x6093,x6091,x6094),f586(x6093,x6092,x6094))
% 173.53/173.43 [610]~E(x6101,x6102)+E(f586(x6103,x6104,x6101),f586(x6103,x6104,x6102))
% 173.53/173.43 [611]~E(x6111,x6112)+E(f755(x6111,x6113,x6114),f755(x6112,x6113,x6114))
% 173.53/173.43 [612]~E(x6121,x6122)+E(f755(x6123,x6121,x6124),f755(x6123,x6122,x6124))
% 173.53/173.43 [613]~E(x6131,x6132)+E(f755(x6133,x6134,x6131),f755(x6133,x6134,x6132))
% 173.53/173.43 [614]~E(x6141,x6142)+E(f675(x6141,x6143,x6144),f675(x6142,x6143,x6144))
% 173.53/173.43 [615]~E(x6151,x6152)+E(f675(x6153,x6151,x6154),f675(x6153,x6152,x6154))
% 173.53/173.43 [616]~E(x6161,x6162)+E(f675(x6163,x6164,x6161),f675(x6163,x6164,x6162))
% 173.53/173.43 [617]~E(x6171,x6172)+E(f765(x6171,x6173,x6174,x6175,x6176),f765(x6172,x6173,x6174,x6175,x6176))
% 173.53/173.43 [618]~E(x6181,x6182)+E(f765(x6183,x6181,x6184,x6185,x6186),f765(x6183,x6182,x6184,x6185,x6186))
% 173.53/173.43 [619]~E(x6191,x6192)+E(f765(x6193,x6194,x6191,x6195,x6196),f765(x6193,x6194,x6192,x6195,x6196))
% 173.53/173.43 [620]~E(x6201,x6202)+E(f765(x6203,x6204,x6205,x6201,x6206),f765(x6203,x6204,x6205,x6202,x6206))
% 173.53/173.43 [621]~E(x6211,x6212)+E(f765(x6213,x6214,x6215,x6216,x6211),f765(x6213,x6214,x6215,x6216,x6212))
% 173.53/173.43 [622]~E(x6221,x6222)+E(f183(x6221,x6223,x6224,x6225),f183(x6222,x6223,x6224,x6225))
% 173.53/173.43 [623]~E(x6231,x6232)+E(f183(x6233,x6231,x6234,x6235),f183(x6233,x6232,x6234,x6235))
% 173.53/173.43 [624]~E(x6241,x6242)+E(f183(x6243,x6244,x6241,x6245),f183(x6243,x6244,x6242,x6245))
% 173.53/173.43 [625]~E(x6251,x6252)+E(f183(x6253,x6254,x6255,x6251),f183(x6253,x6254,x6255,x6252))
% 173.53/173.43 [626]~E(x6261,x6262)+E(f634(x6261,x6263,x6264,x6265),f634(x6262,x6263,x6264,x6265))
% 173.53/173.43 [627]~E(x6271,x6272)+E(f634(x6273,x6271,x6274,x6275),f634(x6273,x6272,x6274,x6275))
% 173.53/173.43 [628]~E(x6281,x6282)+E(f634(x6283,x6284,x6281,x6285),f634(x6283,x6284,x6282,x6285))
% 173.53/173.43 [629]~E(x6291,x6292)+E(f634(x6293,x6294,x6295,x6291),f634(x6293,x6294,x6295,x6292))
% 173.53/173.43 [630]~E(x6301,x6302)+E(f781(x6301,x6303,x6304),f781(x6302,x6303,x6304))
% 173.53/173.43 [631]~E(x6311,x6312)+E(f781(x6313,x6311,x6314),f781(x6313,x6312,x6314))
% 173.53/173.43 [632]~E(x6321,x6322)+E(f781(x6323,x6324,x6321),f781(x6323,x6324,x6322))
% 173.53/173.43 [633]~E(x6331,x6332)+E(f123(x6331),f123(x6332))
% 173.53/173.43 [634]~E(x6341,x6342)+E(f15(x6341,x6343),f15(x6342,x6343))
% 173.53/173.43 [635]~E(x6351,x6352)+E(f15(x6353,x6351),f15(x6353,x6352))
% 173.53/173.43 [636]~E(x6361,x6362)+E(f747(x6361,x6363,x6364),f747(x6362,x6363,x6364))
% 173.53/173.43 [637]~E(x6371,x6372)+E(f747(x6373,x6371,x6374),f747(x6373,x6372,x6374))
% 173.53/173.43 [638]~E(x6381,x6382)+E(f747(x6383,x6384,x6381),f747(x6383,x6384,x6382))
% 173.53/173.43 [639]~E(x6391,x6392)+E(f218(x6391,x6393),f218(x6392,x6393))
% 173.53/173.43 [640]~E(x6401,x6402)+E(f218(x6403,x6401),f218(x6403,x6402))
% 173.53/173.43 [641]~E(x6411,x6412)+E(f492(x6411,x6413,x6414),f492(x6412,x6413,x6414))
% 173.53/173.43 [642]~E(x6421,x6422)+E(f492(x6423,x6421,x6424),f492(x6423,x6422,x6424))
% 173.53/173.43 [643]~E(x6431,x6432)+E(f492(x6433,x6434,x6431),f492(x6433,x6434,x6432))
% 173.53/173.43 [644]~E(x6441,x6442)+E(f223(x6441),f223(x6442))
% 173.53/173.43 [645]~E(x6451,x6452)+E(f281(x6451),f281(x6452))
% 173.53/173.43 [646]~E(x6461,x6462)+E(f813(x6461,x6463,x6464),f813(x6462,x6463,x6464))
% 173.53/173.43 [647]~E(x6471,x6472)+E(f813(x6473,x6471,x6474),f813(x6473,x6472,x6474))
% 173.53/173.43 [648]~E(x6481,x6482)+E(f813(x6483,x6484,x6481),f813(x6483,x6484,x6482))
% 173.53/173.43 [649]~E(x6491,x6492)+E(f166(x6491,x6493,x6494),f166(x6492,x6493,x6494))
% 173.53/173.43 [650]~E(x6501,x6502)+E(f166(x6503,x6501,x6504),f166(x6503,x6502,x6504))
% 173.53/173.43 [651]~E(x6511,x6512)+E(f166(x6513,x6514,x6511),f166(x6513,x6514,x6512))
% 173.53/173.43 [652]~E(x6521,x6522)+E(f744(x6521,x6523,x6524),f744(x6522,x6523,x6524))
% 173.53/173.43 [653]~E(x6531,x6532)+E(f744(x6533,x6531,x6534),f744(x6533,x6532,x6534))
% 173.53/173.43 [654]~E(x6541,x6542)+E(f744(x6543,x6544,x6541),f744(x6543,x6544,x6542))
% 173.53/173.43 [655]~E(x6551,x6552)+E(f63(x6551,x6553,x6554),f63(x6552,x6553,x6554))
% 173.53/173.43 [656]~E(x6561,x6562)+E(f63(x6563,x6561,x6564),f63(x6563,x6562,x6564))
% 173.53/173.43 [657]~E(x6571,x6572)+E(f63(x6573,x6574,x6571),f63(x6573,x6574,x6572))
% 173.53/173.43 [658]~E(x6581,x6582)+E(f567(x6581,x6583,x6584,x6585),f567(x6582,x6583,x6584,x6585))
% 173.53/173.43 [659]~E(x6591,x6592)+E(f567(x6593,x6591,x6594,x6595),f567(x6593,x6592,x6594,x6595))
% 173.53/173.43 [660]~E(x6601,x6602)+E(f567(x6603,x6604,x6601,x6605),f567(x6603,x6604,x6602,x6605))
% 173.53/173.43 [661]~E(x6611,x6612)+E(f567(x6613,x6614,x6615,x6611),f567(x6613,x6614,x6615,x6612))
% 173.53/173.43 [662]~E(x6621,x6622)+E(f789(x6621,x6623,x6624),f789(x6622,x6623,x6624))
% 173.53/173.43 [663]~E(x6631,x6632)+E(f789(x6633,x6631,x6634),f789(x6633,x6632,x6634))
% 173.53/173.43 [664]~E(x6641,x6642)+E(f789(x6643,x6644,x6641),f789(x6643,x6644,x6642))
% 173.53/173.43 [665]~E(x6651,x6652)+E(f673(x6651,x6653,x6654,x6655,x6656,x6657,x6658,x6659),f673(x6652,x6653,x6654,x6655,x6656,x6657,x6658,x6659))
% 173.53/173.43 [666]~E(x6661,x6662)+E(f673(x6663,x6661,x6664,x6665,x6666,x6667,x6668,x6669),f673(x6663,x6662,x6664,x6665,x6666,x6667,x6668,x6669))
% 173.53/173.43 [667]~E(x6671,x6672)+E(f673(x6673,x6674,x6671,x6675,x6676,x6677,x6678,x6679),f673(x6673,x6674,x6672,x6675,x6676,x6677,x6678,x6679))
% 173.53/173.43 [668]~E(x6681,x6682)+E(f673(x6683,x6684,x6685,x6681,x6686,x6687,x6688,x6689),f673(x6683,x6684,x6685,x6682,x6686,x6687,x6688,x6689))
% 173.53/173.43 [669]~E(x6691,x6692)+E(f673(x6693,x6694,x6695,x6696,x6691,x6697,x6698,x6699),f673(x6693,x6694,x6695,x6696,x6692,x6697,x6698,x6699))
% 173.53/173.43 [670]~E(x6701,x6702)+E(f673(x6703,x6704,x6705,x6706,x6707,x6701,x6708,x6709),f673(x6703,x6704,x6705,x6706,x6707,x6702,x6708,x6709))
% 173.53/173.43 [671]~E(x6711,x6712)+E(f673(x6713,x6714,x6715,x6716,x6717,x6718,x6711,x6719),f673(x6713,x6714,x6715,x6716,x6717,x6718,x6712,x6719))
% 173.53/173.43 [672]~E(x6721,x6722)+E(f673(x6723,x6724,x6725,x6726,x6727,x6728,x6729,x6721),f673(x6723,x6724,x6725,x6726,x6727,x6728,x6729,x6722))
% 173.53/173.43 [673]~E(x6731,x6732)+E(f477(x6731,x6733,x6734,x6735,x6736),f477(x6732,x6733,x6734,x6735,x6736))
% 173.53/173.43 [674]~E(x6741,x6742)+E(f477(x6743,x6741,x6744,x6745,x6746),f477(x6743,x6742,x6744,x6745,x6746))
% 173.53/173.43 [675]~E(x6751,x6752)+E(f477(x6753,x6754,x6751,x6755,x6756),f477(x6753,x6754,x6752,x6755,x6756))
% 173.53/173.43 [676]~E(x6761,x6762)+E(f477(x6763,x6764,x6765,x6761,x6766),f477(x6763,x6764,x6765,x6762,x6766))
% 173.53/173.43 [677]~E(x6771,x6772)+E(f477(x6773,x6774,x6775,x6776,x6771),f477(x6773,x6774,x6775,x6776,x6772))
% 173.53/173.43 [678]~E(x6781,x6782)+E(f636(x6781,x6783,x6784,x6785,x6786),f636(x6782,x6783,x6784,x6785,x6786))
% 173.53/173.43 [679]~E(x6791,x6792)+E(f636(x6793,x6791,x6794,x6795,x6796),f636(x6793,x6792,x6794,x6795,x6796))
% 173.53/173.43 [680]~E(x6801,x6802)+E(f636(x6803,x6804,x6801,x6805,x6806),f636(x6803,x6804,x6802,x6805,x6806))
% 173.53/173.43 [681]~E(x6811,x6812)+E(f636(x6813,x6814,x6815,x6811,x6816),f636(x6813,x6814,x6815,x6812,x6816))
% 173.53/173.43 [682]~E(x6821,x6822)+E(f636(x6823,x6824,x6825,x6826,x6821),f636(x6823,x6824,x6825,x6826,x6822))
% 173.53/173.43 [683]~E(x6831,x6832)+E(f587(x6831,x6833,x6834),f587(x6832,x6833,x6834))
% 173.53/173.43 [684]~E(x6841,x6842)+E(f587(x6843,x6841,x6844),f587(x6843,x6842,x6844))
% 173.53/173.43 [685]~E(x6851,x6852)+E(f587(x6853,x6854,x6851),f587(x6853,x6854,x6852))
% 173.53/173.43 [686]~E(x6861,x6862)+E(f517(x6861,x6863,x6864,x6865,x6866),f517(x6862,x6863,x6864,x6865,x6866))
% 173.53/173.43 [687]~E(x6871,x6872)+E(f517(x6873,x6871,x6874,x6875,x6876),f517(x6873,x6872,x6874,x6875,x6876))
% 173.53/173.43 [688]~E(x6881,x6882)+E(f517(x6883,x6884,x6881,x6885,x6886),f517(x6883,x6884,x6882,x6885,x6886))
% 173.53/173.43 [689]~E(x6891,x6892)+E(f517(x6893,x6894,x6895,x6891,x6896),f517(x6893,x6894,x6895,x6892,x6896))
% 173.53/173.43 [690]~E(x6901,x6902)+E(f517(x6903,x6904,x6905,x6906,x6901),f517(x6903,x6904,x6905,x6906,x6902))
% 173.53/173.43 [691]~E(x6911,x6912)+E(f770(x6911,x6913,x6914,x6915,x6916),f770(x6912,x6913,x6914,x6915,x6916))
% 173.53/173.43 [692]~E(x6921,x6922)+E(f770(x6923,x6921,x6924,x6925,x6926),f770(x6923,x6922,x6924,x6925,x6926))
% 173.53/173.43 [693]~E(x6931,x6932)+E(f770(x6933,x6934,x6931,x6935,x6936),f770(x6933,x6934,x6932,x6935,x6936))
% 173.53/173.43 [694]~E(x6941,x6942)+E(f770(x6943,x6944,x6945,x6941,x6946),f770(x6943,x6944,x6945,x6942,x6946))
% 173.53/173.43 [695]~E(x6951,x6952)+E(f770(x6953,x6954,x6955,x6956,x6951),f770(x6953,x6954,x6955,x6956,x6952))
% 173.53/173.43 [696]~E(x6961,x6962)+E(f690(x6961,x6963,x6964),f690(x6962,x6963,x6964))
% 173.53/173.43 [697]~E(x6971,x6972)+E(f690(x6973,x6971,x6974),f690(x6973,x6972,x6974))
% 173.53/173.43 [698]~E(x6981,x6982)+E(f690(x6983,x6984,x6981),f690(x6983,x6984,x6982))
% 173.53/173.43 [699]~E(x6991,x6992)+E(f377(x6991,x6993),f377(x6992,x6993))
% 173.53/173.43 [700]~E(x7001,x7002)+E(f377(x7003,x7001),f377(x7003,x7002))
% 173.53/173.43 [701]~E(x7011,x7012)+E(f659(x7011,x7013,x7014),f659(x7012,x7013,x7014))
% 173.53/173.43 [702]~E(x7021,x7022)+E(f659(x7023,x7021,x7024),f659(x7023,x7022,x7024))
% 173.53/173.43 [703]~E(x7031,x7032)+E(f659(x7033,x7034,x7031),f659(x7033,x7034,x7032))
% 173.53/173.43 [704]~E(x7041,x7042)+E(f71(x7041,x7043,x7044),f71(x7042,x7043,x7044))
% 173.53/173.43 [705]~E(x7051,x7052)+E(f71(x7053,x7051,x7054),f71(x7053,x7052,x7054))
% 173.53/173.43 [706]~E(x7061,x7062)+E(f71(x7063,x7064,x7061),f71(x7063,x7064,x7062))
% 173.53/173.43 [707]~E(x7071,x7072)+E(f101(x7071,x7073,x7074),f101(x7072,x7073,x7074))
% 173.53/173.43 [708]~E(x7081,x7082)+E(f101(x7083,x7081,x7084),f101(x7083,x7082,x7084))
% 173.53/173.43 [709]~E(x7091,x7092)+E(f101(x7093,x7094,x7091),f101(x7093,x7094,x7092))
% 173.53/173.43 [710]~E(x7101,x7102)+E(f55(x7101,x7103),f55(x7102,x7103))
% 173.53/173.43 [711]~E(x7111,x7112)+E(f55(x7113,x7111),f55(x7113,x7112))
% 173.53/173.43 [712]~E(x7121,x7122)+E(f359(x7121,x7123,x7124,x7125,x7126),f359(x7122,x7123,x7124,x7125,x7126))
% 173.53/173.43 [713]~E(x7131,x7132)+E(f359(x7133,x7131,x7134,x7135,x7136),f359(x7133,x7132,x7134,x7135,x7136))
% 173.53/173.43 [714]~E(x7141,x7142)+E(f359(x7143,x7144,x7141,x7145,x7146),f359(x7143,x7144,x7142,x7145,x7146))
% 173.53/173.43 [715]~E(x7151,x7152)+E(f359(x7153,x7154,x7155,x7151,x7156),f359(x7153,x7154,x7155,x7152,x7156))
% 173.53/173.43 [716]~E(x7161,x7162)+E(f359(x7163,x7164,x7165,x7166,x7161),f359(x7163,x7164,x7165,x7166,x7162))
% 173.53/173.43 [717]~E(x7171,x7172)+E(f687(x7171,x7173),f687(x7172,x7173))
% 173.53/173.43 [718]~E(x7181,x7182)+E(f687(x7183,x7181),f687(x7183,x7182))
% 173.53/173.43 [719]~E(x7191,x7192)+E(f604(x7191,x7193,x7194,x7195),f604(x7192,x7193,x7194,x7195))
% 173.53/173.43 [720]~E(x7201,x7202)+E(f604(x7203,x7201,x7204,x7205),f604(x7203,x7202,x7204,x7205))
% 173.53/173.43 [721]~E(x7211,x7212)+E(f604(x7213,x7214,x7211,x7215),f604(x7213,x7214,x7212,x7215))
% 173.53/173.43 [722]~E(x7221,x7222)+E(f604(x7223,x7224,x7225,x7221),f604(x7223,x7224,x7225,x7222))
% 173.53/173.43 [723]~E(x7231,x7232)+E(f800(x7231,x7233,x7234,x7235,x7236,x7237,x7238),f800(x7232,x7233,x7234,x7235,x7236,x7237,x7238))
% 173.53/173.43 [724]~E(x7241,x7242)+E(f800(x7243,x7241,x7244,x7245,x7246,x7247,x7248),f800(x7243,x7242,x7244,x7245,x7246,x7247,x7248))
% 173.53/173.43 [725]~E(x7251,x7252)+E(f800(x7253,x7254,x7251,x7255,x7256,x7257,x7258),f800(x7253,x7254,x7252,x7255,x7256,x7257,x7258))
% 173.53/173.43 [726]~E(x7261,x7262)+E(f800(x7263,x7264,x7265,x7261,x7266,x7267,x7268),f800(x7263,x7264,x7265,x7262,x7266,x7267,x7268))
% 173.53/173.43 [727]~E(x7271,x7272)+E(f800(x7273,x7274,x7275,x7276,x7271,x7277,x7278),f800(x7273,x7274,x7275,x7276,x7272,x7277,x7278))
% 173.53/173.43 [728]~E(x7281,x7282)+E(f800(x7283,x7284,x7285,x7286,x7287,x7281,x7288),f800(x7283,x7284,x7285,x7286,x7287,x7282,x7288))
% 173.53/173.43 [729]~E(x7291,x7292)+E(f800(x7293,x7294,x7295,x7296,x7297,x7298,x7291),f800(x7293,x7294,x7295,x7296,x7297,x7298,x7292))
% 173.53/173.43 [730]~E(x7301,x7302)+E(f73(x7301,x7303,x7304),f73(x7302,x7303,x7304))
% 173.53/173.43 [731]~E(x7311,x7312)+E(f73(x7313,x7311,x7314),f73(x7313,x7312,x7314))
% 173.53/173.43 [732]~E(x7321,x7322)+E(f73(x7323,x7324,x7321),f73(x7323,x7324,x7322))
% 173.53/173.43 [733]~E(x7331,x7332)+E(f262(x7331,x7333,x7334,x7335),f262(x7332,x7333,x7334,x7335))
% 173.53/173.43 [734]~E(x7341,x7342)+E(f262(x7343,x7341,x7344,x7345),f262(x7343,x7342,x7344,x7345))
% 173.53/173.43 [735]~E(x7351,x7352)+E(f262(x7353,x7354,x7351,x7355),f262(x7353,x7354,x7352,x7355))
% 173.53/173.43 [736]~E(x7361,x7362)+E(f262(x7363,x7364,x7365,x7361),f262(x7363,x7364,x7365,x7362))
% 173.53/173.43 [737]~E(x7371,x7372)+E(f774(x7371,x7373,x7374,x7375),f774(x7372,x7373,x7374,x7375))
% 173.53/173.43 [738]~E(x7381,x7382)+E(f774(x7383,x7381,x7384,x7385),f774(x7383,x7382,x7384,x7385))
% 173.53/173.43 [739]~E(x7391,x7392)+E(f774(x7393,x7394,x7391,x7395),f774(x7393,x7394,x7392,x7395))
% 173.53/173.43 [740]~E(x7401,x7402)+E(f774(x7403,x7404,x7405,x7401),f774(x7403,x7404,x7405,x7402))
% 173.53/173.43 [741]~E(x7411,x7412)+E(f372(x7411),f372(x7412))
% 173.53/173.43 [742]~E(x7421,x7422)+E(f714(x7421,x7423,x7424,x7425,x7426,x7427),f714(x7422,x7423,x7424,x7425,x7426,x7427))
% 173.53/173.43 [743]~E(x7431,x7432)+E(f714(x7433,x7431,x7434,x7435,x7436,x7437),f714(x7433,x7432,x7434,x7435,x7436,x7437))
% 173.53/173.43 [744]~E(x7441,x7442)+E(f714(x7443,x7444,x7441,x7445,x7446,x7447),f714(x7443,x7444,x7442,x7445,x7446,x7447))
% 173.53/173.43 [745]~E(x7451,x7452)+E(f714(x7453,x7454,x7455,x7451,x7456,x7457),f714(x7453,x7454,x7455,x7452,x7456,x7457))
% 173.53/173.43 [746]~E(x7461,x7462)+E(f714(x7463,x7464,x7465,x7466,x7461,x7467),f714(x7463,x7464,x7465,x7466,x7462,x7467))
% 173.53/173.43 [747]~E(x7471,x7472)+E(f714(x7473,x7474,x7475,x7476,x7477,x7471),f714(x7473,x7474,x7475,x7476,x7477,x7472))
% 173.53/173.43 [748]~E(x7481,x7482)+E(f612(x7481,x7483,x7484,x7485,x7486),f612(x7482,x7483,x7484,x7485,x7486))
% 173.53/173.43 [749]~E(x7491,x7492)+E(f612(x7493,x7491,x7494,x7495,x7496),f612(x7493,x7492,x7494,x7495,x7496))
% 173.53/173.43 [750]~E(x7501,x7502)+E(f612(x7503,x7504,x7501,x7505,x7506),f612(x7503,x7504,x7502,x7505,x7506))
% 173.53/173.43 [751]~E(x7511,x7512)+E(f612(x7513,x7514,x7515,x7511,x7516),f612(x7513,x7514,x7515,x7512,x7516))
% 173.53/173.43 [752]~E(x7521,x7522)+E(f612(x7523,x7524,x7525,x7526,x7521),f612(x7523,x7524,x7525,x7526,x7522))
% 173.53/173.43 [753]~E(x7531,x7532)+E(f761(x7531,x7533,x7534),f761(x7532,x7533,x7534))
% 173.53/173.43 [754]~E(x7541,x7542)+E(f761(x7543,x7541,x7544),f761(x7543,x7542,x7544))
% 173.53/173.43 [755]~E(x7551,x7552)+E(f761(x7553,x7554,x7551),f761(x7553,x7554,x7552))
% 173.53/173.43 [756]~E(x7561,x7562)+E(f391(x7561,x7563),f391(x7562,x7563))
% 173.53/173.43 [757]~E(x7571,x7572)+E(f391(x7573,x7571),f391(x7573,x7572))
% 173.53/173.43 [758]~E(x7581,x7582)+E(f324(x7581,x7583,x7584,x7585),f324(x7582,x7583,x7584,x7585))
% 173.53/173.43 [759]~E(x7591,x7592)+E(f324(x7593,x7591,x7594,x7595),f324(x7593,x7592,x7594,x7595))
% 173.53/173.43 [760]~E(x7601,x7602)+E(f324(x7603,x7604,x7601,x7605),f324(x7603,x7604,x7602,x7605))
% 173.53/173.43 [761]~E(x7611,x7612)+E(f324(x7613,x7614,x7615,x7611),f324(x7613,x7614,x7615,x7612))
% 173.53/173.43 [762]~E(x7621,x7622)+E(f771(x7621,x7623,x7624,x7625,x7626),f771(x7622,x7623,x7624,x7625,x7626))
% 173.53/173.43 [763]~E(x7631,x7632)+E(f771(x7633,x7631,x7634,x7635,x7636),f771(x7633,x7632,x7634,x7635,x7636))
% 173.53/173.43 [764]~E(x7641,x7642)+E(f771(x7643,x7644,x7641,x7645,x7646),f771(x7643,x7644,x7642,x7645,x7646))
% 173.53/173.43 [765]~E(x7651,x7652)+E(f771(x7653,x7654,x7655,x7651,x7656),f771(x7653,x7654,x7655,x7652,x7656))
% 173.53/173.43 [766]~E(x7661,x7662)+E(f771(x7663,x7664,x7665,x7666,x7661),f771(x7663,x7664,x7665,x7666,x7662))
% 173.53/173.43 [767]~E(x7671,x7672)+E(f554(x7671,x7673),f554(x7672,x7673))
% 173.53/173.43 [768]~E(x7681,x7682)+E(f554(x7683,x7681),f554(x7683,x7682))
% 173.53/173.43 [769]~E(x7691,x7692)+E(f669(x7691,x7693),f669(x7692,x7693))
% 173.53/173.43 [770]~E(x7701,x7702)+E(f669(x7703,x7701),f669(x7703,x7702))
% 173.53/173.43 [771]~E(x7711,x7712)+E(f365(x7711,x7713,x7714),f365(x7712,x7713,x7714))
% 173.53/173.43 [772]~E(x7721,x7722)+E(f365(x7723,x7721,x7724),f365(x7723,x7722,x7724))
% 173.53/173.43 [773]~E(x7731,x7732)+E(f365(x7733,x7734,x7731),f365(x7733,x7734,x7732))
% 173.53/173.43 [774]~E(x7741,x7742)+E(f695(x7741,x7743,x7744,x7745,x7746),f695(x7742,x7743,x7744,x7745,x7746))
% 173.53/173.43 [775]~E(x7751,x7752)+E(f695(x7753,x7751,x7754,x7755,x7756),f695(x7753,x7752,x7754,x7755,x7756))
% 173.53/173.43 [776]~E(x7761,x7762)+E(f695(x7763,x7764,x7761,x7765,x7766),f695(x7763,x7764,x7762,x7765,x7766))
% 173.53/173.43 [777]~E(x7771,x7772)+E(f695(x7773,x7774,x7775,x7771,x7776),f695(x7773,x7774,x7775,x7772,x7776))
% 173.53/173.43 [778]~E(x7781,x7782)+E(f695(x7783,x7784,x7785,x7786,x7781),f695(x7783,x7784,x7785,x7786,x7782))
% 173.53/173.43 [779]~E(x7791,x7792)+E(f787(x7791,x7793,x7794),f787(x7792,x7793,x7794))
% 173.53/173.43 [780]~E(x7801,x7802)+E(f787(x7803,x7801,x7804),f787(x7803,x7802,x7804))
% 173.53/173.43 [781]~E(x7811,x7812)+E(f787(x7813,x7814,x7811),f787(x7813,x7814,x7812))
% 173.53/173.43 [782]~E(x7821,x7822)+E(f352(x7821,x7823,x7824,x7825),f352(x7822,x7823,x7824,x7825))
% 173.53/173.43 [783]~E(x7831,x7832)+E(f352(x7833,x7831,x7834,x7835),f352(x7833,x7832,x7834,x7835))
% 173.53/173.43 [784]~E(x7841,x7842)+E(f352(x7843,x7844,x7841,x7845),f352(x7843,x7844,x7842,x7845))
% 173.53/173.43 [785]~E(x7851,x7852)+E(f352(x7853,x7854,x7855,x7851),f352(x7853,x7854,x7855,x7852))
% 173.53/173.43 [786]~E(x7861,x7862)+E(f387(x7861,x7863,x7864),f387(x7862,x7863,x7864))
% 173.53/173.43 [787]~E(x7871,x7872)+E(f387(x7873,x7871,x7874),f387(x7873,x7872,x7874))
% 173.53/173.43 [788]~E(x7881,x7882)+E(f387(x7883,x7884,x7881),f387(x7883,x7884,x7882))
% 173.53/173.43 [789]~E(x7891,x7892)+E(f840(x7891,x7893),f840(x7892,x7893))
% 173.53/173.43 [790]~E(x7901,x7902)+E(f840(x7903,x7901),f840(x7903,x7902))
% 173.53/173.43 [791]~E(x7911,x7912)+E(f790(x7911,x7913,x7914),f790(x7912,x7913,x7914))
% 173.53/173.43 [792]~E(x7921,x7922)+E(f790(x7923,x7921,x7924),f790(x7923,x7922,x7924))
% 173.53/173.43 [793]~E(x7931,x7932)+E(f790(x7933,x7934,x7931),f790(x7933,x7934,x7932))
% 173.53/173.43 [794]~E(x7941,x7942)+E(f369(x7941,x7943,x7944,x7945,x7946),f369(x7942,x7943,x7944,x7945,x7946))
% 173.53/173.43 [795]~E(x7951,x7952)+E(f369(x7953,x7951,x7954,x7955,x7956),f369(x7953,x7952,x7954,x7955,x7956))
% 173.53/173.43 [796]~E(x7961,x7962)+E(f369(x7963,x7964,x7961,x7965,x7966),f369(x7963,x7964,x7962,x7965,x7966))
% 173.53/173.43 [797]~E(x7971,x7972)+E(f369(x7973,x7974,x7975,x7971,x7976),f369(x7973,x7974,x7975,x7972,x7976))
% 173.53/173.43 [798]~E(x7981,x7982)+E(f369(x7983,x7984,x7985,x7986,x7981),f369(x7983,x7984,x7985,x7986,x7982))
% 173.53/173.43 [799]~E(x7991,x7992)+E(f815(x7991,x7993,x7994,x7995,x7996),f815(x7992,x7993,x7994,x7995,x7996))
% 173.53/173.43 [800]~E(x8001,x8002)+E(f815(x8003,x8001,x8004,x8005,x8006),f815(x8003,x8002,x8004,x8005,x8006))
% 173.53/173.43 [801]~E(x8011,x8012)+E(f815(x8013,x8014,x8011,x8015,x8016),f815(x8013,x8014,x8012,x8015,x8016))
% 173.53/173.43 [802]~E(x8021,x8022)+E(f815(x8023,x8024,x8025,x8021,x8026),f815(x8023,x8024,x8025,x8022,x8026))
% 173.53/173.43 [803]~E(x8031,x8032)+E(f815(x8033,x8034,x8035,x8036,x8031),f815(x8033,x8034,x8035,x8036,x8032))
% 173.53/173.43 [804]~E(x8041,x8042)+E(f825(x8041,x8043,x8044,x8045,x8046),f825(x8042,x8043,x8044,x8045,x8046))
% 173.53/173.43 [805]~E(x8051,x8052)+E(f825(x8053,x8051,x8054,x8055,x8056),f825(x8053,x8052,x8054,x8055,x8056))
% 173.53/173.43 [806]~E(x8061,x8062)+E(f825(x8063,x8064,x8061,x8065,x8066),f825(x8063,x8064,x8062,x8065,x8066))
% 173.53/173.43 [807]~E(x8071,x8072)+E(f825(x8073,x8074,x8075,x8071,x8076),f825(x8073,x8074,x8075,x8072,x8076))
% 173.53/173.43 [808]~E(x8081,x8082)+E(f825(x8083,x8084,x8085,x8086,x8081),f825(x8083,x8084,x8085,x8086,x8082))
% 173.53/173.43 [809]~E(x8091,x8092)+E(f181(x8091,x8093,x8094),f181(x8092,x8093,x8094))
% 173.53/173.43 [810]~E(x8101,x8102)+E(f181(x8103,x8101,x8104),f181(x8103,x8102,x8104))
% 173.53/173.43 [811]~E(x8111,x8112)+E(f181(x8113,x8114,x8111),f181(x8113,x8114,x8112))
% 173.53/173.43 [812]~E(x8121,x8122)+E(f776(x8121,x8123,x8124,x8125,x8126),f776(x8122,x8123,x8124,x8125,x8126))
% 173.53/173.43 [813]~E(x8131,x8132)+E(f776(x8133,x8131,x8134,x8135,x8136),f776(x8133,x8132,x8134,x8135,x8136))
% 173.53/173.43 [814]~E(x8141,x8142)+E(f776(x8143,x8144,x8141,x8145,x8146),f776(x8143,x8144,x8142,x8145,x8146))
% 173.53/173.43 [815]~E(x8151,x8152)+E(f776(x8153,x8154,x8155,x8151,x8156),f776(x8153,x8154,x8155,x8152,x8156))
% 173.53/173.43 [816]~E(x8161,x8162)+E(f776(x8163,x8164,x8165,x8166,x8161),f776(x8163,x8164,x8165,x8166,x8162))
% 173.53/173.43 [817]~E(x8171,x8172)+E(f140(x8171,x8173),f140(x8172,x8173))
% 173.53/173.43 [818]~E(x8181,x8182)+E(f140(x8183,x8181),f140(x8183,x8182))
% 173.53/173.43 [819]~E(x8191,x8192)+E(f804(x8191,x8193,x8194,x8195),f804(x8192,x8193,x8194,x8195))
% 173.53/173.43 [820]~E(x8201,x8202)+E(f804(x8203,x8201,x8204,x8205),f804(x8203,x8202,x8204,x8205))
% 173.53/173.43 [821]~E(x8211,x8212)+E(f804(x8213,x8214,x8211,x8215),f804(x8213,x8214,x8212,x8215))
% 173.53/173.43 [822]~E(x8221,x8222)+E(f804(x8223,x8224,x8225,x8221),f804(x8223,x8224,x8225,x8222))
% 173.53/173.43 [823]~E(x8231,x8232)+E(f688(x8231,x8233),f688(x8232,x8233))
% 173.53/173.43 [824]~E(x8241,x8242)+E(f688(x8243,x8241),f688(x8243,x8242))
% 173.53/173.43 [825]~E(x8251,x8252)+E(f613(x8251,x8253,x8254),f613(x8252,x8253,x8254))
% 173.53/173.43 [826]~E(x8261,x8262)+E(f613(x8263,x8261,x8264),f613(x8263,x8262,x8264))
% 173.53/173.43 [827]~E(x8271,x8272)+E(f613(x8273,x8274,x8271),f613(x8273,x8274,x8272))
% 173.53/173.43 [828]~E(x8281,x8282)+E(f97(x8281),f97(x8282))
% 173.53/173.43 [829]~E(x8291,x8292)+E(f419(x8291,x8293,x8294),f419(x8292,x8293,x8294))
% 173.53/173.43 [830]~E(x8301,x8302)+E(f419(x8303,x8301,x8304),f419(x8303,x8302,x8304))
% 173.53/173.43 [831]~E(x8311,x8312)+E(f419(x8313,x8314,x8311),f419(x8313,x8314,x8312))
% 173.53/173.43 [832]~E(x8321,x8322)+E(f680(x8321,x8323,x8324),f680(x8322,x8323,x8324))
% 173.53/173.43 [833]~E(x8331,x8332)+E(f680(x8333,x8331,x8334),f680(x8333,x8332,x8334))
% 173.53/173.43 [834]~E(x8341,x8342)+E(f680(x8343,x8344,x8341),f680(x8343,x8344,x8342))
% 173.53/173.43 [835]~E(x8351,x8352)+E(f584(x8351,x8353,x8354,x8355),f584(x8352,x8353,x8354,x8355))
% 173.53/173.43 [836]~E(x8361,x8362)+E(f584(x8363,x8361,x8364,x8365),f584(x8363,x8362,x8364,x8365))
% 173.53/173.43 [837]~E(x8371,x8372)+E(f584(x8373,x8374,x8371,x8375),f584(x8373,x8374,x8372,x8375))
% 173.53/173.43 [838]~E(x8381,x8382)+E(f584(x8383,x8384,x8385,x8381),f584(x8383,x8384,x8385,x8382))
% 173.53/173.43 [839]~E(x8391,x8392)+E(f176(x8391),f176(x8392))
% 173.53/173.43 [840]~E(x8401,x8402)+E(f17(x8401,x8403,x8404,x8405),f17(x8402,x8403,x8404,x8405))
% 173.53/173.43 [841]~E(x8411,x8412)+E(f17(x8413,x8411,x8414,x8415),f17(x8413,x8412,x8414,x8415))
% 173.53/173.43 [842]~E(x8421,x8422)+E(f17(x8423,x8424,x8421,x8425),f17(x8423,x8424,x8422,x8425))
% 173.53/173.43 [843]~E(x8431,x8432)+E(f17(x8433,x8434,x8435,x8431),f17(x8433,x8434,x8435,x8432))
% 173.53/173.43 [844]~E(x8441,x8442)+E(f617(x8441,x8443,x8444,x8445),f617(x8442,x8443,x8444,x8445))
% 173.53/173.43 [845]~E(x8451,x8452)+E(f617(x8453,x8451,x8454,x8455),f617(x8453,x8452,x8454,x8455))
% 173.53/173.43 [846]~E(x8461,x8462)+E(f617(x8463,x8464,x8461,x8465),f617(x8463,x8464,x8462,x8465))
% 173.53/173.43 [847]~E(x8471,x8472)+E(f617(x8473,x8474,x8475,x8471),f617(x8473,x8474,x8475,x8472))
% 173.53/173.43 [848]~E(x8481,x8482)+E(f251(x8481,x8483,x8484,x8485),f251(x8482,x8483,x8484,x8485))
% 173.53/173.43 [849]~E(x8491,x8492)+E(f251(x8493,x8491,x8494,x8495),f251(x8493,x8492,x8494,x8495))
% 173.53/173.43 [850]~E(x8501,x8502)+E(f251(x8503,x8504,x8501,x8505),f251(x8503,x8504,x8502,x8505))
% 173.53/173.43 [851]~E(x8511,x8512)+E(f251(x8513,x8514,x8515,x8511),f251(x8513,x8514,x8515,x8512))
% 173.53/173.43 [852]~E(x8521,x8522)+E(f210(x8521,x8523),f210(x8522,x8523))
% 173.53/173.43 [853]~E(x8531,x8532)+E(f210(x8533,x8531),f210(x8533,x8532))
% 173.53/173.43 [854]~E(x8541,x8542)+E(f186(x8541,x8543,x8544,x8545),f186(x8542,x8543,x8544,x8545))
% 173.53/173.43 [855]~E(x8551,x8552)+E(f186(x8553,x8551,x8554,x8555),f186(x8553,x8552,x8554,x8555))
% 173.53/173.43 [856]~E(x8561,x8562)+E(f186(x8563,x8564,x8561,x8565),f186(x8563,x8564,x8562,x8565))
% 173.53/173.43 [857]~E(x8571,x8572)+E(f186(x8573,x8574,x8575,x8571),f186(x8573,x8574,x8575,x8572))
% 173.53/173.43 [858]~E(x8581,x8582)+E(f711(x8581,x8583,x8584,x8585),f711(x8582,x8583,x8584,x8585))
% 173.53/173.43 [859]~E(x8591,x8592)+E(f711(x8593,x8591,x8594,x8595),f711(x8593,x8592,x8594,x8595))
% 173.53/173.43 [860]~E(x8601,x8602)+E(f711(x8603,x8604,x8601,x8605),f711(x8603,x8604,x8602,x8605))
% 173.53/173.43 [861]~E(x8611,x8612)+E(f711(x8613,x8614,x8615,x8611),f711(x8613,x8614,x8615,x8612))
% 173.53/173.43 [862]~E(x8621,x8622)+E(f827(x8621,x8623,x8624,x8625),f827(x8622,x8623,x8624,x8625))
% 173.53/173.43 [863]~E(x8631,x8632)+E(f827(x8633,x8631,x8634,x8635),f827(x8633,x8632,x8634,x8635))
% 173.53/173.43 [864]~E(x8641,x8642)+E(f827(x8643,x8644,x8641,x8645),f827(x8643,x8644,x8642,x8645))
% 173.53/173.43 [865]~E(x8651,x8652)+E(f827(x8653,x8654,x8655,x8651),f827(x8653,x8654,x8655,x8652))
% 173.53/173.43 [866]~E(x8661,x8662)+E(f807(x8661,x8663,x8664,x8665),f807(x8662,x8663,x8664,x8665))
% 173.53/173.43 [867]~E(x8671,x8672)+E(f807(x8673,x8671,x8674,x8675),f807(x8673,x8672,x8674,x8675))
% 173.53/173.43 [868]~E(x8681,x8682)+E(f807(x8683,x8684,x8681,x8685),f807(x8683,x8684,x8682,x8685))
% 173.53/173.43 [869]~E(x8691,x8692)+E(f807(x8693,x8694,x8695,x8691),f807(x8693,x8694,x8695,x8692))
% 173.53/173.43 [870]~E(x8701,x8702)+E(f574(x8701,x8703,x8704,x8705),f574(x8702,x8703,x8704,x8705))
% 173.53/173.43 [871]~E(x8711,x8712)+E(f574(x8713,x8711,x8714,x8715),f574(x8713,x8712,x8714,x8715))
% 173.53/173.43 [872]~E(x8721,x8722)+E(f574(x8723,x8724,x8721,x8725),f574(x8723,x8724,x8722,x8725))
% 173.53/173.43 [873]~E(x8731,x8732)+E(f574(x8733,x8734,x8735,x8731),f574(x8733,x8734,x8735,x8732))
% 173.53/173.43 [874]~E(x8741,x8742)+E(f499(x8741,x8743,x8744),f499(x8742,x8743,x8744))
% 173.53/173.43 [875]~E(x8751,x8752)+E(f499(x8753,x8751,x8754),f499(x8753,x8752,x8754))
% 173.53/173.43 [876]~E(x8761,x8762)+E(f499(x8763,x8764,x8761),f499(x8763,x8764,x8762))
% 173.53/173.43 [877]~E(x8771,x8772)+E(f671(x8771,x8773,x8774,x8775),f671(x8772,x8773,x8774,x8775))
% 173.53/173.43 [878]~E(x8781,x8782)+E(f671(x8783,x8781,x8784,x8785),f671(x8783,x8782,x8784,x8785))
% 173.53/173.43 [879]~E(x8791,x8792)+E(f671(x8793,x8794,x8791,x8795),f671(x8793,x8794,x8792,x8795))
% 173.53/173.43 [880]~E(x8801,x8802)+E(f671(x8803,x8804,x8805,x8801),f671(x8803,x8804,x8805,x8802))
% 173.53/173.43 [881]~E(x8811,x8812)+E(f715(x8811,x8813,x8814,x8815,x8816,x8817),f715(x8812,x8813,x8814,x8815,x8816,x8817))
% 173.53/173.43 [882]~E(x8821,x8822)+E(f715(x8823,x8821,x8824,x8825,x8826,x8827),f715(x8823,x8822,x8824,x8825,x8826,x8827))
% 173.53/173.43 [883]~E(x8831,x8832)+E(f715(x8833,x8834,x8831,x8835,x8836,x8837),f715(x8833,x8834,x8832,x8835,x8836,x8837))
% 173.53/173.43 [884]~E(x8841,x8842)+E(f715(x8843,x8844,x8845,x8841,x8846,x8847),f715(x8843,x8844,x8845,x8842,x8846,x8847))
% 173.53/173.43 [885]~E(x8851,x8852)+E(f715(x8853,x8854,x8855,x8856,x8851,x8857),f715(x8853,x8854,x8855,x8856,x8852,x8857))
% 173.53/173.43 [886]~E(x8861,x8862)+E(f715(x8863,x8864,x8865,x8866,x8867,x8861),f715(x8863,x8864,x8865,x8866,x8867,x8862))
% 173.53/173.43 [887]~E(x8871,x8872)+E(f206(x8871),f206(x8872))
% 173.53/173.43 [888]~E(x8881,x8882)+E(f750(x8881,x8883,x8884,x8885),f750(x8882,x8883,x8884,x8885))
% 173.53/173.43 [889]~E(x8891,x8892)+E(f750(x8893,x8891,x8894,x8895),f750(x8893,x8892,x8894,x8895))
% 173.53/173.43 [890]~E(x8901,x8902)+E(f750(x8903,x8904,x8901,x8905),f750(x8903,x8904,x8902,x8905))
% 173.53/173.43 [891]~E(x8911,x8912)+E(f750(x8913,x8914,x8915,x8911),f750(x8913,x8914,x8915,x8912))
% 173.53/173.43 [892]~E(x8921,x8922)+E(f603(x8921,x8923,x8924,x8925),f603(x8922,x8923,x8924,x8925))
% 173.53/173.43 [893]~E(x8931,x8932)+E(f603(x8933,x8931,x8934,x8935),f603(x8933,x8932,x8934,x8935))
% 173.53/173.43 [894]~E(x8941,x8942)+E(f603(x8943,x8944,x8941,x8945),f603(x8943,x8944,x8942,x8945))
% 173.53/173.43 [895]~E(x8951,x8952)+E(f603(x8953,x8954,x8955,x8951),f603(x8953,x8954,x8955,x8952))
% 173.53/173.43 [896]~E(x8961,x8962)+E(f809(x8961,x8963,x8964,x8965),f809(x8962,x8963,x8964,x8965))
% 173.53/173.43 [897]~E(x8971,x8972)+E(f809(x8973,x8971,x8974,x8975),f809(x8973,x8972,x8974,x8975))
% 173.53/173.43 [898]~E(x8981,x8982)+E(f809(x8983,x8984,x8981,x8985),f809(x8983,x8984,x8982,x8985))
% 173.53/173.43 [899]~E(x8991,x8992)+E(f809(x8993,x8994,x8995,x8991),f809(x8993,x8994,x8995,x8992))
% 173.53/173.43 [900]~E(x9001,x9002)+E(f768(x9001,x9003,x9004,x9005,x9006),f768(x9002,x9003,x9004,x9005,x9006))
% 173.53/173.43 [901]~E(x9011,x9012)+E(f768(x9013,x9011,x9014,x9015,x9016),f768(x9013,x9012,x9014,x9015,x9016))
% 173.53/173.43 [902]~E(x9021,x9022)+E(f768(x9023,x9024,x9021,x9025,x9026),f768(x9023,x9024,x9022,x9025,x9026))
% 173.53/173.43 [903]~E(x9031,x9032)+E(f768(x9033,x9034,x9035,x9031,x9036),f768(x9033,x9034,x9035,x9032,x9036))
% 173.53/173.43 [904]~E(x9041,x9042)+E(f768(x9043,x9044,x9045,x9046,x9041),f768(x9043,x9044,x9045,x9046,x9042))
% 173.53/173.43 [905]~E(x9051,x9052)+E(f213(x9051,x9053,x9054,x9055,x9056),f213(x9052,x9053,x9054,x9055,x9056))
% 173.53/173.43 [906]~E(x9061,x9062)+E(f213(x9063,x9061,x9064,x9065,x9066),f213(x9063,x9062,x9064,x9065,x9066))
% 173.53/173.43 [907]~E(x9071,x9072)+E(f213(x9073,x9074,x9071,x9075,x9076),f213(x9073,x9074,x9072,x9075,x9076))
% 173.53/173.43 [908]~E(x9081,x9082)+E(f213(x9083,x9084,x9085,x9081,x9086),f213(x9083,x9084,x9085,x9082,x9086))
% 173.53/173.43 [909]~E(x9091,x9092)+E(f213(x9093,x9094,x9095,x9096,x9091),f213(x9093,x9094,x9095,x9096,x9092))
% 173.53/173.43 [910]~E(x9101,x9102)+E(f826(x9101,x9103,x9104),f826(x9102,x9103,x9104))
% 173.53/173.43 [911]~E(x9111,x9112)+E(f826(x9113,x9111,x9114),f826(x9113,x9112,x9114))
% 173.53/173.43 [912]~E(x9121,x9122)+E(f826(x9123,x9124,x9121),f826(x9123,x9124,x9122))
% 173.53/173.43 [913]~E(x9131,x9132)+E(f531(x9131,x9133,x9134,x9135,x9136,x9137),f531(x9132,x9133,x9134,x9135,x9136,x9137))
% 173.53/173.43 [914]~E(x9141,x9142)+E(f531(x9143,x9141,x9144,x9145,x9146,x9147),f531(x9143,x9142,x9144,x9145,x9146,x9147))
% 173.53/173.43 [915]~E(x9151,x9152)+E(f531(x9153,x9154,x9151,x9155,x9156,x9157),f531(x9153,x9154,x9152,x9155,x9156,x9157))
% 173.53/173.43 [916]~E(x9161,x9162)+E(f531(x9163,x9164,x9165,x9161,x9166,x9167),f531(x9163,x9164,x9165,x9162,x9166,x9167))
% 173.53/173.43 [917]~E(x9171,x9172)+E(f531(x9173,x9174,x9175,x9176,x9171,x9177),f531(x9173,x9174,x9175,x9176,x9172,x9177))
% 173.53/173.43 [918]~E(x9181,x9182)+E(f531(x9183,x9184,x9185,x9186,x9187,x9181),f531(x9183,x9184,x9185,x9186,x9187,x9182))
% 173.53/173.43 [919]~E(x9191,x9192)+E(f339(x9191,x9193,x9194),f339(x9192,x9193,x9194))
% 173.53/173.43 [920]~E(x9201,x9202)+E(f339(x9203,x9201,x9204),f339(x9203,x9202,x9204))
% 173.53/173.43 [921]~E(x9211,x9212)+E(f339(x9213,x9214,x9211),f339(x9213,x9214,x9212))
% 173.53/173.43 [922]~E(x9221,x9222)+E(f684(x9221,x9223,x9224,x9225,x9226),f684(x9222,x9223,x9224,x9225,x9226))
% 173.53/173.43 [923]~E(x9231,x9232)+E(f684(x9233,x9231,x9234,x9235,x9236),f684(x9233,x9232,x9234,x9235,x9236))
% 173.53/173.43 [924]~E(x9241,x9242)+E(f684(x9243,x9244,x9241,x9245,x9246),f684(x9243,x9244,x9242,x9245,x9246))
% 173.53/173.43 [925]~E(x9251,x9252)+E(f684(x9253,x9254,x9255,x9251,x9256),f684(x9253,x9254,x9255,x9252,x9256))
% 173.53/173.43 [926]~E(x9261,x9262)+E(f684(x9263,x9264,x9265,x9266,x9261),f684(x9263,x9264,x9265,x9266,x9262))
% 173.53/173.43 [927]~E(x9271,x9272)+E(f538(x9271),f538(x9272))
% 173.53/173.43 [928]~E(x9281,x9282)+E(f471(x9281,x9283,x9284,x9285),f471(x9282,x9283,x9284,x9285))
% 173.53/173.43 [929]~E(x9291,x9292)+E(f471(x9293,x9291,x9294,x9295),f471(x9293,x9292,x9294,x9295))
% 173.53/173.43 [930]~E(x9301,x9302)+E(f471(x9303,x9304,x9301,x9305),f471(x9303,x9304,x9302,x9305))
% 173.53/173.43 [931]~E(x9311,x9312)+E(f471(x9313,x9314,x9315,x9311),f471(x9313,x9314,x9315,x9312))
% 173.53/173.43 [932]~E(x9321,x9322)+E(f304(x9321,x9323,x9324,x9325),f304(x9322,x9323,x9324,x9325))
% 173.53/173.43 [933]~E(x9331,x9332)+E(f304(x9333,x9331,x9334,x9335),f304(x9333,x9332,x9334,x9335))
% 173.53/173.43 [934]~E(x9341,x9342)+E(f304(x9343,x9344,x9341,x9345),f304(x9343,x9344,x9342,x9345))
% 173.53/173.43 [935]~E(x9351,x9352)+E(f304(x9353,x9354,x9355,x9351),f304(x9353,x9354,x9355,x9352))
% 173.53/173.43 [936]~E(x9361,x9362)+E(f686(x9361,x9363),f686(x9362,x9363))
% 173.53/173.43 [937]~E(x9371,x9372)+E(f686(x9373,x9371),f686(x9373,x9372))
% 173.53/173.43 [938]~E(x9381,x9382)+E(f259(x9381,x9383,x9384,x9385),f259(x9382,x9383,x9384,x9385))
% 173.53/173.43 [939]~E(x9391,x9392)+E(f259(x9393,x9391,x9394,x9395),f259(x9393,x9392,x9394,x9395))
% 173.53/173.43 [940]~E(x9401,x9402)+E(f259(x9403,x9404,x9401,x9405),f259(x9403,x9404,x9402,x9405))
% 173.53/173.43 [941]~E(x9411,x9412)+E(f259(x9413,x9414,x9415,x9411),f259(x9413,x9414,x9415,x9412))
% 173.53/173.43 [942]~E(x9421,x9422)+E(f844(x9421,x9423,x9424,x9425),f844(x9422,x9423,x9424,x9425))
% 173.53/173.43 [943]~E(x9431,x9432)+E(f844(x9433,x9431,x9434,x9435),f844(x9433,x9432,x9434,x9435))
% 173.53/173.43 [944]~E(x9441,x9442)+E(f844(x9443,x9444,x9441,x9445),f844(x9443,x9444,x9442,x9445))
% 173.53/173.43 [945]~E(x9451,x9452)+E(f844(x9453,x9454,x9455,x9451),f844(x9453,x9454,x9455,x9452))
% 173.53/173.43 [946]~E(x9461,x9462)+E(f333(x9461,x9463,x9464),f333(x9462,x9463,x9464))
% 173.53/173.43 [947]~E(x9471,x9472)+E(f333(x9473,x9471,x9474),f333(x9473,x9472,x9474))
% 173.53/173.43 [948]~E(x9481,x9482)+E(f333(x9483,x9484,x9481),f333(x9483,x9484,x9482))
% 173.53/173.43 [949]~E(x9491,x9492)+E(f843(x9491,x9493,x9494),f843(x9492,x9493,x9494))
% 173.53/173.43 [950]~E(x9501,x9502)+E(f843(x9503,x9501,x9504),f843(x9503,x9502,x9504))
% 173.53/173.43 [951]~E(x9511,x9512)+E(f843(x9513,x9514,x9511),f843(x9513,x9514,x9512))
% 173.53/173.43 [952]~E(x9521,x9522)+E(f738(x9521,x9523,x9524,x9525),f738(x9522,x9523,x9524,x9525))
% 173.53/173.43 [953]~E(x9531,x9532)+E(f738(x9533,x9531,x9534,x9535),f738(x9533,x9532,x9534,x9535))
% 173.53/173.43 [954]~E(x9541,x9542)+E(f738(x9543,x9544,x9541,x9545),f738(x9543,x9544,x9542,x9545))
% 173.53/173.43 [955]~E(x9551,x9552)+E(f738(x9553,x9554,x9555,x9551),f738(x9553,x9554,x9555,x9552))
% 173.53/173.43 [956]~E(x9561,x9562)+E(f677(x9561,x9563,x9564),f677(x9562,x9563,x9564))
% 173.53/173.43 [957]~E(x9571,x9572)+E(f677(x9573,x9571,x9574),f677(x9573,x9572,x9574))
% 173.53/173.43 [958]~E(x9581,x9582)+E(f677(x9583,x9584,x9581),f677(x9583,x9584,x9582))
% 173.53/173.43 [959]~E(x9591,x9592)+E(f780(x9591,x9593,x9594),f780(x9592,x9593,x9594))
% 173.53/173.43 [960]~E(x9601,x9602)+E(f780(x9603,x9601,x9604),f780(x9603,x9602,x9604))
% 173.53/173.43 [961]~E(x9611,x9612)+E(f780(x9613,x9614,x9611),f780(x9613,x9614,x9612))
% 173.53/173.43 [962]~E(x9621,x9622)+E(f274(x9621,x9623,x9624,x9625),f274(x9622,x9623,x9624,x9625))
% 173.53/173.43 [963]~E(x9631,x9632)+E(f274(x9633,x9631,x9634,x9635),f274(x9633,x9632,x9634,x9635))
% 173.53/173.43 [964]~E(x9641,x9642)+E(f274(x9643,x9644,x9641,x9645),f274(x9643,x9644,x9642,x9645))
% 173.53/173.43 [965]~E(x9651,x9652)+E(f274(x9653,x9654,x9655,x9651),f274(x9653,x9654,x9655,x9652))
% 173.53/173.43 [966]~E(x9661,x9662)+E(f139(x9661,x9663),f139(x9662,x9663))
% 173.53/173.43 [967]~E(x9671,x9672)+E(f139(x9673,x9671),f139(x9673,x9672))
% 173.53/173.43 [968]~E(x9681,x9682)+E(f580(x9681),f580(x9682))
% 173.53/173.43 [969]~E(x9691,x9692)+E(f388(x9691,x9693,x9694,x9695),f388(x9692,x9693,x9694,x9695))
% 173.53/173.43 [970]~E(x9701,x9702)+E(f388(x9703,x9701,x9704,x9705),f388(x9703,x9702,x9704,x9705))
% 173.53/173.43 [971]~E(x9711,x9712)+E(f388(x9713,x9714,x9711,x9715),f388(x9713,x9714,x9712,x9715))
% 173.53/173.43 [972]~E(x9721,x9722)+E(f388(x9723,x9724,x9725,x9721),f388(x9723,x9724,x9725,x9722))
% 173.53/173.43 [973]~E(x9731,x9732)+E(f702(x9731,x9733),f702(x9732,x9733))
% 173.53/173.43 [974]~E(x9741,x9742)+E(f702(x9743,x9741),f702(x9743,x9742))
% 173.53/173.43 [975]~E(x9751,x9752)+E(f590(x9751,x9753,x9754,x9755),f590(x9752,x9753,x9754,x9755))
% 173.53/173.43 [976]~E(x9761,x9762)+E(f590(x9763,x9761,x9764,x9765),f590(x9763,x9762,x9764,x9765))
% 173.53/173.43 [977]~E(x9771,x9772)+E(f590(x9773,x9774,x9771,x9775),f590(x9773,x9774,x9772,x9775))
% 173.53/173.43 [978]~E(x9781,x9782)+E(f590(x9783,x9784,x9785,x9781),f590(x9783,x9784,x9785,x9782))
% 173.53/173.43 [979]~E(x9791,x9792)+E(f461(x9791,x9793,x9794,x9795),f461(x9792,x9793,x9794,x9795))
% 173.53/173.43 [980]~E(x9801,x9802)+E(f461(x9803,x9801,x9804,x9805),f461(x9803,x9802,x9804,x9805))
% 173.53/173.43 [981]~E(x9811,x9812)+E(f461(x9813,x9814,x9811,x9815),f461(x9813,x9814,x9812,x9815))
% 173.53/173.43 [982]~E(x9821,x9822)+E(f461(x9823,x9824,x9825,x9821),f461(x9823,x9824,x9825,x9822))
% 173.53/173.43 [983]~E(x9831,x9832)+E(f237(x9831,x9833),f237(x9832,x9833))
% 173.53/173.43 [984]~E(x9841,x9842)+E(f237(x9843,x9841),f237(x9843,x9842))
% 173.53/173.43 [985]~E(x9851,x9852)+E(f38(x9851,x9853,x9854,x9855,x9856,x9857,x9858,x9859,x98510,x98511),f38(x9852,x9853,x9854,x9855,x9856,x9857,x9858,x9859,x98510,x98511))
% 173.53/173.43 [986]~E(x9861,x9862)+E(f38(x9863,x9861,x9864,x9865,x9866,x9867,x9868,x9869,x98610,x98611),f38(x9863,x9862,x9864,x9865,x9866,x9867,x9868,x9869,x98610,x98611))
% 173.53/173.43 [987]~E(x9871,x9872)+E(f38(x9873,x9874,x9871,x9875,x9876,x9877,x9878,x9879,x98710,x98711),f38(x9873,x9874,x9872,x9875,x9876,x9877,x9878,x9879,x98710,x98711))
% 173.53/173.43 [988]~E(x9881,x9882)+E(f38(x9883,x9884,x9885,x9881,x9886,x9887,x9888,x9889,x98810,x98811),f38(x9883,x9884,x9885,x9882,x9886,x9887,x9888,x9889,x98810,x98811))
% 173.53/173.43 [989]~E(x9891,x9892)+E(f38(x9893,x9894,x9895,x9896,x9891,x9897,x9898,x9899,x98910,x98911),f38(x9893,x9894,x9895,x9896,x9892,x9897,x9898,x9899,x98910,x98911))
% 173.53/173.43 [990]~E(x9901,x9902)+E(f38(x9903,x9904,x9905,x9906,x9907,x9901,x9908,x9909,x99010,x99011),f38(x9903,x9904,x9905,x9906,x9907,x9902,x9908,x9909,x99010,x99011))
% 173.53/173.43 [991]~E(x9911,x9912)+E(f38(x9913,x9914,x9915,x9916,x9917,x9918,x9911,x9919,x99110,x99111),f38(x9913,x9914,x9915,x9916,x9917,x9918,x9912,x9919,x99110,x99111))
% 173.53/173.43 [992]~E(x9921,x9922)+E(f38(x9923,x9924,x9925,x9926,x9927,x9928,x9929,x9921,x99210,x99211),f38(x9923,x9924,x9925,x9926,x9927,x9928,x9929,x9922,x99210,x99211))
% 173.53/173.43 [993]~E(x9931,x9932)+E(f38(x9933,x9934,x9935,x9936,x9937,x9938,x9939,x99310,x9931,x99311),f38(x9933,x9934,x9935,x9936,x9937,x9938,x9939,x99310,x9932,x99311))
% 173.53/173.43 [994]~E(x9941,x9942)+E(f38(x9943,x9944,x9945,x9946,x9947,x9948,x9949,x99410,x99411,x9941),f38(x9943,x9944,x9945,x9946,x9947,x9948,x9949,x99410,x99411,x9942))
% 173.53/173.43 [995]~E(x9951,x9952)+E(f402(x9951,x9953,x9954,x9955,x9956),f402(x9952,x9953,x9954,x9955,x9956))
% 173.53/173.43 [996]~E(x9961,x9962)+E(f402(x9963,x9961,x9964,x9965,x9966),f402(x9963,x9962,x9964,x9965,x9966))
% 173.53/173.43 [997]~E(x9971,x9972)+E(f402(x9973,x9974,x9971,x9975,x9976),f402(x9973,x9974,x9972,x9975,x9976))
% 173.53/173.43 [998]~E(x9981,x9982)+E(f402(x9983,x9984,x9985,x9981,x9986),f402(x9983,x9984,x9985,x9982,x9986))
% 173.53/173.43 [999]~E(x9991,x9992)+E(f402(x9993,x9994,x9995,x9996,x9991),f402(x9993,x9994,x9995,x9996,x9992))
% 173.53/173.43 [1000]~E(x10001,x10002)+E(f615(x10001,x10003,x10004),f615(x10002,x10003,x10004))
% 173.53/173.43 [1001]~E(x10011,x10012)+E(f615(x10013,x10011,x10014),f615(x10013,x10012,x10014))
% 173.53/173.43 [1002]~E(x10021,x10022)+E(f615(x10023,x10024,x10021),f615(x10023,x10024,x10022))
% 173.53/173.43 [1003]~E(x10031,x10032)+E(f478(x10031,x10033),f478(x10032,x10033))
% 173.53/173.43 [1004]~E(x10041,x10042)+E(f478(x10043,x10041),f478(x10043,x10042))
% 173.53/173.43 [1005]~E(x10051,x10052)+E(f366(x10051),f366(x10052))
% 173.53/173.43 [1006]~E(x10061,x10062)+E(f163(x10061,x10063,x10064),f163(x10062,x10063,x10064))
% 173.53/173.43 [1007]~E(x10071,x10072)+E(f163(x10073,x10071,x10074),f163(x10073,x10072,x10074))
% 173.53/173.43 [1008]~E(x10081,x10082)+E(f163(x10083,x10084,x10081),f163(x10083,x10084,x10082))
% 173.53/173.43 [1009]~E(x10091,x10092)+E(f231(x10091,x10093),f231(x10092,x10093))
% 173.53/173.43 [1010]~E(x10101,x10102)+E(f231(x10103,x10101),f231(x10103,x10102))
% 173.53/173.43 [1011]~E(x10111,x10112)+E(f255(x10111),f255(x10112))
% 173.53/173.43 [1012]~E(x10121,x10122)+E(f607(x10121,x10123,x10124),f607(x10122,x10123,x10124))
% 173.53/173.43 [1013]~E(x10131,x10132)+E(f607(x10133,x10131,x10134),f607(x10133,x10132,x10134))
% 173.53/173.43 [1014]~E(x10141,x10142)+E(f607(x10143,x10144,x10141),f607(x10143,x10144,x10142))
% 173.53/173.43 [1015]~E(x10151,x10152)+E(f728(x10151,x10153,x10154,x10155,x10156),f728(x10152,x10153,x10154,x10155,x10156))
% 173.53/173.43 [1016]~E(x10161,x10162)+E(f728(x10163,x10161,x10164,x10165,x10166),f728(x10163,x10162,x10164,x10165,x10166))
% 173.53/173.43 [1017]~E(x10171,x10172)+E(f728(x10173,x10174,x10171,x10175,x10176),f728(x10173,x10174,x10172,x10175,x10176))
% 173.53/173.43 [1018]~E(x10181,x10182)+E(f728(x10183,x10184,x10185,x10181,x10186),f728(x10183,x10184,x10185,x10182,x10186))
% 173.53/173.43 [1019]~E(x10191,x10192)+E(f728(x10193,x10194,x10195,x10196,x10191),f728(x10193,x10194,x10195,x10196,x10192))
% 173.53/173.43 [1020]~E(x10201,x10202)+E(f766(x10201,x10203,x10204,x10205,x10206),f766(x10202,x10203,x10204,x10205,x10206))
% 173.53/173.43 [1021]~E(x10211,x10212)+E(f766(x10213,x10211,x10214,x10215,x10216),f766(x10213,x10212,x10214,x10215,x10216))
% 173.53/173.43 [1022]~E(x10221,x10222)+E(f766(x10223,x10224,x10221,x10225,x10226),f766(x10223,x10224,x10222,x10225,x10226))
% 173.53/173.43 [1023]~E(x10231,x10232)+E(f766(x10233,x10234,x10235,x10231,x10236),f766(x10233,x10234,x10235,x10232,x10236))
% 173.53/173.43 [1024]~E(x10241,x10242)+E(f766(x10243,x10244,x10245,x10246,x10241),f766(x10243,x10244,x10245,x10246,x10242))
% 173.53/173.43 [1025]~E(x10251,x10252)+E(f193(x10251,x10253),f193(x10252,x10253))
% 173.53/173.43 [1026]~E(x10261,x10262)+E(f193(x10263,x10261),f193(x10263,x10262))
% 173.53/173.43 [1027]~E(x10271,x10272)+E(f105(x10271,x10273,x10274),f105(x10272,x10273,x10274))
% 173.53/173.43 [1028]~E(x10281,x10282)+E(f105(x10283,x10281,x10284),f105(x10283,x10282,x10284))
% 173.53/173.43 [1029]~E(x10291,x10292)+E(f105(x10293,x10294,x10291),f105(x10293,x10294,x10292))
% 173.53/173.43 [1030]~E(x10301,x10302)+E(f484(x10301,x10303),f484(x10302,x10303))
% 173.53/173.43 [1031]~E(x10311,x10312)+E(f484(x10313,x10311),f484(x10313,x10312))
% 173.53/173.43 [1032]~E(x10321,x10322)+E(f364(x10321,x10323),f364(x10322,x10323))
% 173.53/173.44 [1033]~E(x10331,x10332)+E(f364(x10333,x10331),f364(x10333,x10332))
% 173.53/173.44 [1034]~E(x10341,x10342)+E(f414(x10341,x10343,x10344,x10345,x10346),f414(x10342,x10343,x10344,x10345,x10346))
% 173.53/173.44 [1035]~E(x10351,x10352)+E(f414(x10353,x10351,x10354,x10355,x10356),f414(x10353,x10352,x10354,x10355,x10356))
% 173.53/173.44 [1036]~E(x10361,x10362)+E(f414(x10363,x10364,x10361,x10365,x10366),f414(x10363,x10364,x10362,x10365,x10366))
% 173.53/173.44 [1037]~E(x10371,x10372)+E(f414(x10373,x10374,x10375,x10371,x10376),f414(x10373,x10374,x10375,x10372,x10376))
% 173.53/173.44 [1038]~E(x10381,x10382)+E(f414(x10383,x10384,x10385,x10386,x10381),f414(x10383,x10384,x10385,x10386,x10382))
% 173.53/173.44 [1039]~E(x10391,x10392)+E(f44(x10391,x10393,x10394,x10395),f44(x10392,x10393,x10394,x10395))
% 173.53/173.44 [1040]~E(x10401,x10402)+E(f44(x10403,x10401,x10404,x10405),f44(x10403,x10402,x10404,x10405))
% 173.53/173.44 [1041]~E(x10411,x10412)+E(f44(x10413,x10414,x10411,x10415),f44(x10413,x10414,x10412,x10415))
% 173.53/173.44 [1042]~E(x10421,x10422)+E(f44(x10423,x10424,x10425,x10421),f44(x10423,x10424,x10425,x10422))
% 173.53/173.44 [1043]~E(x10431,x10432)+E(f737(x10431,x10433,x10434),f737(x10432,x10433,x10434))
% 173.53/173.44 [1044]~E(x10441,x10442)+E(f737(x10443,x10441,x10444),f737(x10443,x10442,x10444))
% 173.53/173.44 [1045]~E(x10451,x10452)+E(f737(x10453,x10454,x10451),f737(x10453,x10454,x10452))
% 173.53/173.44 [1046]~E(x10461,x10462)+E(f196(x10461,x10463),f196(x10462,x10463))
% 173.53/173.44 [1047]~E(x10471,x10472)+E(f196(x10473,x10471),f196(x10473,x10472))
% 173.53/173.44 [1048]~E(x10481,x10482)+E(f341(x10481,x10483,x10484,x10485,x10486),f341(x10482,x10483,x10484,x10485,x10486))
% 173.53/173.44 [1049]~E(x10491,x10492)+E(f341(x10493,x10491,x10494,x10495,x10496),f341(x10493,x10492,x10494,x10495,x10496))
% 173.53/173.44 [1050]~E(x10501,x10502)+E(f341(x10503,x10504,x10501,x10505,x10506),f341(x10503,x10504,x10502,x10505,x10506))
% 173.53/173.44 [1051]~E(x10511,x10512)+E(f341(x10513,x10514,x10515,x10511,x10516),f341(x10513,x10514,x10515,x10512,x10516))
% 173.53/173.44 [1052]~E(x10521,x10522)+E(f341(x10523,x10524,x10525,x10526,x10521),f341(x10523,x10524,x10525,x10526,x10522))
% 173.53/173.44 [1053]~E(x10531,x10532)+E(f217(x10531,x10533,x10534,x10535),f217(x10532,x10533,x10534,x10535))
% 173.53/173.44 [1054]~E(x10541,x10542)+E(f217(x10543,x10541,x10544,x10545),f217(x10543,x10542,x10544,x10545))
% 173.53/173.44 [1055]~E(x10551,x10552)+E(f217(x10553,x10554,x10551,x10555),f217(x10553,x10554,x10552,x10555))
% 173.53/173.44 [1056]~E(x10561,x10562)+E(f217(x10563,x10564,x10565,x10561),f217(x10563,x10564,x10565,x10562))
% 173.53/173.44 [1057]~E(x10571,x10572)+E(f319(x10571),f319(x10572))
% 173.53/173.44 [1058]~E(x10581,x10582)+E(f496(x10581,x10583,x10584,x10585),f496(x10582,x10583,x10584,x10585))
% 173.53/173.44 [1059]~E(x10591,x10592)+E(f496(x10593,x10591,x10594,x10595),f496(x10593,x10592,x10594,x10595))
% 173.53/173.44 [1060]~E(x10601,x10602)+E(f496(x10603,x10604,x10601,x10605),f496(x10603,x10604,x10602,x10605))
% 173.53/173.44 [1061]~E(x10611,x10612)+E(f496(x10613,x10614,x10615,x10611),f496(x10613,x10614,x10615,x10612))
% 173.53/173.44 [1062]~E(x10621,x10622)+E(f717(x10621,x10623,x10624,x10625,x10626,x10627),f717(x10622,x10623,x10624,x10625,x10626,x10627))
% 173.53/173.44 [1063]~E(x10631,x10632)+E(f717(x10633,x10631,x10634,x10635,x10636,x10637),f717(x10633,x10632,x10634,x10635,x10636,x10637))
% 173.53/173.44 [1064]~E(x10641,x10642)+E(f717(x10643,x10644,x10641,x10645,x10646,x10647),f717(x10643,x10644,x10642,x10645,x10646,x10647))
% 173.53/173.44 [1065]~E(x10651,x10652)+E(f717(x10653,x10654,x10655,x10651,x10656,x10657),f717(x10653,x10654,x10655,x10652,x10656,x10657))
% 173.53/173.44 [1066]~E(x10661,x10662)+E(f717(x10663,x10664,x10665,x10666,x10661,x10667),f717(x10663,x10664,x10665,x10666,x10662,x10667))
% 173.53/173.44 [1067]~E(x10671,x10672)+E(f717(x10673,x10674,x10675,x10676,x10677,x10671),f717(x10673,x10674,x10675,x10676,x10677,x10672))
% 173.53/173.44 [1068]~E(x10681,x10682)+E(f730(x10681,x10683,x10684,x10685,x10686,x10687),f730(x10682,x10683,x10684,x10685,x10686,x10687))
% 173.53/173.44 [1069]~E(x10691,x10692)+E(f730(x10693,x10691,x10694,x10695,x10696,x10697),f730(x10693,x10692,x10694,x10695,x10696,x10697))
% 173.53/173.44 [1070]~E(x10701,x10702)+E(f730(x10703,x10704,x10701,x10705,x10706,x10707),f730(x10703,x10704,x10702,x10705,x10706,x10707))
% 173.53/173.44 [1071]~E(x10711,x10712)+E(f730(x10713,x10714,x10715,x10711,x10716,x10717),f730(x10713,x10714,x10715,x10712,x10716,x10717))
% 173.53/173.44 [1072]~E(x10721,x10722)+E(f730(x10723,x10724,x10725,x10726,x10721,x10727),f730(x10723,x10724,x10725,x10726,x10722,x10727))
% 173.53/173.44 [1073]~E(x10731,x10732)+E(f730(x10733,x10734,x10735,x10736,x10737,x10731),f730(x10733,x10734,x10735,x10736,x10737,x10732))
% 173.53/173.44 [1074]~E(x10741,x10742)+E(f581(x10741,x10743),f581(x10742,x10743))
% 173.53/173.44 [1075]~E(x10751,x10752)+E(f581(x10753,x10751),f581(x10753,x10752))
% 173.53/173.44 [1076]~E(x10761,x10762)+E(f439(x10761,x10763,x10764),f439(x10762,x10763,x10764))
% 173.53/173.44 [1077]~E(x10771,x10772)+E(f439(x10773,x10771,x10774),f439(x10773,x10772,x10774))
% 173.53/173.44 [1078]~E(x10781,x10782)+E(f439(x10783,x10784,x10781),f439(x10783,x10784,x10782))
% 173.53/173.44 [1079]~E(x10791,x10792)+E(f503(x10791,x10793,x10794,x10795,x10796,x10797),f503(x10792,x10793,x10794,x10795,x10796,x10797))
% 173.53/173.44 [1080]~E(x10801,x10802)+E(f503(x10803,x10801,x10804,x10805,x10806,x10807),f503(x10803,x10802,x10804,x10805,x10806,x10807))
% 173.53/173.44 [1081]~E(x10811,x10812)+E(f503(x10813,x10814,x10811,x10815,x10816,x10817),f503(x10813,x10814,x10812,x10815,x10816,x10817))
% 173.53/173.44 [1082]~E(x10821,x10822)+E(f503(x10823,x10824,x10825,x10821,x10826,x10827),f503(x10823,x10824,x10825,x10822,x10826,x10827))
% 173.53/173.44 [1083]~E(x10831,x10832)+E(f503(x10833,x10834,x10835,x10836,x10831,x10837),f503(x10833,x10834,x10835,x10836,x10832,x10837))
% 173.53/173.44 [1084]~E(x10841,x10842)+E(f503(x10843,x10844,x10845,x10846,x10847,x10841),f503(x10843,x10844,x10845,x10846,x10847,x10842))
% 173.53/173.44 [1085]~E(x10851,x10852)+E(f136(x10851,x10853,x10854),f136(x10852,x10853,x10854))
% 173.53/173.44 [1086]~E(x10861,x10862)+E(f136(x10863,x10861,x10864),f136(x10863,x10862,x10864))
% 173.53/173.44 [1087]~E(x10871,x10872)+E(f136(x10873,x10874,x10871),f136(x10873,x10874,x10872))
% 173.53/173.44 [1088]~E(x10881,x10882)+E(f454(x10881,x10883),f454(x10882,x10883))
% 173.53/173.44 [1089]~E(x10891,x10892)+E(f454(x10893,x10891),f454(x10893,x10892))
% 173.53/173.44 [1090]~E(x10901,x10902)+E(f816(x10901,x10903),f816(x10902,x10903))
% 173.53/173.44 [1091]~E(x10911,x10912)+E(f816(x10913,x10911),f816(x10913,x10912))
% 173.53/173.44 [1092]~E(x10921,x10922)+E(f436(x10921,x10923,x10924),f436(x10922,x10923,x10924))
% 173.53/173.44 [1093]~E(x10931,x10932)+E(f436(x10933,x10931,x10934),f436(x10933,x10932,x10934))
% 173.53/173.44 [1094]~E(x10941,x10942)+E(f436(x10943,x10944,x10941),f436(x10943,x10944,x10942))
% 173.53/173.44 [1095]~E(x10951,x10952)+E(f842(x10951,x10953,x10954),f842(x10952,x10953,x10954))
% 173.53/173.44 [1096]~E(x10961,x10962)+E(f842(x10963,x10961,x10964),f842(x10963,x10962,x10964))
% 173.53/173.44 [1097]~E(x10971,x10972)+E(f842(x10973,x10974,x10971),f842(x10973,x10974,x10972))
% 173.53/173.44 [1098]~E(x10981,x10982)+E(f742(x10981,x10983,x10984),f742(x10982,x10983,x10984))
% 173.53/173.44 [1099]~E(x10991,x10992)+E(f742(x10993,x10991,x10994),f742(x10993,x10992,x10994))
% 173.53/173.44 [1100]~E(x11001,x11002)+E(f742(x11003,x11004,x11001),f742(x11003,x11004,x11002))
% 173.53/173.44 [1101]~E(x11011,x11012)+E(f393(x11011,x11013,x11014),f393(x11012,x11013,x11014))
% 173.53/173.44 [1102]~E(x11021,x11022)+E(f393(x11023,x11021,x11024),f393(x11023,x11022,x11024))
% 173.53/173.44 [1103]~E(x11031,x11032)+E(f393(x11033,x11034,x11031),f393(x11033,x11034,x11032))
% 173.53/173.44 [1104]~E(x11041,x11042)+E(f727(x11041,x11043,x11044,x11045,x11046),f727(x11042,x11043,x11044,x11045,x11046))
% 173.53/173.44 [1105]~E(x11051,x11052)+E(f727(x11053,x11051,x11054,x11055,x11056),f727(x11053,x11052,x11054,x11055,x11056))
% 173.53/173.44 [1106]~E(x11061,x11062)+E(f727(x11063,x11064,x11061,x11065,x11066),f727(x11063,x11064,x11062,x11065,x11066))
% 173.53/173.44 [1107]~E(x11071,x11072)+E(f727(x11073,x11074,x11075,x11071,x11076),f727(x11073,x11074,x11075,x11072,x11076))
% 173.53/173.44 [1108]~E(x11081,x11082)+E(f727(x11083,x11084,x11085,x11086,x11081),f727(x11083,x11084,x11085,x11086,x11082))
% 173.53/173.44 [1109]~E(x11091,x11092)+E(f472(x11091,x11093,x11094,x11095),f472(x11092,x11093,x11094,x11095))
% 173.53/173.44 [1110]~E(x11101,x11102)+E(f472(x11103,x11101,x11104,x11105),f472(x11103,x11102,x11104,x11105))
% 173.53/173.44 [1111]~E(x11111,x11112)+E(f472(x11113,x11114,x11111,x11115),f472(x11113,x11114,x11112,x11115))
% 173.53/173.44 [1112]~E(x11121,x11122)+E(f472(x11123,x11124,x11125,x11121),f472(x11123,x11124,x11125,x11122))
% 173.53/173.44 [1113]~E(x11131,x11132)+E(f316(x11131,x11133,x11134,x11135),f316(x11132,x11133,x11134,x11135))
% 173.53/173.44 [1114]~E(x11141,x11142)+E(f316(x11143,x11141,x11144,x11145),f316(x11143,x11142,x11144,x11145))
% 173.53/173.44 [1115]~E(x11151,x11152)+E(f316(x11153,x11154,x11151,x11155),f316(x11153,x11154,x11152,x11155))
% 173.53/173.44 [1116]~E(x11161,x11162)+E(f316(x11163,x11164,x11165,x11161),f316(x11163,x11164,x11165,x11162))
% 173.53/173.44 [1117]~E(x11171,x11172)+E(f565(x11171,x11173,x11174,x11175,x11176,x11177),f565(x11172,x11173,x11174,x11175,x11176,x11177))
% 173.53/173.44 [1118]~E(x11181,x11182)+E(f565(x11183,x11181,x11184,x11185,x11186,x11187),f565(x11183,x11182,x11184,x11185,x11186,x11187))
% 173.53/173.44 [1119]~E(x11191,x11192)+E(f565(x11193,x11194,x11191,x11195,x11196,x11197),f565(x11193,x11194,x11192,x11195,x11196,x11197))
% 173.53/173.44 [1120]~E(x11201,x11202)+E(f565(x11203,x11204,x11205,x11201,x11206,x11207),f565(x11203,x11204,x11205,x11202,x11206,x11207))
% 173.53/173.44 [1121]~E(x11211,x11212)+E(f565(x11213,x11214,x11215,x11216,x11211,x11217),f565(x11213,x11214,x11215,x11216,x11212,x11217))
% 173.53/173.44 [1122]~E(x11221,x11222)+E(f565(x11223,x11224,x11225,x11226,x11227,x11221),f565(x11223,x11224,x11225,x11226,x11227,x11222))
% 173.53/173.44 [1123]~E(x11231,x11232)+E(f68(x11231,x11233,x11234,x11235),f68(x11232,x11233,x11234,x11235))
% 173.53/173.44 [1124]~E(x11241,x11242)+E(f68(x11243,x11241,x11244,x11245),f68(x11243,x11242,x11244,x11245))
% 173.53/173.44 [1125]~E(x11251,x11252)+E(f68(x11253,x11254,x11251,x11255),f68(x11253,x11254,x11252,x11255))
% 173.53/173.44 [1126]~E(x11261,x11262)+E(f68(x11263,x11264,x11265,x11261),f68(x11263,x11264,x11265,x11262))
% 173.53/173.44 [1127]~E(x11271,x11272)+E(f452(x11271,x11273,x11274,x11275),f452(x11272,x11273,x11274,x11275))
% 173.53/173.44 [1128]~E(x11281,x11282)+E(f452(x11283,x11281,x11284,x11285),f452(x11283,x11282,x11284,x11285))
% 173.53/173.44 [1129]~E(x11291,x11292)+E(f452(x11293,x11294,x11291,x11295),f452(x11293,x11294,x11292,x11295))
% 173.53/173.44 [1130]~E(x11301,x11302)+E(f452(x11303,x11304,x11305,x11301),f452(x11303,x11304,x11305,x11302))
% 173.53/173.44 [1131]~E(x11311,x11312)+E(f710(x11311,x11313,x11314),f710(x11312,x11313,x11314))
% 173.53/173.44 [1132]~E(x11321,x11322)+E(f710(x11323,x11321,x11324),f710(x11323,x11322,x11324))
% 173.53/173.44 [1133]~E(x11331,x11332)+E(f710(x11333,x11334,x11331),f710(x11333,x11334,x11332))
% 173.53/173.44 [1134]~E(x11341,x11342)+E(f326(x11341,x11343),f326(x11342,x11343))
% 173.53/173.44 [1135]~E(x11351,x11352)+E(f326(x11353,x11351),f326(x11353,x11352))
% 173.53/173.44 [1136]~E(x11361,x11362)+E(f723(x11361,x11363,x11364),f723(x11362,x11363,x11364))
% 173.53/173.44 [1137]~E(x11371,x11372)+E(f723(x11373,x11371,x11374),f723(x11373,x11372,x11374))
% 173.53/173.44 [1138]~E(x11381,x11382)+E(f723(x11383,x11384,x11381),f723(x11383,x11384,x11382))
% 173.53/173.44 [1139]~E(x11391,x11392)+E(f810(x11391,x11393,x11394,x11395),f810(x11392,x11393,x11394,x11395))
% 173.53/173.44 [1140]~E(x11401,x11402)+E(f810(x11403,x11401,x11404,x11405),f810(x11403,x11402,x11404,x11405))
% 173.53/173.44 [1141]~E(x11411,x11412)+E(f810(x11413,x11414,x11411,x11415),f810(x11413,x11414,x11412,x11415))
% 173.53/173.44 [1142]~E(x11421,x11422)+E(f810(x11423,x11424,x11425,x11421),f810(x11423,x11424,x11425,x11422))
% 173.53/173.44 [1143]~E(x11431,x11432)+E(f794(x11431,x11433,x11434),f794(x11432,x11433,x11434))
% 173.53/173.44 [1144]~E(x11441,x11442)+E(f794(x11443,x11441,x11444),f794(x11443,x11442,x11444))
% 173.53/173.44 [1145]~E(x11451,x11452)+E(f794(x11453,x11454,x11451),f794(x11453,x11454,x11452))
% 173.53/173.44 [1146]~E(x11461,x11462)+E(f773(x11461,x11463),f773(x11462,x11463))
% 173.53/173.44 [1147]~E(x11471,x11472)+E(f773(x11473,x11471),f773(x11473,x11472))
% 173.53/173.44 [1148]~E(x11481,x11482)+E(f469(x11481,x11483,x11484,x11485),f469(x11482,x11483,x11484,x11485))
% 173.53/173.44 [1149]~E(x11491,x11492)+E(f469(x11493,x11491,x11494,x11495),f469(x11493,x11492,x11494,x11495))
% 173.53/173.44 [1150]~E(x11501,x11502)+E(f469(x11503,x11504,x11501,x11505),f469(x11503,x11504,x11502,x11505))
% 173.53/173.44 [1151]~E(x11511,x11512)+E(f469(x11513,x11514,x11515,x11511),f469(x11513,x11514,x11515,x11512))
% 173.53/173.44 [1152]~E(x11521,x11522)+E(f533(x11521,x11523,x11524,x11525,x11526),f533(x11522,x11523,x11524,x11525,x11526))
% 173.53/173.44 [1153]~E(x11531,x11532)+E(f533(x11533,x11531,x11534,x11535,x11536),f533(x11533,x11532,x11534,x11535,x11536))
% 173.53/173.44 [1154]~E(x11541,x11542)+E(f533(x11543,x11544,x11541,x11545,x11546),f533(x11543,x11544,x11542,x11545,x11546))
% 173.53/173.44 [1155]~E(x11551,x11552)+E(f533(x11553,x11554,x11555,x11551,x11556),f533(x11553,x11554,x11555,x11552,x11556))
% 173.53/173.44 [1156]~E(x11561,x11562)+E(f533(x11563,x11564,x11565,x11566,x11561),f533(x11563,x11564,x11565,x11566,x11562))
% 173.53/173.44 [1157]~E(x11571,x11572)+E(f732(x11571,x11573,x11574,x11575,x11576,x11577),f732(x11572,x11573,x11574,x11575,x11576,x11577))
% 173.53/173.44 [1158]~E(x11581,x11582)+E(f732(x11583,x11581,x11584,x11585,x11586,x11587),f732(x11583,x11582,x11584,x11585,x11586,x11587))
% 173.53/173.44 [1159]~E(x11591,x11592)+E(f732(x11593,x11594,x11591,x11595,x11596,x11597),f732(x11593,x11594,x11592,x11595,x11596,x11597))
% 173.53/173.44 [1160]~E(x11601,x11602)+E(f732(x11603,x11604,x11605,x11601,x11606,x11607),f732(x11603,x11604,x11605,x11602,x11606,x11607))
% 173.53/173.44 [1161]~E(x11611,x11612)+E(f732(x11613,x11614,x11615,x11616,x11611,x11617),f732(x11613,x11614,x11615,x11616,x11612,x11617))
% 173.53/173.44 [1162]~E(x11621,x11622)+E(f732(x11623,x11624,x11625,x11626,x11627,x11621),f732(x11623,x11624,x11625,x11626,x11627,x11622))
% 173.53/173.44 [1163]~E(x11631,x11632)+E(f85(x11631,x11633,x11634,x11635,x11636),f85(x11632,x11633,x11634,x11635,x11636))
% 173.53/173.44 [1164]~E(x11641,x11642)+E(f85(x11643,x11641,x11644,x11645,x11646),f85(x11643,x11642,x11644,x11645,x11646))
% 173.53/173.44 [1165]~E(x11651,x11652)+E(f85(x11653,x11654,x11651,x11655,x11656),f85(x11653,x11654,x11652,x11655,x11656))
% 173.53/173.44 [1166]~E(x11661,x11662)+E(f85(x11663,x11664,x11665,x11661,x11666),f85(x11663,x11664,x11665,x11662,x11666))
% 173.53/173.44 [1167]~E(x11671,x11672)+E(f85(x11673,x11674,x11675,x11676,x11671),f85(x11673,x11674,x11675,x11676,x11672))
% 173.53/173.44 [1168]~E(x11681,x11682)+E(f602(x11681,x11683,x11684,x11685),f602(x11682,x11683,x11684,x11685))
% 173.53/173.44 [1169]~E(x11691,x11692)+E(f602(x11693,x11691,x11694,x11695),f602(x11693,x11692,x11694,x11695))
% 173.53/173.44 [1170]~E(x11701,x11702)+E(f602(x11703,x11704,x11701,x11705),f602(x11703,x11704,x11702,x11705))
% 173.53/173.44 [1171]~E(x11711,x11712)+E(f602(x11713,x11714,x11715,x11711),f602(x11713,x11714,x11715,x11712))
% 173.53/173.44 [1172]~E(x11721,x11722)+E(f743(x11721,x11723,x11724),f743(x11722,x11723,x11724))
% 173.53/173.44 [1173]~E(x11731,x11732)+E(f743(x11733,x11731,x11734),f743(x11733,x11732,x11734))
% 173.53/173.44 [1174]~E(x11741,x11742)+E(f743(x11743,x11744,x11741),f743(x11743,x11744,x11742))
% 173.53/173.44 [1175]~E(x11751,x11752)+E(f786(x11751,x11753),f786(x11752,x11753))
% 173.53/173.44 [1176]~E(x11761,x11762)+E(f786(x11763,x11761),f786(x11763,x11762))
% 173.53/173.44 [1177]~E(x11771,x11772)+E(f131(x11771,x11773,x11774,x11775),f131(x11772,x11773,x11774,x11775))
% 173.53/173.44 [1178]~E(x11781,x11782)+E(f131(x11783,x11781,x11784,x11785),f131(x11783,x11782,x11784,x11785))
% 173.53/173.44 [1179]~E(x11791,x11792)+E(f131(x11793,x11794,x11791,x11795),f131(x11793,x11794,x11792,x11795))
% 173.53/173.44 [1180]~E(x11801,x11802)+E(f131(x11803,x11804,x11805,x11801),f131(x11803,x11804,x11805,x11802))
% 173.53/173.44 [1181]~E(x11811,x11812)+E(f573(x11811,x11813),f573(x11812,x11813))
% 173.53/173.44 [1182]~E(x11821,x11822)+E(f573(x11823,x11821),f573(x11823,x11822))
% 173.53/173.44 [1183]~E(x11831,x11832)+E(f370(x11831,x11833,x11834,x11835,x11836,x11837,x11838,x11839,x118310),f370(x11832,x11833,x11834,x11835,x11836,x11837,x11838,x11839,x118310))
% 173.53/173.44 [1184]~E(x11841,x11842)+E(f370(x11843,x11841,x11844,x11845,x11846,x11847,x11848,x11849,x118410),f370(x11843,x11842,x11844,x11845,x11846,x11847,x11848,x11849,x118410))
% 173.53/173.44 [1185]~E(x11851,x11852)+E(f370(x11853,x11854,x11851,x11855,x11856,x11857,x11858,x11859,x118510),f370(x11853,x11854,x11852,x11855,x11856,x11857,x11858,x11859,x118510))
% 173.53/173.44 [1186]~E(x11861,x11862)+E(f370(x11863,x11864,x11865,x11861,x11866,x11867,x11868,x11869,x118610),f370(x11863,x11864,x11865,x11862,x11866,x11867,x11868,x11869,x118610))
% 173.53/173.44 [1187]~E(x11871,x11872)+E(f370(x11873,x11874,x11875,x11876,x11871,x11877,x11878,x11879,x118710),f370(x11873,x11874,x11875,x11876,x11872,x11877,x11878,x11879,x118710))
% 173.53/173.44 [1188]~E(x11881,x11882)+E(f370(x11883,x11884,x11885,x11886,x11887,x11881,x11888,x11889,x118810),f370(x11883,x11884,x11885,x11886,x11887,x11882,x11888,x11889,x118810))
% 173.53/173.44 [1189]~E(x11891,x11892)+E(f370(x11893,x11894,x11895,x11896,x11897,x11898,x11891,x11899,x118910),f370(x11893,x11894,x11895,x11896,x11897,x11898,x11892,x11899,x118910))
% 173.53/173.44 [1190]~E(x11901,x11902)+E(f370(x11903,x11904,x11905,x11906,x11907,x11908,x11909,x11901,x119010),f370(x11903,x11904,x11905,x11906,x11907,x11908,x11909,x11902,x119010))
% 173.53/173.44 [1191]~E(x11911,x11912)+E(f370(x11913,x11914,x11915,x11916,x11917,x11918,x11919,x119110,x11911),f370(x11913,x11914,x11915,x11916,x11917,x11918,x11919,x119110,x11912))
% 173.53/173.44 [1192]~E(x11921,x11922)+E(f348(x11921,x11923,x11924),f348(x11922,x11923,x11924))
% 173.53/173.44 [1193]~E(x11931,x11932)+E(f348(x11933,x11931,x11934),f348(x11933,x11932,x11934))
% 173.53/173.44 [1194]~E(x11941,x11942)+E(f348(x11943,x11944,x11941),f348(x11943,x11944,x11942))
% 173.53/173.44 [1195]~E(x11951,x11952)+E(f191(x11951,x11953,x11954,x11955),f191(x11952,x11953,x11954,x11955))
% 173.53/173.44 [1196]~E(x11961,x11962)+E(f191(x11963,x11961,x11964,x11965),f191(x11963,x11962,x11964,x11965))
% 173.53/173.44 [1197]~E(x11971,x11972)+E(f191(x11973,x11974,x11971,x11975),f191(x11973,x11974,x11972,x11975))
% 173.53/173.44 [1198]~E(x11981,x11982)+E(f191(x11983,x11984,x11985,x11981),f191(x11983,x11984,x11985,x11982))
% 173.53/173.44 [1199]~E(x11991,x11992)+E(f445(x11991,x11993,x11994,x11995,x11996,x11997,x11998,x11999),f445(x11992,x11993,x11994,x11995,x11996,x11997,x11998,x11999))
% 173.53/173.44 [1200]~E(x12001,x12002)+E(f445(x12003,x12001,x12004,x12005,x12006,x12007,x12008,x12009),f445(x12003,x12002,x12004,x12005,x12006,x12007,x12008,x12009))
% 173.53/173.44 [1201]~E(x12011,x12012)+E(f445(x12013,x12014,x12011,x12015,x12016,x12017,x12018,x12019),f445(x12013,x12014,x12012,x12015,x12016,x12017,x12018,x12019))
% 173.53/173.44 [1202]~E(x12021,x12022)+E(f445(x12023,x12024,x12025,x12021,x12026,x12027,x12028,x12029),f445(x12023,x12024,x12025,x12022,x12026,x12027,x12028,x12029))
% 173.53/173.44 [1203]~E(x12031,x12032)+E(f445(x12033,x12034,x12035,x12036,x12031,x12037,x12038,x12039),f445(x12033,x12034,x12035,x12036,x12032,x12037,x12038,x12039))
% 173.53/173.44 [1204]~E(x12041,x12042)+E(f445(x12043,x12044,x12045,x12046,x12047,x12041,x12048,x12049),f445(x12043,x12044,x12045,x12046,x12047,x12042,x12048,x12049))
% 173.53/173.44 [1205]~E(x12051,x12052)+E(f445(x12053,x12054,x12055,x12056,x12057,x12058,x12051,x12059),f445(x12053,x12054,x12055,x12056,x12057,x12058,x12052,x12059))
% 173.53/173.44 [1206]~E(x12061,x12062)+E(f445(x12063,x12064,x12065,x12066,x12067,x12068,x12069,x12061),f445(x12063,x12064,x12065,x12066,x12067,x12068,x12069,x12062))
% 173.53/173.44 [1207]~E(x12071,x12072)+E(f769(x12071,x12073,x12074,x12075,x12076),f769(x12072,x12073,x12074,x12075,x12076))
% 173.53/173.44 [1208]~E(x12081,x12082)+E(f769(x12083,x12081,x12084,x12085,x12086),f769(x12083,x12082,x12084,x12085,x12086))
% 173.53/173.44 [1209]~E(x12091,x12092)+E(f769(x12093,x12094,x12091,x12095,x12096),f769(x12093,x12094,x12092,x12095,x12096))
% 173.53/173.44 [1210]~E(x12101,x12102)+E(f769(x12103,x12104,x12105,x12101,x12106),f769(x12103,x12104,x12105,x12102,x12106))
% 173.53/173.44 [1211]~E(x12111,x12112)+E(f769(x12113,x12114,x12115,x12116,x12111),f769(x12113,x12114,x12115,x12116,x12112))
% 173.53/173.44 [1212]~E(x12121,x12122)+E(f595(x12121,x12123,x12124,x12125,x12126,x12127,x12128),f595(x12122,x12123,x12124,x12125,x12126,x12127,x12128))
% 173.53/173.44 [1213]~E(x12131,x12132)+E(f595(x12133,x12131,x12134,x12135,x12136,x12137,x12138),f595(x12133,x12132,x12134,x12135,x12136,x12137,x12138))
% 173.53/173.44 [1214]~E(x12141,x12142)+E(f595(x12143,x12144,x12141,x12145,x12146,x12147,x12148),f595(x12143,x12144,x12142,x12145,x12146,x12147,x12148))
% 173.53/173.44 [1215]~E(x12151,x12152)+E(f595(x12153,x12154,x12155,x12151,x12156,x12157,x12158),f595(x12153,x12154,x12155,x12152,x12156,x12157,x12158))
% 173.53/173.44 [1216]~E(x12161,x12162)+E(f595(x12163,x12164,x12165,x12166,x12161,x12167,x12168),f595(x12163,x12164,x12165,x12166,x12162,x12167,x12168))
% 173.53/173.44 [1217]~E(x12171,x12172)+E(f595(x12173,x12174,x12175,x12176,x12177,x12171,x12178),f595(x12173,x12174,x12175,x12176,x12177,x12172,x12178))
% 173.53/173.44 [1218]~E(x12181,x12182)+E(f595(x12183,x12184,x12185,x12186,x12187,x12188,x12181),f595(x12183,x12184,x12185,x12186,x12187,x12188,x12182))
% 173.53/173.44 [1219]~E(x12191,x12192)+E(f731(x12191,x12193,x12194,x12195,x12196,x12197,x12198),f731(x12192,x12193,x12194,x12195,x12196,x12197,x12198))
% 173.53/173.44 [1220]~E(x12201,x12202)+E(f731(x12203,x12201,x12204,x12205,x12206,x12207,x12208),f731(x12203,x12202,x12204,x12205,x12206,x12207,x12208))
% 173.53/173.44 [1221]~E(x12211,x12212)+E(f731(x12213,x12214,x12211,x12215,x12216,x12217,x12218),f731(x12213,x12214,x12212,x12215,x12216,x12217,x12218))
% 173.53/173.44 [1222]~E(x12221,x12222)+E(f731(x12223,x12224,x12225,x12221,x12226,x12227,x12228),f731(x12223,x12224,x12225,x12222,x12226,x12227,x12228))
% 173.53/173.44 [1223]~E(x12231,x12232)+E(f731(x12233,x12234,x12235,x12236,x12231,x12237,x12238),f731(x12233,x12234,x12235,x12236,x12232,x12237,x12238))
% 173.53/173.44 [1224]~E(x12241,x12242)+E(f731(x12243,x12244,x12245,x12246,x12247,x12241,x12248),f731(x12243,x12244,x12245,x12246,x12247,x12242,x12248))
% 173.53/173.44 [1225]~E(x12251,x12252)+E(f731(x12253,x12254,x12255,x12256,x12257,x12258,x12251),f731(x12253,x12254,x12255,x12256,x12257,x12258,x12252))
% 173.53/173.44 [1226]~E(x12261,x12262)+E(f739(x12261,x12263,x12264,x12265,x12266),f739(x12262,x12263,x12264,x12265,x12266))
% 173.53/173.44 [1227]~E(x12271,x12272)+E(f739(x12273,x12271,x12274,x12275,x12276),f739(x12273,x12272,x12274,x12275,x12276))
% 173.53/173.44 [1228]~E(x12281,x12282)+E(f739(x12283,x12284,x12281,x12285,x12286),f739(x12283,x12284,x12282,x12285,x12286))
% 173.53/173.44 [1229]~E(x12291,x12292)+E(f739(x12293,x12294,x12295,x12291,x12296),f739(x12293,x12294,x12295,x12292,x12296))
% 173.53/173.44 [1230]~E(x12301,x12302)+E(f739(x12303,x12304,x12305,x12306,x12301),f739(x12303,x12304,x12305,x12306,x12302))
% 173.53/173.44 [1231]~E(x12311,x12312)+E(f497(x12311,x12313,x12314),f497(x12312,x12313,x12314))
% 173.53/173.44 [1232]~E(x12321,x12322)+E(f497(x12323,x12321,x12324),f497(x12323,x12322,x12324))
% 173.53/173.44 [1233]~E(x12331,x12332)+E(f497(x12333,x12334,x12331),f497(x12333,x12334,x12332))
% 173.53/173.44 [1234]~E(x12341,x12342)+E(f691(x12341,x12343,x12344),f691(x12342,x12343,x12344))
% 173.53/173.44 [1235]~E(x12351,x12352)+E(f691(x12353,x12351,x12354),f691(x12353,x12352,x12354))
% 173.53/173.44 [1236]~E(x12361,x12362)+E(f691(x12363,x12364,x12361),f691(x12363,x12364,x12362))
% 173.53/173.44 [1237]~E(x12371,x12372)+E(f519(x12371,x12373,x12374,x12375,x12376),f519(x12372,x12373,x12374,x12375,x12376))
% 173.53/173.44 [1238]~E(x12381,x12382)+E(f519(x12383,x12381,x12384,x12385,x12386),f519(x12383,x12382,x12384,x12385,x12386))
% 173.53/173.44 [1239]~E(x12391,x12392)+E(f519(x12393,x12394,x12391,x12395,x12396),f519(x12393,x12394,x12392,x12395,x12396))
% 173.53/173.44 [1240]~E(x12401,x12402)+E(f519(x12403,x12404,x12405,x12401,x12406),f519(x12403,x12404,x12405,x12402,x12406))
% 173.53/173.44 [1241]~E(x12411,x12412)+E(f519(x12413,x12414,x12415,x12416,x12411),f519(x12413,x12414,x12415,x12416,x12412))
% 173.53/173.44 [1242]~E(x12421,x12422)+E(f630(x12421,x12423,x12424),f630(x12422,x12423,x12424))
% 173.53/173.44 [1243]~E(x12431,x12432)+E(f630(x12433,x12431,x12434),f630(x12433,x12432,x12434))
% 173.53/173.44 [1244]~E(x12441,x12442)+E(f630(x12443,x12444,x12441),f630(x12443,x12444,x12442))
% 173.53/173.44 [1245]~E(x12451,x12452)+E(f646(x12451,x12453,x12454),f646(x12452,x12453,x12454))
% 173.53/173.44 [1246]~E(x12461,x12462)+E(f646(x12463,x12461,x12464),f646(x12463,x12462,x12464))
% 173.53/173.44 [1247]~E(x12471,x12472)+E(f646(x12473,x12474,x12471),f646(x12473,x12474,x12472))
% 173.53/173.44 [1248]~E(x12481,x12482)+E(f821(x12481,x12483),f821(x12482,x12483))
% 173.53/173.44 [1249]~E(x12491,x12492)+E(f821(x12493,x12491),f821(x12493,x12492))
% 173.53/173.44 [1250]~E(x12501,x12502)+E(f799(x12501,x12503,x12504,x12505,x12506),f799(x12502,x12503,x12504,x12505,x12506))
% 173.53/173.44 [1251]~E(x12511,x12512)+E(f799(x12513,x12511,x12514,x12515,x12516),f799(x12513,x12512,x12514,x12515,x12516))
% 173.53/173.44 [1252]~E(x12521,x12522)+E(f799(x12523,x12524,x12521,x12525,x12526),f799(x12523,x12524,x12522,x12525,x12526))
% 173.53/173.44 [1253]~E(x12531,x12532)+E(f799(x12533,x12534,x12535,x12531,x12536),f799(x12533,x12534,x12535,x12532,x12536))
% 173.53/173.44 [1254]~E(x12541,x12542)+E(f799(x12543,x12544,x12545,x12546,x12541),f799(x12543,x12544,x12545,x12546,x12542))
% 173.53/173.44 [1255]~E(x12551,x12552)+E(f693(x12551,x12553,x12554,x12555),f693(x12552,x12553,x12554,x12555))
% 173.53/173.44 [1256]~E(x12561,x12562)+E(f693(x12563,x12561,x12564,x12565),f693(x12563,x12562,x12564,x12565))
% 173.53/173.44 [1257]~E(x12571,x12572)+E(f693(x12573,x12574,x12571,x12575),f693(x12573,x12574,x12572,x12575))
% 173.53/173.44 [1258]~E(x12581,x12582)+E(f693(x12583,x12584,x12585,x12581),f693(x12583,x12584,x12585,x12582))
% 173.53/173.44 [1259]~E(x12591,x12592)+E(f151(x12591,x12593,x12594),f151(x12592,x12593,x12594))
% 173.53/173.44 [1260]~E(x12601,x12602)+E(f151(x12603,x12601,x12604),f151(x12603,x12602,x12604))
% 173.53/173.44 [1261]~E(x12611,x12612)+E(f151(x12613,x12614,x12611),f151(x12613,x12614,x12612))
% 173.53/173.44 [1262]~E(x12621,x12622)+E(f276(x12621,x12623,x12624),f276(x12622,x12623,x12624))
% 173.53/173.44 [1263]~E(x12631,x12632)+E(f276(x12633,x12631,x12634),f276(x12633,x12632,x12634))
% 173.53/173.44 [1264]~E(x12641,x12642)+E(f276(x12643,x12644,x12641),f276(x12643,x12644,x12642))
% 173.53/173.44 [1265]~E(x12651,x12652)+E(f361(x12651,x12653,x12654,x12655,x12656),f361(x12652,x12653,x12654,x12655,x12656))
% 173.53/173.44 [1266]~E(x12661,x12662)+E(f361(x12663,x12661,x12664,x12665,x12666),f361(x12663,x12662,x12664,x12665,x12666))
% 173.53/173.44 [1267]~E(x12671,x12672)+E(f361(x12673,x12674,x12671,x12675,x12676),f361(x12673,x12674,x12672,x12675,x12676))
% 173.53/173.44 [1268]~E(x12681,x12682)+E(f361(x12683,x12684,x12685,x12681,x12686),f361(x12683,x12684,x12685,x12682,x12686))
% 173.53/173.44 [1269]~E(x12691,x12692)+E(f361(x12693,x12694,x12695,x12696,x12691),f361(x12693,x12694,x12695,x12696,x12692))
% 173.53/173.44 [1270]~E(x12701,x12702)+E(f798(x12701,x12703,x12704,x12705),f798(x12702,x12703,x12704,x12705))
% 173.53/173.44 [1271]~E(x12711,x12712)+E(f798(x12713,x12711,x12714,x12715),f798(x12713,x12712,x12714,x12715))
% 173.53/173.44 [1272]~E(x12721,x12722)+E(f798(x12723,x12724,x12721,x12725),f798(x12723,x12724,x12722,x12725))
% 173.53/173.44 [1273]~E(x12731,x12732)+E(f798(x12733,x12734,x12735,x12731),f798(x12733,x12734,x12735,x12732))
% 173.53/173.44 [1274]~E(x12741,x12742)+E(f618(x12741,x12743,x12744),f618(x12742,x12743,x12744))
% 173.53/173.44 [1275]~E(x12751,x12752)+E(f618(x12753,x12751,x12754),f618(x12753,x12752,x12754))
% 173.53/173.44 [1276]~E(x12761,x12762)+E(f618(x12763,x12764,x12761),f618(x12763,x12764,x12762))
% 173.53/173.44 [1277]~E(x12771,x12772)+E(f334(x12771,x12773,x12774),f334(x12772,x12773,x12774))
% 173.53/173.44 [1278]~E(x12781,x12782)+E(f334(x12783,x12781,x12784),f334(x12783,x12782,x12784))
% 173.53/173.44 [1279]~E(x12791,x12792)+E(f334(x12793,x12794,x12791),f334(x12793,x12794,x12792))
% 173.53/173.44 [1280]~E(x12801,x12802)+E(f61(x12801,x12803),f61(x12802,x12803))
% 173.53/173.44 [1281]~E(x12811,x12812)+E(f61(x12813,x12811),f61(x12813,x12812))
% 173.53/173.44 [1282]~E(x12821,x12822)+E(f378(x12821,x12823),f378(x12822,x12823))
% 173.53/173.44 [1283]~E(x12831,x12832)+E(f378(x12833,x12831),f378(x12833,x12832))
% 173.53/173.44 [1284]~E(x12841,x12842)+E(f547(x12841,x12843,x12844),f547(x12842,x12843,x12844))
% 173.53/173.44 [1285]~E(x12851,x12852)+E(f547(x12853,x12851,x12854),f547(x12853,x12852,x12854))
% 173.53/173.44 [1286]~E(x12861,x12862)+E(f547(x12863,x12864,x12861),f547(x12863,x12864,x12862))
% 173.53/173.44 [1287]~E(x12871,x12872)+E(f418(x12871,x12873,x12874),f418(x12872,x12873,x12874))
% 173.53/173.44 [1288]~E(x12881,x12882)+E(f418(x12883,x12881,x12884),f418(x12883,x12882,x12884))
% 173.53/173.44 [1289]~E(x12891,x12892)+E(f418(x12893,x12894,x12891),f418(x12893,x12894,x12892))
% 173.53/173.44 [1290]~E(x12901,x12902)+E(f475(x12901,x12903),f475(x12902,x12903))
% 173.53/173.44 [1291]~E(x12911,x12912)+E(f475(x12913,x12911),f475(x12913,x12912))
% 173.53/173.44 [1292]~E(x12921,x12922)+E(f536(x12921,x12923,x12924),f536(x12922,x12923,x12924))
% 173.53/173.44 [1293]~E(x12931,x12932)+E(f536(x12933,x12931,x12934),f536(x12933,x12932,x12934))
% 173.53/173.44 [1294]~E(x12941,x12942)+E(f536(x12943,x12944,x12941),f536(x12943,x12944,x12942))
% 173.53/173.44 [1295]~E(x12951,x12952)+E(f483(x12951,x12953,x12954),f483(x12952,x12953,x12954))
% 173.53/173.44 [1296]~E(x12961,x12962)+E(f483(x12963,x12961,x12964),f483(x12963,x12962,x12964))
% 173.53/173.44 [1297]~E(x12971,x12972)+E(f483(x12973,x12974,x12971),f483(x12973,x12974,x12972))
% 173.53/173.44 [1298]~E(x12981,x12982)+E(f241(x12981,x12983,x12984),f241(x12982,x12983,x12984))
% 173.53/173.44 [1299]~E(x12991,x12992)+E(f241(x12993,x12991,x12994),f241(x12993,x12992,x12994))
% 173.53/173.44 [1300]~E(x13001,x13002)+E(f241(x13003,x13004,x13001),f241(x13003,x13004,x13002))
% 173.53/173.44 [1301]~E(x13011,x13012)+E(f689(x13011,x13013,x13014),f689(x13012,x13013,x13014))
% 173.53/173.44 [1302]~E(x13021,x13022)+E(f689(x13023,x13021,x13024),f689(x13023,x13022,x13024))
% 173.53/173.44 [1303]~E(x13031,x13032)+E(f689(x13033,x13034,x13031),f689(x13033,x13034,x13032))
% 173.53/173.44 [1304]~E(x13041,x13042)+E(f466(x13041,x13043,x13044),f466(x13042,x13043,x13044))
% 173.53/173.44 [1305]~E(x13051,x13052)+E(f466(x13053,x13051,x13054),f466(x13053,x13052,x13054))
% 173.53/173.44 [1306]~E(x13061,x13062)+E(f466(x13063,x13064,x13061),f466(x13063,x13064,x13062))
% 173.53/173.44 [1307]~E(x13071,x13072)+E(f654(x13071,x13073,x13074),f654(x13072,x13073,x13074))
% 173.53/173.44 [1308]~E(x13081,x13082)+E(f654(x13083,x13081,x13084),f654(x13083,x13082,x13084))
% 173.53/173.44 [1309]~E(x13091,x13092)+E(f654(x13093,x13094,x13091),f654(x13093,x13094,x13092))
% 173.53/173.44 [1310]~E(x13101,x13102)+E(f523(x13101,x13103),f523(x13102,x13103))
% 173.53/173.44 [1311]~E(x13111,x13112)+E(f523(x13113,x13111),f523(x13113,x13112))
% 173.53/173.44 [1312]~E(x13121,x13122)+E(f526(x13121,x13123,x13124),f526(x13122,x13123,x13124))
% 173.53/173.44 [1313]~E(x13131,x13132)+E(f526(x13133,x13131,x13134),f526(x13133,x13132,x13134))
% 173.53/173.44 [1314]~E(x13141,x13142)+E(f526(x13143,x13144,x13141),f526(x13143,x13144,x13142))
% 173.53/173.44 [1315]~E(x13151,x13152)+E(f330(x13151,x13153,x13154),f330(x13152,x13153,x13154))
% 173.53/173.44 [1316]~E(x13161,x13162)+E(f330(x13163,x13161,x13164),f330(x13163,x13162,x13164))
% 173.53/173.44 [1317]~E(x13171,x13172)+E(f330(x13173,x13174,x13171),f330(x13173,x13174,x13172))
% 173.53/173.44 [1318]~E(x13181,x13182)+E(f729(x13181,x13183,x13184,x13185,x13186),f729(x13182,x13183,x13184,x13185,x13186))
% 173.53/173.44 [1319]~E(x13191,x13192)+E(f729(x13193,x13191,x13194,x13195,x13196),f729(x13193,x13192,x13194,x13195,x13196))
% 173.53/173.44 [1320]~E(x13201,x13202)+E(f729(x13203,x13204,x13201,x13205,x13206),f729(x13203,x13204,x13202,x13205,x13206))
% 173.53/173.44 [1321]~E(x13211,x13212)+E(f729(x13213,x13214,x13215,x13211,x13216),f729(x13213,x13214,x13215,x13212,x13216))
% 173.53/173.44 [1322]~E(x13221,x13222)+E(f729(x13223,x13224,x13225,x13226,x13221),f729(x13223,x13224,x13225,x13226,x13222))
% 173.53/173.44 [1323]~E(x13231,x13232)+E(f427(x13231,x13233,x13234,x13235,x13236),f427(x13232,x13233,x13234,x13235,x13236))
% 173.53/173.44 [1324]~E(x13241,x13242)+E(f427(x13243,x13241,x13244,x13245,x13246),f427(x13243,x13242,x13244,x13245,x13246))
% 173.53/173.44 [1325]~E(x13251,x13252)+E(f427(x13253,x13254,x13251,x13255,x13256),f427(x13253,x13254,x13252,x13255,x13256))
% 173.53/173.44 [1326]~E(x13261,x13262)+E(f427(x13263,x13264,x13265,x13261,x13266),f427(x13263,x13264,x13265,x13262,x13266))
% 173.53/173.44 [1327]~E(x13271,x13272)+E(f427(x13273,x13274,x13275,x13276,x13271),f427(x13273,x13274,x13275,x13276,x13272))
% 173.53/173.44 [1328]~E(x13281,x13282)+E(f795(x13281,x13283,x13284),f795(x13282,x13283,x13284))
% 173.53/173.44 [1329]~E(x13291,x13292)+E(f795(x13293,x13291,x13294),f795(x13293,x13292,x13294))
% 173.53/173.44 [1330]~E(x13301,x13302)+E(f795(x13303,x13304,x13301),f795(x13303,x13304,x13302))
% 173.53/173.44 [1331]~E(x13311,x13312)+E(f802(x13311,x13313,x13314,x13315),f802(x13312,x13313,x13314,x13315))
% 173.53/173.44 [1332]~E(x13321,x13322)+E(f802(x13323,x13321,x13324,x13325),f802(x13323,x13322,x13324,x13325))
% 173.53/173.44 [1333]~E(x13331,x13332)+E(f802(x13333,x13334,x13331,x13335),f802(x13333,x13334,x13332,x13335))
% 173.53/173.44 [1334]~E(x13341,x13342)+E(f802(x13343,x13344,x13345,x13341),f802(x13343,x13344,x13345,x13342))
% 173.53/173.44 [1335]~E(x13351,x13352)+E(f806(x13351,x13353,x13354,x13355),f806(x13352,x13353,x13354,x13355))
% 173.53/173.44 [1336]~E(x13361,x13362)+E(f806(x13363,x13361,x13364,x13365),f806(x13363,x13362,x13364,x13365))
% 173.53/173.44 [1337]~E(x13371,x13372)+E(f806(x13373,x13374,x13371,x13375),f806(x13373,x13374,x13372,x13375))
% 173.53/173.44 [1338]~E(x13381,x13382)+E(f806(x13383,x13384,x13385,x13381),f806(x13383,x13384,x13385,x13382))
% 173.53/173.44 [1339]~E(x13391,x13392)+E(f571(x13391,x13393,x13394,x13395),f571(x13392,x13393,x13394,x13395))
% 173.53/173.44 [1340]~E(x13401,x13402)+E(f571(x13403,x13401,x13404,x13405),f571(x13403,x13402,x13404,x13405))
% 173.53/173.44 [1341]~E(x13411,x13412)+E(f571(x13413,x13414,x13411,x13415),f571(x13413,x13414,x13412,x13415))
% 173.53/173.44 [1342]~E(x13421,x13422)+E(f571(x13423,x13424,x13425,x13421),f571(x13423,x13424,x13425,x13422))
% 173.53/173.44 [1343]~E(x13431,x13432)+E(f543(x13431,x13433,x13434),f543(x13432,x13433,x13434))
% 173.53/173.44 [1344]~E(x13441,x13442)+E(f543(x13443,x13441,x13444),f543(x13443,x13442,x13444))
% 173.53/173.44 [1345]~E(x13451,x13452)+E(f543(x13453,x13454,x13451),f543(x13453,x13454,x13452))
% 173.53/173.44 [1346]~E(x13461,x13462)+E(f273(x13461,x13463,x13464),f273(x13462,x13463,x13464))
% 173.53/173.44 [1347]~E(x13471,x13472)+E(f273(x13473,x13471,x13474),f273(x13473,x13472,x13474))
% 173.53/173.44 [1348]~E(x13481,x13482)+E(f273(x13483,x13484,x13481),f273(x13483,x13484,x13482))
% 173.53/173.44 [1349]~E(x13491,x13492)+E(f433(x13491,x13493,x13494),f433(x13492,x13493,x13494))
% 173.53/173.44 [1350]~E(x13501,x13502)+E(f433(x13503,x13501,x13504),f433(x13503,x13502,x13504))
% 173.53/173.44 [1351]~E(x13511,x13512)+E(f433(x13513,x13514,x13511),f433(x13513,x13514,x13512))
% 173.53/173.44 [1352]~E(x13521,x13522)+E(f706(x13521,x13523,x13524,x13525),f706(x13522,x13523,x13524,x13525))
% 173.53/173.44 [1353]~E(x13531,x13532)+E(f706(x13533,x13531,x13534,x13535),f706(x13533,x13532,x13534,x13535))
% 173.53/173.44 [1354]~E(x13541,x13542)+E(f706(x13543,x13544,x13541,x13545),f706(x13543,x13544,x13542,x13545))
% 173.53/173.44 [1355]~E(x13551,x13552)+E(f706(x13553,x13554,x13555,x13551),f706(x13553,x13554,x13555,x13552))
% 173.53/173.44 [1356]~E(x13561,x13562)+E(f529(x13561,x13563,x13564,x13565,x13566,x13567),f529(x13562,x13563,x13564,x13565,x13566,x13567))
% 173.53/173.44 [1357]~E(x13571,x13572)+E(f529(x13573,x13571,x13574,x13575,x13576,x13577),f529(x13573,x13572,x13574,x13575,x13576,x13577))
% 173.53/173.44 [1358]~E(x13581,x13582)+E(f529(x13583,x13584,x13581,x13585,x13586,x13587),f529(x13583,x13584,x13582,x13585,x13586,x13587))
% 173.53/173.44 [1359]~E(x13591,x13592)+E(f529(x13593,x13594,x13595,x13591,x13596,x13597),f529(x13593,x13594,x13595,x13592,x13596,x13597))
% 173.53/173.44 [1360]~E(x13601,x13602)+E(f529(x13603,x13604,x13605,x13606,x13601,x13607),f529(x13603,x13604,x13605,x13606,x13602,x13607))
% 173.53/173.44 [1361]~E(x13611,x13612)+E(f529(x13613,x13614,x13615,x13616,x13617,x13611),f529(x13613,x13614,x13615,x13616,x13617,x13612))
% 173.53/173.44 [1362]~E(x13621,x13622)+E(f346(x13621,x13623,x13624),f346(x13622,x13623,x13624))
% 173.53/173.44 [1363]~E(x13631,x13632)+E(f346(x13633,x13631,x13634),f346(x13633,x13632,x13634))
% 173.53/173.44 [1364]~E(x13641,x13642)+E(f346(x13643,x13644,x13641),f346(x13643,x13644,x13642))
% 173.53/173.44 [1365]~E(x13651,x13652)+E(f735(x13651,x13653,x13654,x13655),f735(x13652,x13653,x13654,x13655))
% 173.53/173.44 [1366]~E(x13661,x13662)+E(f735(x13663,x13661,x13664,x13665),f735(x13663,x13662,x13664,x13665))
% 173.53/173.44 [1367]~E(x13671,x13672)+E(f735(x13673,x13674,x13671,x13675),f735(x13673,x13674,x13672,x13675))
% 173.53/173.44 [1368]~E(x13681,x13682)+E(f735(x13683,x13684,x13685,x13681),f735(x13683,x13684,x13685,x13682))
% 173.53/173.44 [1369]~E(x13691,x13692)+E(f340(x13691,x13693,x13694),f340(x13692,x13693,x13694))
% 173.53/173.44 [1370]~E(x13701,x13702)+E(f340(x13703,x13701,x13704),f340(x13703,x13702,x13704))
% 173.53/173.44 [1371]~E(x13711,x13712)+E(f340(x13713,x13714,x13711),f340(x13713,x13714,x13712))
% 173.53/173.44 [1372]~E(x13721,x13722)+E(f355(x13721,x13723,x13724),f355(x13722,x13723,x13724))
% 173.53/173.44 [1373]~E(x13731,x13732)+E(f355(x13733,x13731,x13734),f355(x13733,x13732,x13734))
% 173.53/173.44 [1374]~E(x13741,x13742)+E(f355(x13743,x13744,x13741),f355(x13743,x13744,x13742))
% 173.53/173.44 [1375]~E(x13751,x13752)+E(f440(x13751,x13753,x13754),f440(x13752,x13753,x13754))
% 173.53/173.44 [1376]~E(x13761,x13762)+E(f440(x13763,x13761,x13764),f440(x13763,x13762,x13764))
% 173.53/173.44 [1377]~E(x13771,x13772)+E(f440(x13773,x13774,x13771),f440(x13773,x13774,x13772))
% 173.53/173.44 [1378]~E(x13781,x13782)+E(f757(x13781,x13783,x13784,x13785),f757(x13782,x13783,x13784,x13785))
% 173.53/173.44 [1379]~E(x13791,x13792)+E(f757(x13793,x13791,x13794,x13795),f757(x13793,x13792,x13794,x13795))
% 173.53/173.44 [1380]~E(x13801,x13802)+E(f757(x13803,x13804,x13801,x13805),f757(x13803,x13804,x13802,x13805))
% 173.53/173.44 [1381]~E(x13811,x13812)+E(f757(x13813,x13814,x13815,x13811),f757(x13813,x13814,x13815,x13812))
% 173.53/173.44 [1382]~E(x13821,x13822)+E(f358(x13821,x13823,x13824),f358(x13822,x13823,x13824))
% 173.53/173.44 [1383]~E(x13831,x13832)+E(f358(x13833,x13831,x13834),f358(x13833,x13832,x13834))
% 173.53/173.44 [1384]~E(x13841,x13842)+E(f358(x13843,x13844,x13841),f358(x13843,x13844,x13842))
% 173.53/173.44 [1385]~E(x13851,x13852)+E(f335(x13851,x13853,x13854),f335(x13852,x13853,x13854))
% 173.53/173.44 [1386]~E(x13861,x13862)+E(f335(x13863,x13861,x13864),f335(x13863,x13862,x13864))
% 173.53/173.44 [1387]~E(x13871,x13872)+E(f335(x13873,x13874,x13871),f335(x13873,x13874,x13872))
% 173.53/173.44 [1388]~E(x13881,x13882)+E(f685(x13881,x13883,x13884,x13885,x13886),f685(x13882,x13883,x13884,x13885,x13886))
% 173.53/173.44 [1389]~E(x13891,x13892)+E(f685(x13893,x13891,x13894,x13895,x13896),f685(x13893,x13892,x13894,x13895,x13896))
% 173.53/173.44 [1390]~E(x13901,x13902)+E(f685(x13903,x13904,x13901,x13905,x13906),f685(x13903,x13904,x13902,x13905,x13906))
% 173.53/173.44 [1391]~E(x13911,x13912)+E(f685(x13913,x13914,x13915,x13911,x13916),f685(x13913,x13914,x13915,x13912,x13916))
% 173.53/173.44 [1392]~E(x13921,x13922)+E(f685(x13923,x13924,x13925,x13926,x13921),f685(x13923,x13924,x13925,x13926,x13922))
% 173.53/173.44 [1393]~E(x13931,x13932)+E(f103(x13931,x13933,x13934),f103(x13932,x13933,x13934))
% 173.53/173.44 [1394]~E(x13941,x13942)+E(f103(x13943,x13941,x13944),f103(x13943,x13942,x13944))
% 173.53/173.44 [1395]~E(x13951,x13952)+E(f103(x13953,x13954,x13951),f103(x13953,x13954,x13952))
% 173.53/173.44 [1396]~E(x13961,x13962)+E(f722(x13961,x13963,x13964),f722(x13962,x13963,x13964))
% 173.53/173.44 [1397]~E(x13971,x13972)+E(f722(x13973,x13971,x13974),f722(x13973,x13972,x13974))
% 173.53/173.44 [1398]~E(x13981,x13982)+E(f722(x13983,x13984,x13981),f722(x13983,x13984,x13982))
% 173.53/173.44 [1399]~E(x13991,x13992)+E(f681(x13991,x13993,x13994),f681(x13992,x13993,x13994))
% 173.53/173.44 [1400]~E(x14001,x14002)+E(f681(x14003,x14001,x14004),f681(x14003,x14002,x14004))
% 173.53/173.44 [1401]~E(x14011,x14012)+E(f681(x14013,x14014,x14011),f681(x14013,x14014,x14012))
% 173.53/173.44 [1402]~E(x14021,x14022)+E(f342(x14021,x14023),f342(x14022,x14023))
% 173.53/173.44 [1403]~E(x14031,x14032)+E(f342(x14033,x14031),f342(x14033,x14032))
% 173.53/173.44 [1404]~E(x14041,x14042)+E(f296(x14041),f296(x14042))
% 173.53/173.44 [1405]~E(x14051,x14052)+E(f670(x14051,x14053,x14054),f670(x14052,x14053,x14054))
% 173.53/173.44 [1406]~E(x14061,x14062)+E(f670(x14063,x14061,x14064),f670(x14063,x14062,x14064))
% 173.53/173.44 [1407]~E(x14071,x14072)+E(f670(x14073,x14074,x14071),f670(x14073,x14074,x14072))
% 173.53/173.44 [1408]~E(x14081,x14082)+E(f801(x14081,x14083,x14084,x14085,x14086,x14087,x14088),f801(x14082,x14083,x14084,x14085,x14086,x14087,x14088))
% 173.53/173.44 [1409]~E(x14091,x14092)+E(f801(x14093,x14091,x14094,x14095,x14096,x14097,x14098),f801(x14093,x14092,x14094,x14095,x14096,x14097,x14098))
% 173.53/173.44 [1410]~E(x14101,x14102)+E(f801(x14103,x14104,x14101,x14105,x14106,x14107,x14108),f801(x14103,x14104,x14102,x14105,x14106,x14107,x14108))
% 173.53/173.44 [1411]~E(x14111,x14112)+E(f801(x14113,x14114,x14115,x14111,x14116,x14117,x14118),f801(x14113,x14114,x14115,x14112,x14116,x14117,x14118))
% 173.53/173.44 [1412]~E(x14121,x14122)+E(f801(x14123,x14124,x14125,x14126,x14121,x14127,x14128),f801(x14123,x14124,x14125,x14126,x14122,x14127,x14128))
% 173.53/173.44 [1413]~E(x14131,x14132)+E(f801(x14133,x14134,x14135,x14136,x14137,x14131,x14138),f801(x14133,x14134,x14135,x14136,x14137,x14132,x14138))
% 173.53/173.44 [1414]~E(x14141,x14142)+E(f801(x14143,x14144,x14145,x14146,x14147,x14148,x14141),f801(x14143,x14144,x14145,x14146,x14147,x14148,x14142))
% 173.53/173.44 [1415]~E(x14151,x14152)+E(f619(x14151,x14153,x14154,x14155,x14156,x14157),f619(x14152,x14153,x14154,x14155,x14156,x14157))
% 173.53/173.44 [1416]~E(x14161,x14162)+E(f619(x14163,x14161,x14164,x14165,x14166,x14167),f619(x14163,x14162,x14164,x14165,x14166,x14167))
% 173.53/173.44 [1417]~E(x14171,x14172)+E(f619(x14173,x14174,x14171,x14175,x14176,x14177),f619(x14173,x14174,x14172,x14175,x14176,x14177))
% 173.53/173.44 [1418]~E(x14181,x14182)+E(f619(x14183,x14184,x14185,x14181,x14186,x14187),f619(x14183,x14184,x14185,x14182,x14186,x14187))
% 173.53/173.44 [1419]~E(x14191,x14192)+E(f619(x14193,x14194,x14195,x14196,x14191,x14197),f619(x14193,x14194,x14195,x14196,x14192,x14197))
% 173.53/173.44 [1420]~E(x14201,x14202)+E(f619(x14203,x14204,x14205,x14206,x14207,x14201),f619(x14203,x14204,x14205,x14206,x14207,x14202))
% 173.53/173.44 [1421]~E(x14211,x14212)+E(f624(x14211,x14213,x14214,x14215),f624(x14212,x14213,x14214,x14215))
% 173.53/173.44 [1422]~E(x14221,x14222)+E(f624(x14223,x14221,x14224,x14225),f624(x14223,x14222,x14224,x14225))
% 173.53/173.44 [1423]~E(x14231,x14232)+E(f624(x14233,x14234,x14231,x14235),f624(x14233,x14234,x14232,x14235))
% 173.53/173.44 [1424]~E(x14241,x14242)+E(f624(x14243,x14244,x14245,x14241),f624(x14243,x14244,x14245,x14242))
% 173.53/173.44 [1425]~E(x14251,x14252)+E(f425(x14251,x14253,x14254,x14255),f425(x14252,x14253,x14254,x14255))
% 173.53/173.44 [1426]~E(x14261,x14262)+E(f425(x14263,x14261,x14264,x14265),f425(x14263,x14262,x14264,x14265))
% 173.53/173.44 [1427]~E(x14271,x14272)+E(f425(x14273,x14274,x14271,x14275),f425(x14273,x14274,x14272,x14275))
% 173.53/173.44 [1428]~E(x14281,x14282)+E(f425(x14283,x14284,x14285,x14281),f425(x14283,x14284,x14285,x14282))
% 173.53/173.44 [1429]~E(x14291,x14292)+E(f725(x14291,x14293,x14294),f725(x14292,x14293,x14294))
% 173.53/173.44 [1430]~E(x14301,x14302)+E(f725(x14303,x14301,x14304),f725(x14303,x14302,x14304))
% 173.53/173.44 [1431]~E(x14311,x14312)+E(f725(x14313,x14314,x14311),f725(x14313,x14314,x14312))
% 173.53/173.44 [1432]~E(x14321,x14322)+E(f243(x14321,x14323),f243(x14322,x14323))
% 173.53/173.44 [1433]~E(x14331,x14332)+E(f243(x14333,x14331),f243(x14333,x14332))
% 173.53/173.44 [1434]~E(x14341,x14342)+E(f220(x14341,x14343,x14344),f220(x14342,x14343,x14344))
% 173.53/173.44 [1435]~E(x14351,x14352)+E(f220(x14353,x14351,x14354),f220(x14353,x14352,x14354))
% 173.53/173.44 [1436]~E(x14361,x14362)+E(f220(x14363,x14364,x14361),f220(x14363,x14364,x14362))
% 173.53/173.44 [1437]~E(x14371,x14372)+E(f758(x14371,x14373),f758(x14372,x14373))
% 173.53/173.44 [1438]~E(x14381,x14382)+E(f758(x14383,x14381),f758(x14383,x14382))
% 173.53/173.44 [1439]~E(x14391,x14392)+E(f292(x14391,x14393),f292(x14392,x14393))
% 173.53/173.44 [1440]~E(x14401,x14402)+E(f292(x14403,x14401),f292(x14403,x14402))
% 173.53/173.44 [1441]~E(x14411,x14412)+E(f611(x14411,x14413),f611(x14412,x14413))
% 173.53/173.44 [1442]~E(x14421,x14422)+E(f611(x14423,x14421),f611(x14423,x14422))
% 173.53/173.44 [1443]~E(x14431,x14432)+E(f600(x14431,x14433,x14434),f600(x14432,x14433,x14434))
% 173.53/173.44 [1444]~E(x14441,x14442)+E(f600(x14443,x14441,x14444),f600(x14443,x14442,x14444))
% 173.53/173.44 [1445]~E(x14451,x14452)+E(f600(x14453,x14454,x14451),f600(x14453,x14454,x14452))
% 173.53/173.44 [1446]~E(x14461,x14462)+E(f699(x14461,x14463,x14464,x14465),f699(x14462,x14463,x14464,x14465))
% 173.53/173.44 [1447]~E(x14471,x14472)+E(f699(x14473,x14471,x14474,x14475),f699(x14473,x14472,x14474,x14475))
% 173.53/173.44 [1448]~E(x14481,x14482)+E(f699(x14483,x14484,x14481,x14485),f699(x14483,x14484,x14482,x14485))
% 173.53/173.44 [1449]~E(x14491,x14492)+E(f699(x14493,x14494,x14495,x14491),f699(x14493,x14494,x14495,x14492))
% 173.53/173.44 [1450]~E(x14501,x14502)+E(f429(x14501),f429(x14502))
% 173.53/173.44 [1451]~E(x14511,x14512)+E(f395(x14511,x14513,x14514),f395(x14512,x14513,x14514))
% 173.53/173.44 [1452]~E(x14521,x14522)+E(f395(x14523,x14521,x14524),f395(x14523,x14522,x14524))
% 173.53/173.44 [1453]~E(x14531,x14532)+E(f395(x14533,x14534,x14531),f395(x14533,x14534,x14532))
% 173.53/173.44 [1454]~E(x14541,x14542)+E(f596(x14541,x14543,x14544),f596(x14542,x14543,x14544))
% 173.53/173.44 [1455]~E(x14551,x14552)+E(f596(x14553,x14551,x14554),f596(x14553,x14552,x14554))
% 173.53/173.44 [1456]~E(x14561,x14562)+E(f596(x14563,x14564,x14561),f596(x14563,x14564,x14562))
% 173.53/173.44 [1457]~E(x14571,x14572)+E(f257(x14571,x14573),f257(x14572,x14573))
% 173.53/173.44 [1458]~E(x14581,x14582)+E(f257(x14583,x14581),f257(x14583,x14582))
% 173.53/173.44 [1459]~E(x14591,x14592)+E(f459(x14591,x14593,x14594,x14595),f459(x14592,x14593,x14594,x14595))
% 173.53/173.44 [1460]~E(x14601,x14602)+E(f459(x14603,x14601,x14604,x14605),f459(x14603,x14602,x14604,x14605))
% 173.53/173.44 [1461]~E(x14611,x14612)+E(f459(x14613,x14614,x14611,x14615),f459(x14613,x14614,x14612,x14615))
% 173.53/173.44 [1462]~E(x14621,x14622)+E(f459(x14623,x14624,x14625,x14621),f459(x14623,x14624,x14625,x14622))
% 173.53/173.44 [1463]~E(x14631,x14632)+E(f751(x14631,x14633,x14634,x14635,x14636,x14637,x14638,x14639),f751(x14632,x14633,x14634,x14635,x14636,x14637,x14638,x14639))
% 173.53/173.44 [1464]~E(x14641,x14642)+E(f751(x14643,x14641,x14644,x14645,x14646,x14647,x14648,x14649),f751(x14643,x14642,x14644,x14645,x14646,x14647,x14648,x14649))
% 173.53/173.44 [1465]~E(x14651,x14652)+E(f751(x14653,x14654,x14651,x14655,x14656,x14657,x14658,x14659),f751(x14653,x14654,x14652,x14655,x14656,x14657,x14658,x14659))
% 173.53/173.44 [1466]~E(x14661,x14662)+E(f751(x14663,x14664,x14665,x14661,x14666,x14667,x14668,x14669),f751(x14663,x14664,x14665,x14662,x14666,x14667,x14668,x14669))
% 173.53/173.44 [1467]~E(x14671,x14672)+E(f751(x14673,x14674,x14675,x14676,x14671,x14677,x14678,x14679),f751(x14673,x14674,x14675,x14676,x14672,x14677,x14678,x14679))
% 173.53/173.44 [1468]~E(x14681,x14682)+E(f751(x14683,x14684,x14685,x14686,x14687,x14681,x14688,x14689),f751(x14683,x14684,x14685,x14686,x14687,x14682,x14688,x14689))
% 173.53/173.44 [1469]~E(x14691,x14692)+E(f751(x14693,x14694,x14695,x14696,x14697,x14698,x14691,x14699),f751(x14693,x14694,x14695,x14696,x14697,x14698,x14692,x14699))
% 173.53/173.44 [1470]~E(x14701,x14702)+E(f751(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x14701),f751(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x14702))
% 173.53/173.44 [1471]~E(x14711,x14712)+E(f616(x14711,x14713,x14714),f616(x14712,x14713,x14714))
% 173.53/173.44 [1472]~E(x14721,x14722)+E(f616(x14723,x14721,x14724),f616(x14723,x14722,x14724))
% 173.53/173.44 [1473]~E(x14731,x14732)+E(f616(x14733,x14734,x14731),f616(x14733,x14734,x14732))
% 173.53/173.44 [1474]~E(x14741,x14742)+E(f495(x14741,x14743,x14744),f495(x14742,x14743,x14744))
% 173.53/173.44 [1475]~E(x14751,x14752)+E(f495(x14753,x14751,x14754),f495(x14753,x14752,x14754))
% 173.53/173.44 [1476]~E(x14761,x14762)+E(f495(x14763,x14764,x14761),f495(x14763,x14764,x14762))
% 173.53/173.44 [1477]~E(x14771,x14772)+E(f345(x14771,x14773,x14774),f345(x14772,x14773,x14774))
% 173.53/173.44 [1478]~E(x14781,x14782)+E(f345(x14783,x14781,x14784),f345(x14783,x14782,x14784))
% 173.53/173.44 [1479]~E(x14791,x14792)+E(f345(x14793,x14794,x14791),f345(x14793,x14794,x14792))
% 173.53/173.44 [1480]~E(x14801,x14802)+E(f298(x14801,x14803,x14804,x14805),f298(x14802,x14803,x14804,x14805))
% 173.53/173.44 [1481]~E(x14811,x14812)+E(f298(x14813,x14811,x14814,x14815),f298(x14813,x14812,x14814,x14815))
% 173.53/173.44 [1482]~E(x14821,x14822)+E(f298(x14823,x14824,x14821,x14825),f298(x14823,x14824,x14822,x14825))
% 173.53/173.44 [1483]~E(x14831,x14832)+E(f298(x14833,x14834,x14835,x14831),f298(x14833,x14834,x14835,x14832))
% 173.53/173.44 [1484]~E(x14841,x14842)+E(f528(x14841,x14843,x14844,x14845,x14846,x14847),f528(x14842,x14843,x14844,x14845,x14846,x14847))
% 173.53/173.44 [1485]~E(x14851,x14852)+E(f528(x14853,x14851,x14854,x14855,x14856,x14857),f528(x14853,x14852,x14854,x14855,x14856,x14857))
% 173.53/173.44 [1486]~E(x14861,x14862)+E(f528(x14863,x14864,x14861,x14865,x14866,x14867),f528(x14863,x14864,x14862,x14865,x14866,x14867))
% 173.53/173.44 [1487]~E(x14871,x14872)+E(f528(x14873,x14874,x14875,x14871,x14876,x14877),f528(x14873,x14874,x14875,x14872,x14876,x14877))
% 173.53/173.44 [1488]~E(x14881,x14882)+E(f528(x14883,x14884,x14885,x14886,x14881,x14887),f528(x14883,x14884,x14885,x14886,x14882,x14887))
% 173.53/173.44 [1489]~E(x14891,x14892)+E(f528(x14893,x14894,x14895,x14896,x14897,x14891),f528(x14893,x14894,x14895,x14896,x14897,x14892))
% 173.53/173.44 [1490]~E(x14901,x14902)+E(f817(x14901,x14903),f817(x14902,x14903))
% 173.53/173.44 [1491]~E(x14911,x14912)+E(f817(x14913,x14911),f817(x14913,x14912))
% 173.53/173.44 [1492]~E(x14921,x14922)+E(f481(x14921,x14923,x14924,x14925),f481(x14922,x14923,x14924,x14925))
% 173.53/173.44 [1493]~E(x14931,x14932)+E(f481(x14933,x14931,x14934,x14935),f481(x14933,x14932,x14934,x14935))
% 173.53/173.44 [1494]~E(x14941,x14942)+E(f481(x14943,x14944,x14941,x14945),f481(x14943,x14944,x14942,x14945))
% 173.53/173.44 [1495]~E(x14951,x14952)+E(f481(x14953,x14954,x14955,x14951),f481(x14953,x14954,x14955,x14952))
% 173.53/173.44 [1496]~E(x14961,x14962)+E(f539(x14961),f539(x14962))
% 173.53/173.44 [1497]~E(x14971,x14972)+E(f515(x14971,x14973,x14974),f515(x14972,x14973,x14974))
% 173.53/173.44 [1498]~E(x14981,x14982)+E(f515(x14983,x14981,x14984),f515(x14983,x14982,x14984))
% 173.53/173.44 [1499]~E(x14991,x14992)+E(f515(x14993,x14994,x14991),f515(x14993,x14994,x14992))
% 173.53/173.44 [1500]~E(x15001,x15002)+E(f752(x15001,x15003,x15004,x15005,x15006,x15007,x15008,x15009),f752(x15002,x15003,x15004,x15005,x15006,x15007,x15008,x15009))
% 173.53/173.44 [1501]~E(x15011,x15012)+E(f752(x15013,x15011,x15014,x15015,x15016,x15017,x15018,x15019),f752(x15013,x15012,x15014,x15015,x15016,x15017,x15018,x15019))
% 173.53/173.44 [1502]~E(x15021,x15022)+E(f752(x15023,x15024,x15021,x15025,x15026,x15027,x15028,x15029),f752(x15023,x15024,x15022,x15025,x15026,x15027,x15028,x15029))
% 173.53/173.44 [1503]~E(x15031,x15032)+E(f752(x15033,x15034,x15035,x15031,x15036,x15037,x15038,x15039),f752(x15033,x15034,x15035,x15032,x15036,x15037,x15038,x15039))
% 173.53/173.44 [1504]~E(x15041,x15042)+E(f752(x15043,x15044,x15045,x15046,x15041,x15047,x15048,x15049),f752(x15043,x15044,x15045,x15046,x15042,x15047,x15048,x15049))
% 173.53/173.44 [1505]~E(x15051,x15052)+E(f752(x15053,x15054,x15055,x15056,x15057,x15051,x15058,x15059),f752(x15053,x15054,x15055,x15056,x15057,x15052,x15058,x15059))
% 173.53/173.44 [1506]~E(x15061,x15062)+E(f752(x15063,x15064,x15065,x15066,x15067,x15068,x15061,x15069),f752(x15063,x15064,x15065,x15066,x15067,x15068,x15062,x15069))
% 173.53/173.44 [1507]~E(x15071,x15072)+E(f752(x15073,x15074,x15075,x15076,x15077,x15078,x15079,x15071),f752(x15073,x15074,x15075,x15076,x15077,x15078,x15079,x15072))
% 173.53/173.44 [1508]~E(x15081,x15082)+E(f544(x15081,x15083,x15084),f544(x15082,x15083,x15084))
% 173.53/173.44 [1509]~E(x15091,x15092)+E(f544(x15093,x15091,x15094),f544(x15093,x15092,x15094))
% 173.53/173.44 [1510]~E(x15101,x15102)+E(f544(x15103,x15104,x15101),f544(x15103,x15104,x15102))
% 173.53/173.44 [1511]~E(x15111,x15112)+E(f83(x15111,x15113),f83(x15112,x15113))
% 173.53/173.44 [1512]~E(x15121,x15122)+E(f83(x15123,x15121),f83(x15123,x15122))
% 173.53/173.44 [1513]~E(x15131,x15132)+E(f704(x15131,x15133,x15134),f704(x15132,x15133,x15134))
% 173.53/173.44 [1514]~E(x15141,x15142)+E(f704(x15143,x15141,x15144),f704(x15143,x15142,x15144))
% 173.53/173.44 [1515]~E(x15151,x15152)+E(f704(x15153,x15154,x15151),f704(x15153,x15154,x15152))
% 173.53/173.44 [1516]~E(x15161,x15162)+E(f724(x15161,x15163),f724(x15162,x15163))
% 173.53/173.44 [1517]~E(x15171,x15172)+E(f724(x15173,x15171),f724(x15173,x15172))
% 173.53/173.44 [1518]~E(x15181,x15182)+E(f160(x15181,x15183,x15184,x15185),f160(x15182,x15183,x15184,x15185))
% 173.53/173.44 [1519]~E(x15191,x15192)+E(f160(x15193,x15191,x15194,x15195),f160(x15193,x15192,x15194,x15195))
% 173.53/173.44 [1520]~E(x15201,x15202)+E(f160(x15203,x15204,x15201,x15205),f160(x15203,x15204,x15202,x15205))
% 173.53/173.44 [1521]~E(x15211,x15212)+E(f160(x15213,x15214,x15215,x15211),f160(x15213,x15214,x15215,x15212))
% 173.53/173.44 [1522]~E(x15221,x15222)+E(f831(x15221),f831(x15222))
% 173.53/173.44 [1523]~E(x15231,x15232)+E(f820(x15231,x15233),f820(x15232,x15233))
% 173.53/173.44 [1524]~E(x15241,x15242)+E(f820(x15243,x15241),f820(x15243,x15242))
% 173.53/173.44 [1525]~E(x15251,x15252)+E(f331(x15251,x15253,x15254),f331(x15252,x15253,x15254))
% 173.53/173.44 [1526]~E(x15261,x15262)+E(f331(x15263,x15261,x15264),f331(x15263,x15262,x15264))
% 173.53/173.44 [1527]~E(x15271,x15272)+E(f331(x15273,x15274,x15271),f331(x15273,x15274,x15272))
% 173.53/173.44 [1528]~E(x15281,x15282)+E(f741(x15281,x15283,x15284,x15285,x15286),f741(x15282,x15283,x15284,x15285,x15286))
% 173.53/173.44 [1529]~E(x15291,x15292)+E(f741(x15293,x15291,x15294,x15295,x15296),f741(x15293,x15292,x15294,x15295,x15296))
% 173.53/173.44 [1530]~E(x15301,x15302)+E(f741(x15303,x15304,x15301,x15305,x15306),f741(x15303,x15304,x15302,x15305,x15306))
% 173.53/173.44 [1531]~E(x15311,x15312)+E(f741(x15313,x15314,x15315,x15311,x15316),f741(x15313,x15314,x15315,x15312,x15316))
% 173.53/173.44 [1532]~E(x15321,x15322)+E(f741(x15323,x15324,x15325,x15326,x15321),f741(x15323,x15324,x15325,x15326,x15322))
% 173.53/173.44 [1533]~E(x15331,x15332)+E(f682(x15331,x15333,x15334,x15335),f682(x15332,x15333,x15334,x15335))
% 173.53/173.44 [1534]~E(x15341,x15342)+E(f682(x15343,x15341,x15344,x15345),f682(x15343,x15342,x15344,x15345))
% 173.53/173.44 [1535]~E(x15351,x15352)+E(f682(x15353,x15354,x15351,x15355),f682(x15353,x15354,x15352,x15355))
% 173.53/173.44 [1536]~E(x15361,x15362)+E(f682(x15363,x15364,x15365,x15361),f682(x15363,x15364,x15365,x15362))
% 173.53/173.44 [1537]~E(x15371,x15372)+E(f559(x15371,x15373,x15374,x15375,x15376),f559(x15372,x15373,x15374,x15375,x15376))
% 173.53/173.44 [1538]~E(x15381,x15382)+E(f559(x15383,x15381,x15384,x15385,x15386),f559(x15383,x15382,x15384,x15385,x15386))
% 173.53/173.44 [1539]~E(x15391,x15392)+E(f559(x15393,x15394,x15391,x15395,x15396),f559(x15393,x15394,x15392,x15395,x15396))
% 173.53/173.44 [1540]~E(x15401,x15402)+E(f559(x15403,x15404,x15405,x15401,x15406),f559(x15403,x15404,x15405,x15402,x15406))
% 173.53/173.44 [1541]~E(x15411,x15412)+E(f559(x15413,x15414,x15415,x15416,x15411),f559(x15413,x15414,x15415,x15416,x15412))
% 173.53/173.44 [1542]~E(x15421,x15422)+E(f524(x15421,x15423,x15424),f524(x15422,x15423,x15424))
% 173.53/173.44 [1543]~E(x15431,x15432)+E(f524(x15433,x15431,x15434),f524(x15433,x15432,x15434))
% 173.53/173.44 [1544]~E(x15441,x15442)+E(f524(x15443,x15444,x15441),f524(x15443,x15444,x15442))
% 173.53/173.44 [1545]~E(x15451,x15452)+E(f556(x15451,x15453),f556(x15452,x15453))
% 173.53/173.44 [1546]~E(x15461,x15462)+E(f556(x15463,x15461),f556(x15463,x15462))
% 173.53/173.44 [1547]~E(x15471,x15472)+E(f360(x15471,x15473),f360(x15472,x15473))
% 173.53/173.44 [1548]~E(x15481,x15482)+E(f360(x15483,x15481),f360(x15483,x15482))
% 173.53/173.44 [1549]~E(x15491,x15492)+E(f462(x15491,x15493),f462(x15492,x15493))
% 173.53/173.44 [1550]~E(x15501,x15502)+E(f462(x15503,x15501),f462(x15503,x15502))
% 173.53/173.44 [1551]~E(x15511,x15512)+E(f516(x15511,x15513,x15514,x15515),f516(x15512,x15513,x15514,x15515))
% 173.53/173.44 [1552]~E(x15521,x15522)+E(f516(x15523,x15521,x15524,x15525),f516(x15523,x15522,x15524,x15525))
% 173.53/173.44 [1553]~E(x15531,x15532)+E(f516(x15533,x15534,x15531,x15535),f516(x15533,x15534,x15532,x15535))
% 173.53/173.44 [1554]~E(x15541,x15542)+E(f516(x15543,x15544,x15545,x15541),f516(x15543,x15544,x15545,x15542))
% 173.53/173.44 [1555]~E(x15551,x15552)+E(f321(x15551),f321(x15552))
% 173.53/173.44 [1556]~E(x15561,x15562)+E(f712(x15561,x15563,x15564,x15565,x15566),f712(x15562,x15563,x15564,x15565,x15566))
% 173.53/173.44 [1557]~E(x15571,x15572)+E(f712(x15573,x15571,x15574,x15575,x15576),f712(x15573,x15572,x15574,x15575,x15576))
% 173.53/173.44 [1558]~E(x15581,x15582)+E(f712(x15583,x15584,x15581,x15585,x15586),f712(x15583,x15584,x15582,x15585,x15586))
% 173.53/173.44 [1559]~E(x15591,x15592)+E(f712(x15593,x15594,x15595,x15591,x15596),f712(x15593,x15594,x15595,x15592,x15596))
% 173.53/173.44 [1560]~E(x15601,x15602)+E(f712(x15603,x15604,x15605,x15606,x15601),f712(x15603,x15604,x15605,x15606,x15602))
% 173.53/173.44 [1561]~E(x15611,x15612)+E(f726(x15611,x15613,x15614,x15615,x15616),f726(x15612,x15613,x15614,x15615,x15616))
% 173.53/173.44 [1562]~E(x15621,x15622)+E(f726(x15623,x15621,x15624,x15625,x15626),f726(x15623,x15622,x15624,x15625,x15626))
% 173.53/173.44 [1563]~E(x15631,x15632)+E(f726(x15633,x15634,x15631,x15635,x15636),f726(x15633,x15634,x15632,x15635,x15636))
% 173.53/173.44 [1564]~E(x15641,x15642)+E(f726(x15643,x15644,x15645,x15641,x15646),f726(x15643,x15644,x15645,x15642,x15646))
% 173.53/173.44 [1565]~E(x15651,x15652)+E(f726(x15653,x15654,x15655,x15656,x15651),f726(x15653,x15654,x15655,x15656,x15652))
% 173.53/173.44 [1566]~E(x15661,x15662)+E(f446(x15661,x15663,x15664,x15665,x15666),f446(x15662,x15663,x15664,x15665,x15666))
% 173.53/173.44 [1567]~E(x15671,x15672)+E(f446(x15673,x15671,x15674,x15675,x15676),f446(x15673,x15672,x15674,x15675,x15676))
% 173.53/173.44 [1568]~E(x15681,x15682)+E(f446(x15683,x15684,x15681,x15685,x15686),f446(x15683,x15684,x15682,x15685,x15686))
% 173.53/173.44 [1569]~E(x15691,x15692)+E(f446(x15693,x15694,x15695,x15691,x15696),f446(x15693,x15694,x15695,x15692,x15696))
% 173.53/173.44 [1570]~E(x15701,x15702)+E(f446(x15703,x15704,x15705,x15706,x15701),f446(x15703,x15704,x15705,x15706,x15702))
% 173.53/173.44 [1571]~E(x15711,x15712)+E(f385(x15711),f385(x15712))
% 173.53/173.44 [1572]~E(x15721,x15722)+E(f416(x15721,x15723,x15724,x15725,x15726,x15727,x15728),f416(x15722,x15723,x15724,x15725,x15726,x15727,x15728))
% 173.53/173.44 [1573]~E(x15731,x15732)+E(f416(x15733,x15731,x15734,x15735,x15736,x15737,x15738),f416(x15733,x15732,x15734,x15735,x15736,x15737,x15738))
% 173.53/173.44 [1574]~E(x15741,x15742)+E(f416(x15743,x15744,x15741,x15745,x15746,x15747,x15748),f416(x15743,x15744,x15742,x15745,x15746,x15747,x15748))
% 173.53/173.44 [1575]~E(x15751,x15752)+E(f416(x15753,x15754,x15755,x15751,x15756,x15757,x15758),f416(x15753,x15754,x15755,x15752,x15756,x15757,x15758))
% 173.53/173.44 [1576]~E(x15761,x15762)+E(f416(x15763,x15764,x15765,x15766,x15761,x15767,x15768),f416(x15763,x15764,x15765,x15766,x15762,x15767,x15768))
% 173.53/173.44 [1577]~E(x15771,x15772)+E(f416(x15773,x15774,x15775,x15776,x15777,x15771,x15778),f416(x15773,x15774,x15775,x15776,x15777,x15772,x15778))
% 173.53/173.44 [1578]~E(x15781,x15782)+E(f416(x15783,x15784,x15785,x15786,x15787,x15788,x15781),f416(x15783,x15784,x15785,x15786,x15787,x15788,x15782))
% 173.53/173.44 [1579]~E(x15791,x15792)+E(f648(x15791),f648(x15792))
% 173.53/173.44 [1580]~E(x15801,x15802)+E(f467(x15801,x15803,x15804,x15805),f467(x15802,x15803,x15804,x15805))
% 173.53/173.44 [1581]~E(x15811,x15812)+E(f467(x15813,x15811,x15814,x15815),f467(x15813,x15812,x15814,x15815))
% 173.53/173.44 [1582]~E(x15821,x15822)+E(f467(x15823,x15824,x15821,x15825),f467(x15823,x15824,x15822,x15825))
% 173.53/173.44 [1583]~E(x15831,x15832)+E(f467(x15833,x15834,x15835,x15831),f467(x15833,x15834,x15835,x15832))
% 173.53/173.44 [1584]~E(x15841,x15842)+E(f748(x15841,x15843,x15844),f748(x15842,x15843,x15844))
% 173.53/173.44 [1585]~E(x15851,x15852)+E(f748(x15853,x15851,x15854),f748(x15853,x15852,x15854))
% 173.53/173.44 [1586]~E(x15861,x15862)+E(f748(x15863,x15864,x15861),f748(x15863,x15864,x15862))
% 173.53/173.44 [1587]~E(x15871,x15872)+E(f601(x15871,x15873,x15874,x15875),f601(x15872,x15873,x15874,x15875))
% 173.53/173.44 [1588]~E(x15881,x15882)+E(f601(x15883,x15881,x15884,x15885),f601(x15883,x15882,x15884,x15885))
% 173.53/173.44 [1589]~E(x15891,x15892)+E(f601(x15893,x15894,x15891,x15895),f601(x15893,x15894,x15892,x15895))
% 173.53/173.44 [1590]~E(x15901,x15902)+E(f601(x15903,x15904,x15905,x15901),f601(x15903,x15904,x15905,x15902))
% 173.53/173.44 [1591]~E(x15911,x15912)+E(f420(x15911,x15913,x15914),f420(x15912,x15913,x15914))
% 173.53/173.44 [1592]~E(x15921,x15922)+E(f420(x15923,x15921,x15924),f420(x15923,x15922,x15924))
% 173.53/173.44 [1593]~E(x15931,x15932)+E(f420(x15933,x15934,x15931),f420(x15933,x15934,x15932))
% 173.53/173.44 [1594]~E(x15941,x15942)+E(f480(x15941,x15943,x15944,x15945),f480(x15942,x15943,x15944,x15945))
% 173.53/173.44 [1595]~E(x15951,x15952)+E(f480(x15953,x15951,x15954,x15955),f480(x15953,x15952,x15954,x15955))
% 173.53/173.44 [1596]~E(x15961,x15962)+E(f480(x15963,x15964,x15961,x15965),f480(x15963,x15964,x15962,x15965))
% 173.53/173.44 [1597]~E(x15971,x15972)+E(f480(x15973,x15974,x15975,x15971),f480(x15973,x15974,x15975,x15972))
% 173.53/173.44 [1598]~E(x15981,x15982)+E(f373(x15981,x15983,x15984,x15985),f373(x15982,x15983,x15984,x15985))
% 173.53/173.44 [1599]~E(x15991,x15992)+E(f373(x15993,x15991,x15994,x15995),f373(x15993,x15992,x15994,x15995))
% 173.53/173.44 [1600]~E(x16001,x16002)+E(f373(x16003,x16004,x16001,x16005),f373(x16003,x16004,x16002,x16005))
% 173.53/173.44 [1601]~E(x16011,x16012)+E(f373(x16013,x16014,x16015,x16011),f373(x16013,x16014,x16015,x16012))
% 173.53/173.44 [1602]~E(x16021,x16022)+E(f343(x16021,x16023,x16024),f343(x16022,x16023,x16024))
% 173.53/173.44 [1603]~E(x16031,x16032)+E(f343(x16033,x16031,x16034),f343(x16033,x16032,x16034))
% 173.53/173.44 [1604]~E(x16041,x16042)+E(f343(x16043,x16044,x16041),f343(x16043,x16044,x16042))
% 173.53/173.44 [1605]~E(x16051,x16052)+E(f824(x16051,x16053,x16054,x16055),f824(x16052,x16053,x16054,x16055))
% 173.53/173.44 [1606]~E(x16061,x16062)+E(f824(x16063,x16061,x16064,x16065),f824(x16063,x16062,x16064,x16065))
% 173.53/173.44 [1607]~E(x16071,x16072)+E(f824(x16073,x16074,x16071,x16075),f824(x16073,x16074,x16072,x16075))
% 173.53/173.44 [1608]~E(x16081,x16082)+E(f824(x16083,x16084,x16085,x16081),f824(x16083,x16084,x16085,x16082))
% 173.53/173.44 [1609]~E(x16091,x16092)+E(f577(x16091,x16093,x16094,x16095),f577(x16092,x16093,x16094,x16095))
% 173.53/173.44 [1610]~E(x16101,x16102)+E(f577(x16103,x16101,x16104,x16105),f577(x16103,x16102,x16104,x16105))
% 173.53/173.44 [1611]~E(x16111,x16112)+E(f577(x16113,x16114,x16111,x16115),f577(x16113,x16114,x16112,x16115))
% 173.53/173.44 [1612]~E(x16121,x16122)+E(f577(x16123,x16124,x16125,x16121),f577(x16123,x16124,x16125,x16122))
% 173.53/173.44 [1613]~E(x16131,x16132)+E(f322(x16131,x16133,x16134),f322(x16132,x16133,x16134))
% 173.53/173.44 [1614]~E(x16141,x16142)+E(f322(x16143,x16141,x16144),f322(x16143,x16142,x16144))
% 173.53/173.44 [1615]~E(x16151,x16152)+E(f322(x16153,x16154,x16151),f322(x16153,x16154,x16152))
% 173.53/173.44 [1616]~E(x16161,x16162)+E(f808(x16161,x16163,x16164,x16165),f808(x16162,x16163,x16164,x16165))
% 173.53/173.44 [1617]~E(x16171,x16172)+E(f808(x16173,x16171,x16174,x16175),f808(x16173,x16172,x16174,x16175))
% 173.53/173.44 [1618]~E(x16181,x16182)+E(f808(x16183,x16184,x16181,x16185),f808(x16183,x16184,x16182,x16185))
% 173.53/173.44 [1619]~E(x16191,x16192)+E(f808(x16193,x16194,x16195,x16191),f808(x16193,x16194,x16195,x16192))
% 173.53/173.44 [1620]~E(x16201,x16202)+E(f698(x16201,x16203,x16204,x16205),f698(x16202,x16203,x16204,x16205))
% 173.53/173.44 [1621]~E(x16211,x16212)+E(f698(x16213,x16211,x16214,x16215),f698(x16213,x16212,x16214,x16215))
% 173.53/173.44 [1622]~E(x16221,x16222)+E(f698(x16223,x16224,x16221,x16225),f698(x16223,x16224,x16222,x16225))
% 173.53/173.44 [1623]~E(x16231,x16232)+E(f698(x16233,x16234,x16235,x16231),f698(x16233,x16234,x16235,x16232))
% 173.53/173.44 [1624]~E(x16241,x16242)+E(f380(x16241,x16243),f380(x16242,x16243))
% 173.53/173.44 [1625]~E(x16251,x16252)+E(f380(x16253,x16251),f380(x16253,x16252))
% 173.53/173.44 [1626]~E(x16261,x16262)+E(f389(x16261,x16263),f389(x16262,x16263))
% 173.53/173.44 [1627]~E(x16271,x16272)+E(f389(x16273,x16271),f389(x16273,x16272))
% 173.53/173.44 [1628]~E(x16281,x16282)+E(f553(x16281,x16283),f553(x16282,x16283))
% 173.53/173.44 [1629]~E(x16291,x16292)+E(f553(x16293,x16291),f553(x16293,x16292))
% 173.53/173.44 [1630]~E(x16301,x16302)+E(f535(x16301,x16303,x16304,x16305,x16306,x16307,x16308,x16309),f535(x16302,x16303,x16304,x16305,x16306,x16307,x16308,x16309))
% 173.53/173.44 [1631]~E(x16311,x16312)+E(f535(x16313,x16311,x16314,x16315,x16316,x16317,x16318,x16319),f535(x16313,x16312,x16314,x16315,x16316,x16317,x16318,x16319))
% 173.53/173.44 [1632]~E(x16321,x16322)+E(f535(x16323,x16324,x16321,x16325,x16326,x16327,x16328,x16329),f535(x16323,x16324,x16322,x16325,x16326,x16327,x16328,x16329))
% 173.53/173.44 [1633]~E(x16331,x16332)+E(f535(x16333,x16334,x16335,x16331,x16336,x16337,x16338,x16339),f535(x16333,x16334,x16335,x16332,x16336,x16337,x16338,x16339))
% 173.53/173.44 [1634]~E(x16341,x16342)+E(f535(x16343,x16344,x16345,x16346,x16341,x16347,x16348,x16349),f535(x16343,x16344,x16345,x16346,x16342,x16347,x16348,x16349))
% 173.53/173.44 [1635]~E(x16351,x16352)+E(f535(x16353,x16354,x16355,x16356,x16357,x16351,x16358,x16359),f535(x16353,x16354,x16355,x16356,x16357,x16352,x16358,x16359))
% 173.53/173.44 [1636]~E(x16361,x16362)+E(f535(x16363,x16364,x16365,x16366,x16367,x16368,x16361,x16369),f535(x16363,x16364,x16365,x16366,x16367,x16368,x16362,x16369))
% 173.53/173.44 [1637]~E(x16371,x16372)+E(f535(x16373,x16374,x16375,x16376,x16377,x16378,x16379,x16371),f535(x16373,x16374,x16375,x16376,x16377,x16378,x16379,x16372))
% 173.53/173.44 [1638]~E(x16381,x16382)+E(f763(x16381,x16383,x16384),f763(x16382,x16383,x16384))
% 173.53/173.44 [1639]~E(x16391,x16392)+E(f763(x16393,x16391,x16394),f763(x16393,x16392,x16394))
% 173.53/173.44 [1640]~E(x16401,x16402)+E(f763(x16403,x16404,x16401),f763(x16403,x16404,x16402))
% 173.53/173.44 [1641]~E(x16411,x16412)+E(f443(x16411,x16413,x16414,x16415,x16416),f443(x16412,x16413,x16414,x16415,x16416))
% 173.53/173.44 [1642]~E(x16421,x16422)+E(f443(x16423,x16421,x16424,x16425,x16426),f443(x16423,x16422,x16424,x16425,x16426))
% 173.53/173.44 [1643]~E(x16431,x16432)+E(f443(x16433,x16434,x16431,x16435,x16436),f443(x16433,x16434,x16432,x16435,x16436))
% 173.53/173.44 [1644]~E(x16441,x16442)+E(f443(x16443,x16444,x16445,x16441,x16446),f443(x16443,x16444,x16445,x16442,x16446))
% 173.53/173.44 [1645]~E(x16451,x16452)+E(f443(x16453,x16454,x16455,x16456,x16451),f443(x16453,x16454,x16455,x16456,x16452))
% 173.53/173.44 [1646]~E(x16461,x16462)+E(f486(x16461,x16463,x16464,x16465,x16466),f486(x16462,x16463,x16464,x16465,x16466))
% 173.53/173.44 [1647]~E(x16471,x16472)+E(f486(x16473,x16471,x16474,x16475,x16476),f486(x16473,x16472,x16474,x16475,x16476))
% 173.53/173.44 [1648]~E(x16481,x16482)+E(f486(x16483,x16484,x16481,x16485,x16486),f486(x16483,x16484,x16482,x16485,x16486))
% 173.53/173.44 [1649]~E(x16491,x16492)+E(f486(x16493,x16494,x16495,x16491,x16496),f486(x16493,x16494,x16495,x16492,x16496))
% 173.53/173.44 [1650]~E(x16501,x16502)+E(f486(x16503,x16504,x16505,x16506,x16501),f486(x16503,x16504,x16505,x16506,x16502))
% 173.53/173.44 [1651]~E(x16511,x16512)+E(f566(x16511,x16513,x16514,x16515,x16516,x16517),f566(x16512,x16513,x16514,x16515,x16516,x16517))
% 173.53/173.44 [1652]~E(x16521,x16522)+E(f566(x16523,x16521,x16524,x16525,x16526,x16527),f566(x16523,x16522,x16524,x16525,x16526,x16527))
% 173.53/173.44 [1653]~E(x16531,x16532)+E(f566(x16533,x16534,x16531,x16535,x16536,x16537),f566(x16533,x16534,x16532,x16535,x16536,x16537))
% 173.53/173.44 [1654]~E(x16541,x16542)+E(f566(x16543,x16544,x16545,x16541,x16546,x16547),f566(x16543,x16544,x16545,x16542,x16546,x16547))
% 173.53/173.44 [1655]~E(x16551,x16552)+E(f566(x16553,x16554,x16555,x16556,x16551,x16557),f566(x16553,x16554,x16555,x16556,x16552,x16557))
% 173.53/173.44 [1656]~E(x16561,x16562)+E(f566(x16563,x16564,x16565,x16566,x16567,x16561),f566(x16563,x16564,x16565,x16566,x16567,x16562))
% 173.53/173.44 [1657]~E(x16571,x16572)+E(f716(x16571,x16573,x16574,x16575,x16576,x16577),f716(x16572,x16573,x16574,x16575,x16576,x16577))
% 173.53/173.44 [1658]~E(x16581,x16582)+E(f716(x16583,x16581,x16584,x16585,x16586,x16587),f716(x16583,x16582,x16584,x16585,x16586,x16587))
% 173.53/173.44 [1659]~E(x16591,x16592)+E(f716(x16593,x16594,x16591,x16595,x16596,x16597),f716(x16593,x16594,x16592,x16595,x16596,x16597))
% 173.53/173.44 [1660]~E(x16601,x16602)+E(f716(x16603,x16604,x16605,x16601,x16606,x16607),f716(x16603,x16604,x16605,x16602,x16606,x16607))
% 173.53/173.44 [1661]~E(x16611,x16612)+E(f716(x16613,x16614,x16615,x16616,x16611,x16617),f716(x16613,x16614,x16615,x16616,x16612,x16617))
% 173.53/173.44 [1662]~E(x16621,x16622)+E(f716(x16623,x16624,x16625,x16626,x16627,x16621),f716(x16623,x16624,x16625,x16626,x16627,x16622))
% 173.53/173.44 [1663]~E(x16631,x16632)+E(f635(x16631,x16633,x16634,x16635,x16636),f635(x16632,x16633,x16634,x16635,x16636))
% 173.53/173.44 [1664]~E(x16641,x16642)+E(f635(x16643,x16641,x16644,x16645,x16646),f635(x16643,x16642,x16644,x16645,x16646))
% 173.53/173.44 [1665]~E(x16651,x16652)+E(f635(x16653,x16654,x16651,x16655,x16656),f635(x16653,x16654,x16652,x16655,x16656))
% 173.53/173.44 [1666]~E(x16661,x16662)+E(f635(x16663,x16664,x16665,x16661,x16666),f635(x16663,x16664,x16665,x16662,x16666))
% 173.53/173.44 [1667]~E(x16671,x16672)+E(f635(x16673,x16674,x16675,x16676,x16671),f635(x16673,x16674,x16675,x16676,x16672))
% 173.53/173.44 [1668]~E(x16681,x16682)+E(f660(x16681,x16683,x16684),f660(x16682,x16683,x16684))
% 173.53/173.44 [1669]~E(x16691,x16692)+E(f660(x16693,x16691,x16694),f660(x16693,x16692,x16694))
% 173.53/173.44 [1670]~E(x16701,x16702)+E(f660(x16703,x16704,x16701),f660(x16703,x16704,x16702))
% 173.53/173.44 [1671]~E(x16711,x16712)+E(f668(x16711,x16713),f668(x16712,x16713))
% 173.53/173.44 [1672]~E(x16721,x16722)+E(f668(x16723,x16721),f668(x16723,x16722))
% 173.53/173.44 [1673]~E(x16731,x16732)+E(f513(x16731,x16733,x16734,x16735,x16736),f513(x16732,x16733,x16734,x16735,x16736))
% 173.53/173.44 [1674]~E(x16741,x16742)+E(f513(x16743,x16741,x16744,x16745,x16746),f513(x16743,x16742,x16744,x16745,x16746))
% 173.53/173.44 [1675]~E(x16751,x16752)+E(f513(x16753,x16754,x16751,x16755,x16756),f513(x16753,x16754,x16752,x16755,x16756))
% 173.53/173.44 [1676]~E(x16761,x16762)+E(f513(x16763,x16764,x16765,x16761,x16766),f513(x16763,x16764,x16765,x16762,x16766))
% 173.53/173.44 [1677]~E(x16771,x16772)+E(f513(x16773,x16774,x16775,x16776,x16771),f513(x16773,x16774,x16775,x16776,x16772))
% 173.53/173.44 [1678]~E(x16781,x16782)+E(f683(x16781,x16783,x16784,x16785),f683(x16782,x16783,x16784,x16785))
% 173.53/173.44 [1679]~E(x16791,x16792)+E(f683(x16793,x16791,x16794,x16795),f683(x16793,x16792,x16794,x16795))
% 173.53/173.44 [1680]~E(x16801,x16802)+E(f683(x16803,x16804,x16801,x16805),f683(x16803,x16804,x16802,x16805))
% 173.53/173.44 [1681]~E(x16811,x16812)+E(f683(x16813,x16814,x16815,x16811),f683(x16813,x16814,x16815,x16812))
% 173.53/173.44 [1682]~E(x16821,x16822)+E(f667(x16821,x16823,x16824),f667(x16822,x16823,x16824))
% 173.53/173.44 [1683]~E(x16831,x16832)+E(f667(x16833,x16831,x16834),f667(x16833,x16832,x16834))
% 173.53/173.44 [1684]~E(x16841,x16842)+E(f667(x16843,x16844,x16841),f667(x16843,x16844,x16842))
% 173.53/173.44 [1685]~E(x16851,x16852)+E(f836(x16851,x16853,x16854,x16855),f836(x16852,x16853,x16854,x16855))
% 173.53/173.44 [1686]~E(x16861,x16862)+E(f836(x16863,x16861,x16864,x16865),f836(x16863,x16862,x16864,x16865))
% 173.53/173.44 [1687]~E(x16871,x16872)+E(f836(x16873,x16874,x16871,x16875),f836(x16873,x16874,x16872,x16875))
% 173.53/173.44 [1688]~E(x16881,x16882)+E(f836(x16883,x16884,x16885,x16881),f836(x16883,x16884,x16885,x16882))
% 173.53/173.44 [1689]~E(x16891,x16892)+E(f451(x16891,x16893,x16894,x16895),f451(x16892,x16893,x16894,x16895))
% 173.53/173.44 [1690]~E(x16901,x16902)+E(f451(x16903,x16901,x16904,x16905),f451(x16903,x16902,x16904,x16905))
% 173.53/173.44 [1691]~E(x16911,x16912)+E(f451(x16913,x16914,x16911,x16915),f451(x16913,x16914,x16912,x16915))
% 173.53/173.44 [1692]~E(x16921,x16922)+E(f451(x16923,x16924,x16925,x16921),f451(x16923,x16924,x16925,x16922))
% 173.53/173.44 [1693]~E(x16931,x16932)+E(f578(x16931,x16933,x16934,x16935),f578(x16932,x16933,x16934,x16935))
% 173.53/173.44 [1694]~E(x16941,x16942)+E(f578(x16943,x16941,x16944,x16945),f578(x16943,x16942,x16944,x16945))
% 173.53/173.44 [1695]~E(x16951,x16952)+E(f578(x16953,x16954,x16951,x16955),f578(x16953,x16954,x16952,x16955))
% 173.53/173.44 [1696]~E(x16961,x16962)+E(f578(x16963,x16964,x16965,x16961),f578(x16963,x16964,x16965,x16962))
% 173.53/173.44 [1697]~E(x16971,x16972)+E(f349(x16971,x16973,x16974),f349(x16972,x16973,x16974))
% 173.53/173.44 [1698]~E(x16981,x16982)+E(f349(x16983,x16981,x16984),f349(x16983,x16982,x16984))
% 173.53/173.44 [1699]~E(x16991,x16992)+E(f349(x16993,x16994,x16991),f349(x16993,x16994,x16992))
% 173.53/173.44 [1700]~E(x17001,x17002)+E(f605(x17001,x17003,x17004,x17005),f605(x17002,x17003,x17004,x17005))
% 173.53/173.44 [1701]~E(x17011,x17012)+E(f605(x17013,x17011,x17014,x17015),f605(x17013,x17012,x17014,x17015))
% 173.53/173.44 [1702]~E(x17021,x17022)+E(f605(x17023,x17024,x17021,x17025),f605(x17023,x17024,x17022,x17025))
% 173.53/173.44 [1703]~E(x17031,x17032)+E(f605(x17033,x17034,x17035,x17031),f605(x17033,x17034,x17035,x17032))
% 173.53/173.44 [1704]~E(x17041,x17042)+E(f705(x17041,x17043,x17044,x17045),f705(x17042,x17043,x17044,x17045))
% 173.53/173.44 [1705]~E(x17051,x17052)+E(f705(x17053,x17051,x17054,x17055),f705(x17053,x17052,x17054,x17055))
% 173.53/173.44 [1706]~E(x17061,x17062)+E(f705(x17063,x17064,x17061,x17065),f705(x17063,x17064,x17062,x17065))
% 173.53/173.44 [1707]~E(x17071,x17072)+E(f705(x17073,x17074,x17075,x17071),f705(x17073,x17074,x17075,x17072))
% 173.53/173.44 [1708]~E(x17081,x17082)+E(f552(x17081,x17083,x17084,x17085,x17086,x17087,x17088),f552(x17082,x17083,x17084,x17085,x17086,x17087,x17088))
% 173.53/173.44 [1709]~E(x17091,x17092)+E(f552(x17093,x17091,x17094,x17095,x17096,x17097,x17098),f552(x17093,x17092,x17094,x17095,x17096,x17097,x17098))
% 173.53/173.44 [1710]~E(x17101,x17102)+E(f552(x17103,x17104,x17101,x17105,x17106,x17107,x17108),f552(x17103,x17104,x17102,x17105,x17106,x17107,x17108))
% 173.53/173.44 [1711]~E(x17111,x17112)+E(f552(x17113,x17114,x17115,x17111,x17116,x17117,x17118),f552(x17113,x17114,x17115,x17112,x17116,x17117,x17118))
% 173.53/173.44 [1712]~E(x17121,x17122)+E(f552(x17123,x17124,x17125,x17126,x17121,x17127,x17128),f552(x17123,x17124,x17125,x17126,x17122,x17127,x17128))
% 173.53/173.44 [1713]~E(x17131,x17132)+E(f552(x17133,x17134,x17135,x17136,x17137,x17131,x17138),f552(x17133,x17134,x17135,x17136,x17137,x17132,x17138))
% 173.53/173.44 [1714]~E(x17141,x17142)+E(f552(x17143,x17144,x17145,x17146,x17147,x17148,x17141),f552(x17143,x17144,x17145,x17146,x17147,x17148,x17142))
% 173.53/173.44 [1715]~E(x17151,x17152)+E(f614(x17151,x17153),f614(x17152,x17153))
% 173.53/173.44 [1716]~E(x17161,x17162)+E(f614(x17163,x17161),f614(x17163,x17162))
% 173.53/173.44 [1717]~E(x17171,x17172)+E(f568(x17171,x17173,x17174,x17175),f568(x17172,x17173,x17174,x17175))
% 173.53/173.44 [1718]~E(x17181,x17182)+E(f568(x17183,x17181,x17184,x17185),f568(x17183,x17182,x17184,x17185))
% 173.53/173.44 [1719]~E(x17191,x17192)+E(f568(x17193,x17194,x17191,x17195),f568(x17193,x17194,x17192,x17195))
% 173.53/173.44 [1720]~E(x17201,x17202)+E(f568(x17203,x17204,x17205,x17201),f568(x17203,x17204,x17205,x17202))
% 173.53/173.44 [1721]~E(x17211,x17212)+E(f488(x17211,x17213,x17214,x17215,x17216),f488(x17212,x17213,x17214,x17215,x17216))
% 173.53/173.44 [1722]~E(x17221,x17222)+E(f488(x17223,x17221,x17224,x17225,x17226),f488(x17223,x17222,x17224,x17225,x17226))
% 173.53/173.44 [1723]~E(x17231,x17232)+E(f488(x17233,x17234,x17231,x17235,x17236),f488(x17233,x17234,x17232,x17235,x17236))
% 173.53/173.44 [1724]~E(x17241,x17242)+E(f488(x17243,x17244,x17245,x17241,x17246),f488(x17243,x17244,x17245,x17242,x17246))
% 173.53/173.44 [1725]~E(x17251,x17252)+E(f488(x17253,x17254,x17255,x17256,x17251),f488(x17253,x17254,x17255,x17256,x17252))
% 173.53/173.44 [1726]~E(x17261,x17262)+E(f823(x17261),f823(x17262))
% 173.53/173.44 [1727]~E(x17271,x17272)+E(f588(x17271,x17273,x17274,x17275,x17276),f588(x17272,x17273,x17274,x17275,x17276))
% 173.53/173.44 [1728]~E(x17281,x17282)+E(f588(x17283,x17281,x17284,x17285,x17286),f588(x17283,x17282,x17284,x17285,x17286))
% 173.53/173.44 [1729]~E(x17291,x17292)+E(f588(x17293,x17294,x17291,x17295,x17296),f588(x17293,x17294,x17292,x17295,x17296))
% 173.53/173.44 [1730]~E(x17301,x17302)+E(f588(x17303,x17304,x17305,x17301,x17306),f588(x17303,x17304,x17305,x17302,x17306))
% 173.53/173.44 [1731]~E(x17311,x17312)+E(f588(x17313,x17314,x17315,x17316,x17311),f588(x17313,x17314,x17315,x17316,x17312))
% 173.53/173.44 [1732]~E(x17321,x17322)+E(f208(x17321,x17323),f208(x17322,x17323))
% 173.53/173.44 [1733]~E(x17331,x17332)+E(f208(x17333,x17331),f208(x17333,x17332))
% 173.53/173.44 [1734]~E(x17341,x17342)+E(f814(x17341,x17343,x17344,x17345),f814(x17342,x17343,x17344,x17345))
% 173.53/173.44 [1735]~E(x17351,x17352)+E(f814(x17353,x17351,x17354,x17355),f814(x17353,x17352,x17354,x17355))
% 173.53/173.44 [1736]~E(x17361,x17362)+E(f814(x17363,x17364,x17361,x17365),f814(x17363,x17364,x17362,x17365))
% 173.53/173.44 [1737]~E(x17371,x17372)+E(f814(x17373,x17374,x17375,x17371),f814(x17373,x17374,x17375,x17372))
% 173.53/173.44 [1738]~E(x17381,x17382)+E(f703(x17381,x17383,x17384),f703(x17382,x17383,x17384))
% 173.53/173.44 [1739]~E(x17391,x17392)+E(f703(x17393,x17391,x17394),f703(x17393,x17392,x17394))
% 173.53/173.44 [1740]~E(x17401,x17402)+E(f703(x17403,x17404,x17401),f703(x17403,x17404,x17402))
% 173.53/173.44 [1741]~E(x17411,x17412)+E(f664(x17411,x17413,x17414,x17415,x17416),f664(x17412,x17413,x17414,x17415,x17416))
% 173.53/173.44 [1742]~E(x17421,x17422)+E(f664(x17423,x17421,x17424,x17425,x17426),f664(x17423,x17422,x17424,x17425,x17426))
% 173.53/173.44 [1743]~E(x17431,x17432)+E(f664(x17433,x17434,x17431,x17435,x17436),f664(x17433,x17434,x17432,x17435,x17436))
% 173.53/173.44 [1744]~E(x17441,x17442)+E(f664(x17443,x17444,x17445,x17441,x17446),f664(x17443,x17444,x17445,x17442,x17446))
% 173.53/173.44 [1745]~E(x17451,x17452)+E(f664(x17453,x17454,x17455,x17456,x17451),f664(x17453,x17454,x17455,x17456,x17452))
% 173.53/173.44 [1746]~E(x17461,x17462)+E(f347(x17461,x17463,x17464),f347(x17462,x17463,x17464))
% 173.53/173.44 [1747]~E(x17471,x17472)+E(f347(x17473,x17471,x17474),f347(x17473,x17472,x17474))
% 173.53/173.44 [1748]~E(x17481,x17482)+E(f347(x17483,x17484,x17481),f347(x17483,x17484,x17482))
% 173.53/173.44 [1749]~E(x17491,x17492)+E(f697(x17491,x17493,x17494),f697(x17492,x17493,x17494))
% 173.53/173.44 [1750]~E(x17501,x17502)+E(f697(x17503,x17501,x17504),f697(x17503,x17502,x17504))
% 173.53/173.44 [1751]~E(x17511,x17512)+E(f697(x17513,x17514,x17511),f697(x17513,x17514,x17512))
% 173.53/173.44 [1752]~E(x17521,x17522)+E(f527(x17521,x17523,x17524,x17525),f527(x17522,x17523,x17524,x17525))
% 173.53/173.44 [1753]~E(x17531,x17532)+E(f527(x17533,x17531,x17534,x17535),f527(x17533,x17532,x17534,x17535))
% 173.53/173.44 [1754]~E(x17541,x17542)+E(f527(x17543,x17544,x17541,x17545),f527(x17543,x17544,x17542,x17545))
% 173.53/173.44 [1755]~E(x17551,x17552)+E(f527(x17553,x17554,x17555,x17551),f527(x17553,x17554,x17555,x17552))
% 173.53/173.44 [1756]~E(x17561,x17562)+E(f230(x17561,x17563),f230(x17562,x17563))
% 173.53/173.44 [1757]~E(x17571,x17572)+E(f230(x17573,x17571),f230(x17573,x17572))
% 173.53/173.44 [1758]~E(x17581,x17582)+E(f229(x17581,x17583),f229(x17582,x17583))
% 173.53/173.44 [1759]~E(x17591,x17592)+E(f229(x17593,x17591),f229(x17593,x17592))
% 173.53/173.44 [1760]~E(x17601,x17602)+E(f679(x17601,x17603,x17604),f679(x17602,x17603,x17604))
% 173.53/173.44 [1761]~E(x17611,x17612)+E(f679(x17613,x17611,x17614),f679(x17613,x17612,x17614))
% 173.53/173.44 [1762]~E(x17621,x17622)+E(f679(x17623,x17624,x17621),f679(x17623,x17624,x17622))
% 173.53/173.44 [1763]~E(x17631,x17632)+E(f464(x17631,x17633),f464(x17632,x17633))
% 173.53/173.44 [1764]~E(x17641,x17642)+E(f464(x17643,x17641),f464(x17643,x17642))
% 173.53/173.44 [1765]~E(x17651,x17652)+E(f158(x17651,x17653),f158(x17652,x17653))
% 173.53/173.44 [1766]~E(x17661,x17662)+E(f158(x17663,x17661),f158(x17663,x17662))
% 173.53/173.44 [1767]~E(x17671,x17672)+E(f598(x17671,x17673),f598(x17672,x17673))
% 173.53/173.44 [1768]~E(x17681,x17682)+E(f598(x17683,x17681),f598(x17683,x17682))
% 173.53/173.44 [1769]~E(x17691,x17692)+E(f621(x17691,x17693,x17694,x17695,x17696),f621(x17692,x17693,x17694,x17695,x17696))
% 173.53/173.44 [1770]~E(x17701,x17702)+E(f621(x17703,x17701,x17704,x17705,x17706),f621(x17703,x17702,x17704,x17705,x17706))
% 173.53/173.44 [1771]~E(x17711,x17712)+E(f621(x17713,x17714,x17711,x17715,x17716),f621(x17713,x17714,x17712,x17715,x17716))
% 173.53/173.44 [1772]~E(x17721,x17722)+E(f621(x17723,x17724,x17725,x17721,x17726),f621(x17723,x17724,x17725,x17722,x17726))
% 173.53/173.44 [1773]~E(x17731,x17732)+E(f621(x17733,x17734,x17735,x17736,x17731),f621(x17733,x17734,x17735,x17736,x17732))
% 173.53/173.44 [1774]~E(x17741,x17742)+E(f707(x17741,x17743,x17744,x17745,x17746,x17747),f707(x17742,x17743,x17744,x17745,x17746,x17747))
% 173.53/173.44 [1775]~E(x17751,x17752)+E(f707(x17753,x17751,x17754,x17755,x17756,x17757),f707(x17753,x17752,x17754,x17755,x17756,x17757))
% 173.53/173.44 [1776]~E(x17761,x17762)+E(f707(x17763,x17764,x17761,x17765,x17766,x17767),f707(x17763,x17764,x17762,x17765,x17766,x17767))
% 173.53/173.44 [1777]~E(x17771,x17772)+E(f707(x17773,x17774,x17775,x17771,x17776,x17777),f707(x17773,x17774,x17775,x17772,x17776,x17777))
% 173.53/173.44 [1778]~E(x17781,x17782)+E(f707(x17783,x17784,x17785,x17786,x17781,x17787),f707(x17783,x17784,x17785,x17786,x17782,x17787))
% 173.53/173.44 [1779]~E(x17791,x17792)+E(f707(x17793,x17794,x17795,x17796,x17797,x17791),f707(x17793,x17794,x17795,x17796,x17797,x17792))
% 173.53/173.44 [1780]~E(x17801,x17802)+E(f444(x17801,x17803,x17804,x17805,x17806),f444(x17802,x17803,x17804,x17805,x17806))
% 173.53/173.44 [1781]~E(x17811,x17812)+E(f444(x17813,x17811,x17814,x17815,x17816),f444(x17813,x17812,x17814,x17815,x17816))
% 173.53/173.44 [1782]~E(x17821,x17822)+E(f444(x17823,x17824,x17821,x17825,x17826),f444(x17823,x17824,x17822,x17825,x17826))
% 173.53/173.44 [1783]~E(x17831,x17832)+E(f444(x17833,x17834,x17835,x17831,x17836),f444(x17833,x17834,x17835,x17832,x17836))
% 173.53/173.44 [1784]~E(x17841,x17842)+E(f444(x17843,x17844,x17845,x17846,x17841),f444(x17843,x17844,x17845,x17846,x17842))
% 173.53/173.44 [1785]~E(x17851,x17852)+E(f337(x17851,x17853,x17854),f337(x17852,x17853,x17854))
% 173.53/173.44 [1786]~E(x17861,x17862)+E(f337(x17863,x17861,x17864),f337(x17863,x17862,x17864))
% 173.53/173.44 [1787]~E(x17871,x17872)+E(f337(x17873,x17874,x17871),f337(x17873,x17874,x17872))
% 173.53/173.44 [1788]~E(x17881,x17882)+E(f447(x17881,x17883,x17884,x17885),f447(x17882,x17883,x17884,x17885))
% 173.53/173.44 [1789]~E(x17891,x17892)+E(f447(x17893,x17891,x17894,x17895),f447(x17893,x17892,x17894,x17895))
% 173.53/173.44 [1790]~E(x17901,x17902)+E(f447(x17903,x17904,x17901,x17905),f447(x17903,x17904,x17902,x17905))
% 173.53/173.44 [1791]~E(x17911,x17912)+E(f447(x17913,x17914,x17915,x17911),f447(x17913,x17914,x17915,x17912))
% 173.53/173.44 [1792]~E(x17921,x17922)+E(f434(x17921,x17923,x17924),f434(x17922,x17923,x17924))
% 173.53/173.44 [1793]~E(x17931,x17932)+E(f434(x17933,x17931,x17934),f434(x17933,x17932,x17934))
% 173.53/173.44 [1794]~E(x17941,x17942)+E(f434(x17943,x17944,x17941),f434(x17943,x17944,x17942))
% 173.53/173.44 [1795]~E(x17951,x17952)+E(f37(x17951,x17953,x17954,x17955,x17956,x17957,x17958,x17959,x179510,x179511),f37(x17952,x17953,x17954,x17955,x17956,x17957,x17958,x17959,x179510,x179511))
% 173.53/173.44 [1796]~E(x17961,x17962)+E(f37(x17963,x17961,x17964,x17965,x17966,x17967,x17968,x17969,x179610,x179611),f37(x17963,x17962,x17964,x17965,x17966,x17967,x17968,x17969,x179610,x179611))
% 173.53/173.44 [1797]~E(x17971,x17972)+E(f37(x17973,x17974,x17971,x17975,x17976,x17977,x17978,x17979,x179710,x179711),f37(x17973,x17974,x17972,x17975,x17976,x17977,x17978,x17979,x179710,x179711))
% 173.53/173.44 [1798]~E(x17981,x17982)+E(f37(x17983,x17984,x17985,x17981,x17986,x17987,x17988,x17989,x179810,x179811),f37(x17983,x17984,x17985,x17982,x17986,x17987,x17988,x17989,x179810,x179811))
% 173.53/173.44 [1799]~E(x17991,x17992)+E(f37(x17993,x17994,x17995,x17996,x17991,x17997,x17998,x17999,x179910,x179911),f37(x17993,x17994,x17995,x17996,x17992,x17997,x17998,x17999,x179910,x179911))
% 173.53/173.44 [1800]~E(x18001,x18002)+E(f37(x18003,x18004,x18005,x18006,x18007,x18001,x18008,x18009,x180010,x180011),f37(x18003,x18004,x18005,x18006,x18007,x18002,x18008,x18009,x180010,x180011))
% 173.53/173.44 [1801]~E(x18011,x18012)+E(f37(x18013,x18014,x18015,x18016,x18017,x18018,x18011,x18019,x180110,x180111),f37(x18013,x18014,x18015,x18016,x18017,x18018,x18012,x18019,x180110,x180111))
% 173.53/173.44 [1802]~E(x18021,x18022)+E(f37(x18023,x18024,x18025,x18026,x18027,x18028,x18029,x18021,x180210,x180211),f37(x18023,x18024,x18025,x18026,x18027,x18028,x18029,x18022,x180210,x180211))
% 173.53/173.44 [1803]~E(x18031,x18032)+E(f37(x18033,x18034,x18035,x18036,x18037,x18038,x18039,x180310,x18031,x180311),f37(x18033,x18034,x18035,x18036,x18037,x18038,x18039,x180310,x18032,x180311))
% 173.53/173.44 [1804]~E(x18041,x18042)+E(f37(x18043,x18044,x18045,x18046,x18047,x18048,x18049,x180410,x180411,x18041),f37(x18043,x18044,x18045,x18046,x18047,x18048,x18049,x180410,x180411,x18042))
% 173.53/173.44 [1805]~E(x18051,x18052)+E(f546(x18051,x18053),f546(x18052,x18053))
% 173.53/173.44 [1806]~E(x18061,x18062)+E(f546(x18063,x18061),f546(x18063,x18062))
% 173.53/173.44 [1807]~E(x18071,x18072)+E(f107(x18071,x18073,x18074,x18075),f107(x18072,x18073,x18074,x18075))
% 173.53/173.44 [1808]~E(x18081,x18082)+E(f107(x18083,x18081,x18084,x18085),f107(x18083,x18082,x18084,x18085))
% 173.53/173.44 [1809]~E(x18091,x18092)+E(f107(x18093,x18094,x18091,x18095),f107(x18093,x18094,x18092,x18095))
% 173.53/173.44 [1810]~E(x18101,x18102)+E(f107(x18103,x18104,x18105,x18101),f107(x18103,x18104,x18105,x18102))
% 173.53/173.44 [1811]~E(x18111,x18112)+E(f542(x18111,x18113,x18114),f542(x18112,x18113,x18114))
% 173.53/173.44 [1812]~E(x18121,x18122)+E(f542(x18123,x18121,x18124),f542(x18123,x18122,x18124))
% 173.53/173.44 [1813]~E(x18131,x18132)+E(f542(x18133,x18134,x18131),f542(x18133,x18134,x18132))
% 173.53/173.44 [1814]~E(x18141,x18142)+E(f383(x18141,x18143,x18144,x18145),f383(x18142,x18143,x18144,x18145))
% 173.53/173.44 [1815]~E(x18151,x18152)+E(f383(x18153,x18151,x18154,x18155),f383(x18153,x18152,x18154,x18155))
% 173.53/173.44 [1816]~E(x18161,x18162)+E(f383(x18163,x18164,x18161,x18165),f383(x18163,x18164,x18162,x18165))
% 173.53/173.44 [1817]~E(x18171,x18172)+E(f383(x18173,x18174,x18175,x18171),f383(x18173,x18174,x18175,x18172))
% 173.53/173.44 [1818]~E(x18181,x18182)+E(f412(x18181,x18183,x18184,x18185),f412(x18182,x18183,x18184,x18185))
% 173.53/173.44 [1819]~E(x18191,x18192)+E(f412(x18193,x18191,x18194,x18195),f412(x18193,x18192,x18194,x18195))
% 173.53/173.44 [1820]~E(x18201,x18202)+E(f412(x18203,x18204,x18201,x18205),f412(x18203,x18204,x18202,x18205))
% 173.53/173.44 [1821]~E(x18211,x18212)+E(f412(x18213,x18214,x18215,x18211),f412(x18213,x18214,x18215,x18212))
% 173.53/173.44 [1822]~E(x18221,x18222)+E(f520(x18221,x18223,x18224,x18225,x18226),f520(x18222,x18223,x18224,x18225,x18226))
% 173.53/173.44 [1823]~E(x18231,x18232)+E(f520(x18233,x18231,x18234,x18235,x18236),f520(x18233,x18232,x18234,x18235,x18236))
% 173.53/173.44 [1824]~E(x18241,x18242)+E(f520(x18243,x18244,x18241,x18245,x18246),f520(x18243,x18244,x18242,x18245,x18246))
% 173.53/173.44 [1825]~E(x18251,x18252)+E(f520(x18253,x18254,x18255,x18251,x18256),f520(x18253,x18254,x18255,x18252,x18256))
% 173.53/173.44 [1826]~E(x18261,x18262)+E(f520(x18263,x18264,x18265,x18266,x18261),f520(x18263,x18264,x18265,x18266,x18262))
% 173.53/173.44 [1827]~E(x18271,x18272)+E(f623(x18271,x18273,x18274,x18275,x18276),f623(x18272,x18273,x18274,x18275,x18276))
% 173.53/173.44 [1828]~E(x18281,x18282)+E(f623(x18283,x18281,x18284,x18285,x18286),f623(x18283,x18282,x18284,x18285,x18286))
% 173.53/173.44 [1829]~E(x18291,x18292)+E(f623(x18293,x18294,x18291,x18295,x18296),f623(x18293,x18294,x18292,x18295,x18296))
% 173.53/173.44 [1830]~E(x18301,x18302)+E(f623(x18303,x18304,x18305,x18301,x18306),f623(x18303,x18304,x18305,x18302,x18306))
% 173.53/173.44 [1831]~E(x18311,x18312)+E(f623(x18313,x18314,x18315,x18316,x18311),f623(x18313,x18314,x18315,x18316,x18312))
% 173.53/173.44 [1832]~E(x18321,x18322)+E(f756(x18321,x18323,x18324),f756(x18322,x18323,x18324))
% 173.53/173.44 [1833]~E(x18331,x18332)+E(f756(x18333,x18331,x18334),f756(x18333,x18332,x18334))
% 173.53/173.44 [1834]~E(x18341,x18342)+E(f756(x18343,x18344,x18341),f756(x18343,x18344,x18342))
% 173.53/173.44 [1835]~E(x18351,x18352)+E(f430(x18351,x18353),f430(x18352,x18353))
% 173.53/173.44 [1836]~E(x18361,x18362)+E(f430(x18363,x18361),f430(x18363,x18362))
% 173.53/173.44 [1837]~E(x18371,x18372)+E(f642(x18371,x18373,x18374),f642(x18372,x18373,x18374))
% 173.53/173.44 [1838]~E(x18381,x18382)+E(f642(x18383,x18381,x18384),f642(x18383,x18382,x18384))
% 173.53/173.44 [1839]~E(x18391,x18392)+E(f642(x18393,x18394,x18391),f642(x18393,x18394,x18392))
% 173.53/173.44 [1840]~E(x18401,x18402)+E(f351(x18401,x18403,x18404,x18405),f351(x18402,x18403,x18404,x18405))
% 173.53/173.44 [1841]~E(x18411,x18412)+E(f351(x18413,x18411,x18414,x18415),f351(x18413,x18412,x18414,x18415))
% 173.53/173.44 [1842]~E(x18421,x18422)+E(f351(x18423,x18424,x18421,x18425),f351(x18423,x18424,x18422,x18425))
% 173.53/173.44 [1843]~E(x18431,x18432)+E(f351(x18433,x18434,x18435,x18431),f351(x18433,x18434,x18435,x18432))
% 173.53/173.44 [1844]~E(x18441,x18442)+E(f837(x18441,x18443,x18444),f837(x18442,x18443,x18444))
% 173.53/173.44 [1845]~E(x18451,x18452)+E(f837(x18453,x18451,x18454),f837(x18453,x18452,x18454))
% 173.53/173.44 [1846]~E(x18461,x18462)+E(f837(x18463,x18464,x18461),f837(x18463,x18464,x18462))
% 173.53/173.44 [1847]~E(x18471,x18472)+E(f485(x18471,x18473,x18474,x18475,x18476,x18477),f485(x18472,x18473,x18474,x18475,x18476,x18477))
% 173.53/173.44 [1848]~E(x18481,x18482)+E(f485(x18483,x18481,x18484,x18485,x18486,x18487),f485(x18483,x18482,x18484,x18485,x18486,x18487))
% 173.53/173.44 [1849]~E(x18491,x18492)+E(f485(x18493,x18494,x18491,x18495,x18496,x18497),f485(x18493,x18494,x18492,x18495,x18496,x18497))
% 173.53/173.44 [1850]~E(x18501,x18502)+E(f485(x18503,x18504,x18505,x18501,x18506,x18507),f485(x18503,x18504,x18505,x18502,x18506,x18507))
% 173.53/173.44 [1851]~E(x18511,x18512)+E(f485(x18513,x18514,x18515,x18516,x18511,x18517),f485(x18513,x18514,x18515,x18516,x18512,x18517))
% 173.53/173.44 [1852]~E(x18521,x18522)+E(f485(x18523,x18524,x18525,x18526,x18527,x18521),f485(x18523,x18524,x18525,x18526,x18527,x18522))
% 173.53/173.44 [1853]~E(x18531,x18532)+E(f775(x18531,x18533,x18534,x18535,x18536),f775(x18532,x18533,x18534,x18535,x18536))
% 173.53/173.44 [1854]~E(x18541,x18542)+E(f775(x18543,x18541,x18544,x18545,x18546),f775(x18543,x18542,x18544,x18545,x18546))
% 173.53/173.44 [1855]~E(x18551,x18552)+E(f775(x18553,x18554,x18551,x18555,x18556),f775(x18553,x18554,x18552,x18555,x18556))
% 173.53/173.44 [1856]~E(x18561,x18562)+E(f775(x18563,x18564,x18565,x18561,x18566),f775(x18563,x18564,x18565,x18562,x18566))
% 173.53/173.44 [1857]~E(x18571,x18572)+E(f775(x18573,x18574,x18575,x18576,x18571),f775(x18573,x18574,x18575,x18576,x18572))
% 173.53/173.44 [1858]~E(x18581,x18582)+E(f252(x18581,x18583,x18584,x18585,x18586),f252(x18582,x18583,x18584,x18585,x18586))
% 173.53/173.44 [1859]~E(x18591,x18592)+E(f252(x18593,x18591,x18594,x18595,x18596),f252(x18593,x18592,x18594,x18595,x18596))
% 173.53/173.44 [1860]~E(x18601,x18602)+E(f252(x18603,x18604,x18601,x18605,x18606),f252(x18603,x18604,x18602,x18605,x18606))
% 173.53/173.44 [1861]~E(x18611,x18612)+E(f252(x18613,x18614,x18615,x18611,x18616),f252(x18613,x18614,x18615,x18612,x18616))
% 173.53/173.44 [1862]~E(x18621,x18622)+E(f252(x18623,x18624,x18625,x18626,x18621),f252(x18623,x18624,x18625,x18626,x18622))
% 173.53/173.44 [1863]~E(x18631,x18632)+E(f415(x18631,x18633,x18634,x18635,x18636,x18637,x18638),f415(x18632,x18633,x18634,x18635,x18636,x18637,x18638))
% 173.53/173.44 [1864]~E(x18641,x18642)+E(f415(x18643,x18641,x18644,x18645,x18646,x18647,x18648),f415(x18643,x18642,x18644,x18645,x18646,x18647,x18648))
% 173.53/173.44 [1865]~E(x18651,x18652)+E(f415(x18653,x18654,x18651,x18655,x18656,x18657,x18658),f415(x18653,x18654,x18652,x18655,x18656,x18657,x18658))
% 173.53/173.44 [1866]~E(x18661,x18662)+E(f415(x18663,x18664,x18665,x18661,x18666,x18667,x18668),f415(x18663,x18664,x18665,x18662,x18666,x18667,x18668))
% 173.53/173.44 [1867]~E(x18671,x18672)+E(f415(x18673,x18674,x18675,x18676,x18671,x18677,x18678),f415(x18673,x18674,x18675,x18676,x18672,x18677,x18678))
% 173.53/173.44 [1868]~E(x18681,x18682)+E(f415(x18683,x18684,x18685,x18686,x18687,x18681,x18688),f415(x18683,x18684,x18685,x18686,x18687,x18682,x18688))
% 173.53/173.44 [1869]~E(x18691,x18692)+E(f415(x18693,x18694,x18695,x18696,x18697,x18698,x18691),f415(x18693,x18694,x18695,x18696,x18697,x18698,x18692))
% 173.53/173.44 [1870]~E(x18701,x18702)+E(f597(x18701,x18703,x18704),f597(x18702,x18703,x18704))
% 173.53/173.44 [1871]~E(x18711,x18712)+E(f597(x18713,x18711,x18714),f597(x18713,x18712,x18714))
% 173.53/173.44 [1872]~E(x18721,x18722)+E(f597(x18723,x18724,x18721),f597(x18723,x18724,x18722))
% 173.53/173.44 [1873]~E(x18731,x18732)+E(f332(x18731,x18733,x18734),f332(x18732,x18733,x18734))
% 173.53/173.44 [1874]~E(x18741,x18742)+E(f332(x18743,x18741,x18744),f332(x18743,x18742,x18744))
% 173.53/173.44 [1875]~E(x18751,x18752)+E(f332(x18753,x18754,x18751),f332(x18753,x18754,x18752))
% 173.53/173.44 [1876]~E(x18761,x18762)+E(f458(x18761,x18763,x18764),f458(x18762,x18763,x18764))
% 173.53/173.44 [1877]~E(x18771,x18772)+E(f458(x18773,x18771,x18774),f458(x18773,x18772,x18774))
% 173.53/173.44 [1878]~E(x18781,x18782)+E(f458(x18783,x18784,x18781),f458(x18783,x18784,x18782))
% 173.53/173.44 [1879]~E(x18791,x18792)+E(f409(x18791,x18793,x18794,x18795,x18796),f409(x18792,x18793,x18794,x18795,x18796))
% 173.53/173.44 [1880]~E(x18801,x18802)+E(f409(x18803,x18801,x18804,x18805,x18806),f409(x18803,x18802,x18804,x18805,x18806))
% 173.53/173.44 [1881]~E(x18811,x18812)+E(f409(x18813,x18814,x18811,x18815,x18816),f409(x18813,x18814,x18812,x18815,x18816))
% 173.53/173.44 [1882]~E(x18821,x18822)+E(f409(x18823,x18824,x18825,x18821,x18826),f409(x18823,x18824,x18825,x18822,x18826))
% 173.53/173.44 [1883]~E(x18831,x18832)+E(f409(x18833,x18834,x18835,x18836,x18831),f409(x18833,x18834,x18835,x18836,x18832))
% 173.53/173.44 [1884]~E(x18841,x18842)+E(f575(x18841,x18843,x18844,x18845),f575(x18842,x18843,x18844,x18845))
% 173.53/173.44 [1885]~E(x18851,x18852)+E(f575(x18853,x18851,x18854,x18855),f575(x18853,x18852,x18854,x18855))
% 173.53/173.44 [1886]~E(x18861,x18862)+E(f575(x18863,x18864,x18861,x18865),f575(x18863,x18864,x18862,x18865))
% 173.53/173.44 [1887]~E(x18871,x18872)+E(f575(x18873,x18874,x18875,x18871),f575(x18873,x18874,x18875,x18872))
% 173.53/173.44 [1888]~E(x18881,x18882)+E(f569(x18881,x18883,x18884,x18885),f569(x18882,x18883,x18884,x18885))
% 173.53/173.44 [1889]~E(x18891,x18892)+E(f569(x18893,x18891,x18894,x18895),f569(x18893,x18892,x18894,x18895))
% 173.53/173.44 [1890]~E(x18901,x18902)+E(f569(x18903,x18904,x18901,x18905),f569(x18903,x18904,x18902,x18905))
% 173.53/173.44 [1891]~E(x18911,x18912)+E(f569(x18913,x18914,x18915,x18911),f569(x18913,x18914,x18915,x18912))
% 173.53/173.44 [1892]~E(x18921,x18922)+E(f541(x18921),f541(x18922))
% 173.53/173.44 [1893]~E(x18931,x18932)+E(f142(x18931,x18933),f142(x18932,x18933))
% 173.53/173.44 [1894]~E(x18941,x18942)+E(f142(x18943,x18941),f142(x18943,x18942))
% 173.53/173.44 [1895]~E(x18951,x18952)+E(f562(x18951,x18953,x18954,x18955),f562(x18952,x18953,x18954,x18955))
% 173.53/173.44 [1896]~E(x18961,x18962)+E(f562(x18963,x18961,x18964,x18965),f562(x18963,x18962,x18964,x18965))
% 173.53/173.44 [1897]~E(x18971,x18972)+E(f562(x18973,x18974,x18971,x18975),f562(x18973,x18974,x18972,x18975))
% 173.53/173.44 [1898]~E(x18981,x18982)+E(f562(x18983,x18984,x18985,x18981),f562(x18983,x18984,x18985,x18982))
% 173.53/173.44 [1899]~E(x18991,x18992)+E(f438(x18991,x18993,x18994),f438(x18992,x18993,x18994))
% 173.53/173.44 [1900]~E(x19001,x19002)+E(f438(x19003,x19001,x19004),f438(x19003,x19002,x19004))
% 173.53/173.44 [1901]~E(x19011,x19012)+E(f438(x19013,x19014,x19011),f438(x19013,x19014,x19012))
% 173.53/173.44 [1902]~E(x19021,x19022)+E(f665(x19021,x19023),f665(x19022,x19023))
% 173.53/173.44 [1903]~E(x19031,x19032)+E(f665(x19033,x19031),f665(x19033,x19032))
% 173.53/173.44 [1904]~E(x19041,x19042)+E(f407(x19041,x19043,x19044,x19045,x19046),f407(x19042,x19043,x19044,x19045,x19046))
% 173.53/173.44 [1905]~E(x19051,x19052)+E(f407(x19053,x19051,x19054,x19055,x19056),f407(x19053,x19052,x19054,x19055,x19056))
% 173.53/173.44 [1906]~E(x19061,x19062)+E(f407(x19063,x19064,x19061,x19065,x19066),f407(x19063,x19064,x19062,x19065,x19066))
% 173.53/173.44 [1907]~E(x19071,x19072)+E(f407(x19073,x19074,x19075,x19071,x19076),f407(x19073,x19074,x19075,x19072,x19076))
% 173.53/173.44 [1908]~E(x19081,x19082)+E(f407(x19083,x19084,x19085,x19086,x19081),f407(x19083,x19084,x19085,x19086,x19082))
% 173.53/173.44 [1909]~E(x19091,x19092)+E(f403(x19091,x19093,x19094,x19095),f403(x19092,x19093,x19094,x19095))
% 173.53/173.44 [1910]~E(x19101,x19102)+E(f403(x19103,x19101,x19104,x19105),f403(x19103,x19102,x19104,x19105))
% 173.53/173.44 [1911]~E(x19111,x19112)+E(f403(x19113,x19114,x19111,x19115),f403(x19113,x19114,x19112,x19115))
% 173.53/173.44 [1912]~E(x19121,x19122)+E(f403(x19123,x19124,x19125,x19121),f403(x19123,x19124,x19125,x19122))
% 173.53/173.44 [1913]~E(x19131,x19132)+E(f834(x19131),f834(x19132))
% 173.53/173.44 [1914]~E(x19141,x19142)+E(f803(x19141,x19143,x19144,x19145),f803(x19142,x19143,x19144,x19145))
% 173.53/173.44 [1915]~E(x19151,x19152)+E(f803(x19153,x19151,x19154,x19155),f803(x19153,x19152,x19154,x19155))
% 173.53/173.44 [1916]~E(x19161,x19162)+E(f803(x19163,x19164,x19161,x19165),f803(x19163,x19164,x19162,x19165))
% 173.53/173.44 [1917]~E(x19171,x19172)+E(f803(x19173,x19174,x19175,x19171),f803(x19173,x19174,x19175,x19172))
% 173.53/173.44 [1918]~E(x19181,x19182)+E(f661(x19181,x19183,x19184),f661(x19182,x19183,x19184))
% 173.53/173.44 [1919]~E(x19191,x19192)+E(f661(x19193,x19191,x19194),f661(x19193,x19192,x19194))
% 173.53/173.44 [1920]~E(x19201,x19202)+E(f661(x19203,x19204,x19201),f661(x19203,x19204,x19202))
% 173.53/173.44 [1921]~E(x19211,x19212)+E(f405(x19211,x19213,x19214,x19215,x19216),f405(x19212,x19213,x19214,x19215,x19216))
% 173.53/173.44 [1922]~E(x19221,x19222)+E(f405(x19223,x19221,x19224,x19225,x19226),f405(x19223,x19222,x19224,x19225,x19226))
% 173.53/173.44 [1923]~E(x19231,x19232)+E(f405(x19233,x19234,x19231,x19235,x19236),f405(x19233,x19234,x19232,x19235,x19236))
% 173.53/173.44 [1924]~E(x19241,x19242)+E(f405(x19243,x19244,x19245,x19241,x19246),f405(x19243,x19244,x19245,x19242,x19246))
% 173.53/173.44 [1925]~E(x19251,x19252)+E(f405(x19253,x19254,x19255,x19256,x19251),f405(x19253,x19254,x19255,x19256,x19252))
% 173.53/173.44 [1926]~E(x19261,x19262)+E(f422(x19261,x19263,x19264,x19265,x19266,x19267,x19268),f422(x19262,x19263,x19264,x19265,x19266,x19267,x19268))
% 173.53/173.44 [1927]~E(x19271,x19272)+E(f422(x19273,x19271,x19274,x19275,x19276,x19277,x19278),f422(x19273,x19272,x19274,x19275,x19276,x19277,x19278))
% 173.53/173.44 [1928]~E(x19281,x19282)+E(f422(x19283,x19284,x19281,x19285,x19286,x19287,x19288),f422(x19283,x19284,x19282,x19285,x19286,x19287,x19288))
% 173.53/173.44 [1929]~E(x19291,x19292)+E(f422(x19293,x19294,x19295,x19291,x19296,x19297,x19298),f422(x19293,x19294,x19295,x19292,x19296,x19297,x19298))
% 173.53/173.44 [1930]~E(x19301,x19302)+E(f422(x19303,x19304,x19305,x19306,x19301,x19307,x19308),f422(x19303,x19304,x19305,x19306,x19302,x19307,x19308))
% 173.53/173.44 [1931]~E(x19311,x19312)+E(f422(x19313,x19314,x19315,x19316,x19317,x19311,x19318),f422(x19313,x19314,x19315,x19316,x19317,x19312,x19318))
% 173.53/173.44 [1932]~E(x19321,x19322)+E(f422(x19323,x19324,x19325,x19326,x19327,x19328,x19321),f422(x19323,x19324,x19325,x19326,x19327,x19328,x19322))
% 173.53/173.44 [1933]~E(x19331,x19332)+E(f275(x19331,x19333,x19334,x19335,x19336),f275(x19332,x19333,x19334,x19335,x19336))
% 173.53/173.44 [1934]~E(x19341,x19342)+E(f275(x19343,x19341,x19344,x19345,x19346),f275(x19343,x19342,x19344,x19345,x19346))
% 173.53/173.44 [1935]~E(x19351,x19352)+E(f275(x19353,x19354,x19351,x19355,x19356),f275(x19353,x19354,x19352,x19355,x19356))
% 173.53/173.44 [1936]~E(x19361,x19362)+E(f275(x19363,x19364,x19365,x19361,x19366),f275(x19363,x19364,x19365,x19362,x19366))
% 173.53/173.44 [1937]~E(x19371,x19372)+E(f275(x19373,x19374,x19375,x19376,x19371),f275(x19373,x19374,x19375,x19376,x19372))
% 173.53/173.44 [1938]~E(x19381,x19382)+E(f222(x19381,x19383,x19384,x19385,x19386),f222(x19382,x19383,x19384,x19385,x19386))
% 173.53/173.44 [1939]~E(x19391,x19392)+E(f222(x19393,x19391,x19394,x19395,x19396),f222(x19393,x19392,x19394,x19395,x19396))
% 173.53/173.44 [1940]~E(x19401,x19402)+E(f222(x19403,x19404,x19401,x19405,x19406),f222(x19403,x19404,x19402,x19405,x19406))
% 173.53/173.44 [1941]~E(x19411,x19412)+E(f222(x19413,x19414,x19415,x19411,x19416),f222(x19413,x19414,x19415,x19412,x19416))
% 173.53/173.44 [1942]~E(x19421,x19422)+E(f222(x19423,x19424,x19425,x19426,x19421),f222(x19423,x19424,x19425,x19426,x19422))
% 173.53/173.44 [1943]~E(x19431,x19432)+E(f532(x19431,x19433,x19434,x19435,x19436),f532(x19432,x19433,x19434,x19435,x19436))
% 173.53/173.44 [1944]~E(x19441,x19442)+E(f532(x19443,x19441,x19444,x19445,x19446),f532(x19443,x19442,x19444,x19445,x19446))
% 173.53/173.44 [1945]~E(x19451,x19452)+E(f532(x19453,x19454,x19451,x19455,x19456),f532(x19453,x19454,x19452,x19455,x19456))
% 173.53/173.44 [1946]~E(x19461,x19462)+E(f532(x19463,x19464,x19465,x19461,x19466),f532(x19463,x19464,x19465,x19462,x19466))
% 173.53/173.44 [1947]~E(x19471,x19472)+E(f532(x19473,x19474,x19475,x19476,x19471),f532(x19473,x19474,x19475,x19476,x19472))
% 173.53/173.44 [1948]~E(x19481,x19482)+E(f453(x19481,x19483,x19484,x19485,x19486,x19487),f453(x19482,x19483,x19484,x19485,x19486,x19487))
% 173.53/173.44 [1949]~E(x19491,x19492)+E(f453(x19493,x19491,x19494,x19495,x19496,x19497),f453(x19493,x19492,x19494,x19495,x19496,x19497))
% 173.53/173.44 [1950]~E(x19501,x19502)+E(f453(x19503,x19504,x19501,x19505,x19506,x19507),f453(x19503,x19504,x19502,x19505,x19506,x19507))
% 173.53/173.44 [1951]~E(x19511,x19512)+E(f453(x19513,x19514,x19515,x19511,x19516,x19517),f453(x19513,x19514,x19515,x19512,x19516,x19517))
% 173.53/173.44 [1952]~E(x19521,x19522)+E(f453(x19523,x19524,x19525,x19526,x19521,x19527),f453(x19523,x19524,x19525,x19526,x19522,x19527))
% 173.53/173.44 [1953]~E(x19531,x19532)+E(f453(x19533,x19534,x19535,x19536,x19537,x19531),f453(x19533,x19534,x19535,x19536,x19537,x19532))
% 173.53/173.44 [1954]~E(x19541,x19542)+E(f721(x19541,x19543,x19544,x19545,x19546),f721(x19542,x19543,x19544,x19545,x19546))
% 173.53/173.44 [1955]~E(x19551,x19552)+E(f721(x19553,x19551,x19554,x19555,x19556),f721(x19553,x19552,x19554,x19555,x19556))
% 173.53/173.44 [1956]~E(x19561,x19562)+E(f721(x19563,x19564,x19561,x19565,x19566),f721(x19563,x19564,x19562,x19565,x19566))
% 173.53/173.44 [1957]~E(x19571,x19572)+E(f721(x19573,x19574,x19575,x19571,x19576),f721(x19573,x19574,x19575,x19572,x19576))
% 173.53/173.44 [1958]~E(x19581,x19582)+E(f721(x19583,x19584,x19585,x19586,x19581),f721(x19583,x19584,x19585,x19586,x19582))
% 173.53/173.44 [1959]~E(x19591,x19592)+E(f43(x19591,x19593,x19594,x19595),f43(x19592,x19593,x19594,x19595))
% 173.53/173.44 [1960]~E(x19601,x19602)+E(f43(x19603,x19601,x19604,x19605),f43(x19603,x19602,x19604,x19605))
% 173.53/173.44 [1961]~E(x19611,x19612)+E(f43(x19613,x19614,x19611,x19615),f43(x19613,x19614,x19612,x19615))
% 173.53/173.44 [1962]~E(x19621,x19622)+E(f43(x19623,x19624,x19625,x19621),f43(x19623,x19624,x19625,x19622))
% 173.53/173.44 [1963]~E(x19631,x19632)+E(f589(x19631,x19633,x19634,x19635,x19636),f589(x19632,x19633,x19634,x19635,x19636))
% 173.53/173.44 [1964]~E(x19641,x19642)+E(f589(x19643,x19641,x19644,x19645,x19646),f589(x19643,x19642,x19644,x19645,x19646))
% 173.53/173.44 [1965]~E(x19651,x19652)+E(f589(x19653,x19654,x19651,x19655,x19656),f589(x19653,x19654,x19652,x19655,x19656))
% 173.53/173.44 [1966]~E(x19661,x19662)+E(f589(x19663,x19664,x19665,x19661,x19666),f589(x19663,x19664,x19665,x19662,x19666))
% 173.53/173.44 [1967]~E(x19671,x19672)+E(f589(x19673,x19674,x19675,x19676,x19671),f589(x19673,x19674,x19675,x19676,x19672))
% 173.53/173.44 [1968]~E(x19681,x19682)+E(f653(x19681,x19683),f653(x19682,x19683))
% 173.53/173.44 [1969]~E(x19691,x19692)+E(f653(x19693,x19691),f653(x19693,x19692))
% 173.53/173.44 [1970]~E(x19701,x19702)+E(f437(x19701,x19703,x19704),f437(x19702,x19703,x19704))
% 173.53/173.44 [1971]~E(x19711,x19712)+E(f437(x19713,x19711,x19714),f437(x19713,x19712,x19714))
% 173.53/173.44 [1972]~E(x19721,x19722)+E(f437(x19723,x19724,x19721),f437(x19723,x19724,x19722))
% 173.53/173.44 [1973]~E(x19731,x19732)+E(f512(x19731,x19733,x19734,x19735,x19736),f512(x19732,x19733,x19734,x19735,x19736))
% 173.53/173.44 [1974]~E(x19741,x19742)+E(f512(x19743,x19741,x19744,x19745,x19746),f512(x19743,x19742,x19744,x19745,x19746))
% 173.53/173.44 [1975]~E(x19751,x19752)+E(f512(x19753,x19754,x19751,x19755,x19756),f512(x19753,x19754,x19752,x19755,x19756))
% 173.53/173.44 [1976]~E(x19761,x19762)+E(f512(x19763,x19764,x19765,x19761,x19766),f512(x19763,x19764,x19765,x19762,x19766))
% 173.53/173.44 [1977]~E(x19771,x19772)+E(f512(x19773,x19774,x19775,x19776,x19771),f512(x19773,x19774,x19775,x19776,x19772))
% 173.53/173.44 [1978]~E(x19781,x19782)+E(f277(x19781,x19783,x19784,x19785),f277(x19782,x19783,x19784,x19785))
% 173.53/173.44 [1979]~E(x19791,x19792)+E(f277(x19793,x19791,x19794,x19795),f277(x19793,x19792,x19794,x19795))
% 173.53/173.44 [1980]~E(x19801,x19802)+E(f277(x19803,x19804,x19801,x19805),f277(x19803,x19804,x19802,x19805))
% 173.53/173.44 [1981]~E(x19811,x19812)+E(f277(x19813,x19814,x19815,x19811),f277(x19813,x19814,x19815,x19812))
% 173.53/173.44 [1982]~E(x19821,x19822)+E(f367(x19821,x19823),f367(x19822,x19823))
% 173.53/173.44 [1983]~E(x19831,x19832)+E(f367(x19833,x19831),f367(x19833,x19832))
% 173.53/173.44 [1984]~E(x19841,x19842)+E(f504(x19841,x19843,x19844,x19845,x19846,x19847),f504(x19842,x19843,x19844,x19845,x19846,x19847))
% 173.53/173.44 [1985]~E(x19851,x19852)+E(f504(x19853,x19851,x19854,x19855,x19856,x19857),f504(x19853,x19852,x19854,x19855,x19856,x19857))
% 173.53/173.44 [1986]~E(x19861,x19862)+E(f504(x19863,x19864,x19861,x19865,x19866,x19867),f504(x19863,x19864,x19862,x19865,x19866,x19867))
% 173.53/173.44 [1987]~E(x19871,x19872)+E(f504(x19873,x19874,x19875,x19871,x19876,x19877),f504(x19873,x19874,x19875,x19872,x19876,x19877))
% 173.53/173.44 [1988]~E(x19881,x19882)+E(f504(x19883,x19884,x19885,x19886,x19881,x19887),f504(x19883,x19884,x19885,x19886,x19882,x19887))
% 173.53/173.44 [1989]~E(x19891,x19892)+E(f504(x19893,x19894,x19895,x19896,x19897,x19891),f504(x19893,x19894,x19895,x19896,x19897,x19892))
% 173.53/173.44 [1990]~E(x19901,x19902)+E(f620(x19901,x19903,x19904,x19905,x19906),f620(x19902,x19903,x19904,x19905,x19906))
% 173.53/173.44 [1991]~E(x19911,x19912)+E(f620(x19913,x19911,x19914,x19915,x19916),f620(x19913,x19912,x19914,x19915,x19916))
% 173.53/173.44 [1992]~E(x19921,x19922)+E(f620(x19923,x19924,x19921,x19925,x19926),f620(x19923,x19924,x19922,x19925,x19926))
% 173.53/173.44 [1993]~E(x19931,x19932)+E(f620(x19933,x19934,x19935,x19931,x19936),f620(x19933,x19934,x19935,x19932,x19936))
% 173.53/173.44 [1994]~E(x19941,x19942)+E(f620(x19943,x19944,x19945,x19946,x19941),f620(x19943,x19944,x19945,x19946,x19942))
% 173.53/173.44 [1995]~E(x19951,x19952)+E(f376(x19951,x19953,x19954,x19955,x19956),f376(x19952,x19953,x19954,x19955,x19956))
% 173.53/173.44 [1996]~E(x19961,x19962)+E(f376(x19963,x19961,x19964,x19965,x19966),f376(x19963,x19962,x19964,x19965,x19966))
% 173.53/173.44 [1997]~E(x19971,x19972)+E(f376(x19973,x19974,x19971,x19975,x19976),f376(x19973,x19974,x19972,x19975,x19976))
% 173.53/173.44 [1998]~E(x19981,x19982)+E(f376(x19983,x19984,x19985,x19981,x19986),f376(x19983,x19984,x19985,x19982,x19986))
% 173.53/173.44 [1999]~E(x19991,x19992)+E(f376(x19993,x19994,x19995,x19996,x19991),f376(x19993,x19994,x19995,x19996,x19992))
% 173.53/173.44 [2000]~E(x20001,x20002)+E(f508(x20001,x20003,x20004,x20005,x20006),f508(x20002,x20003,x20004,x20005,x20006))
% 173.53/173.44 [2001]~E(x20011,x20012)+E(f508(x20013,x20011,x20014,x20015,x20016),f508(x20013,x20012,x20014,x20015,x20016))
% 173.53/173.44 [2002]~E(x20021,x20022)+E(f508(x20023,x20024,x20021,x20025,x20026),f508(x20023,x20024,x20022,x20025,x20026))
% 173.53/173.44 [2003]~E(x20031,x20032)+E(f508(x20033,x20034,x20035,x20031,x20036),f508(x20033,x20034,x20035,x20032,x20036))
% 173.53/173.44 [2004]~E(x20041,x20042)+E(f508(x20043,x20044,x20045,x20046,x20041),f508(x20043,x20044,x20045,x20046,x20042))
% 173.53/173.44 [2005]~E(x20051,x20052)+E(f260(x20051,x20053,x20054),f260(x20052,x20053,x20054))
% 173.53/173.44 [2006]~E(x20061,x20062)+E(f260(x20063,x20061,x20064),f260(x20063,x20062,x20064))
% 173.53/173.44 [2007]~E(x20071,x20072)+E(f260(x20073,x20074,x20071),f260(x20073,x20074,x20072))
% 173.53/173.44 [2008]~E(x20081,x20082)+E(f736(x20081,x20083,x20084),f736(x20082,x20083,x20084))
% 173.53/173.44 [2009]~E(x20091,x20092)+E(f736(x20093,x20091,x20094),f736(x20093,x20092,x20094))
% 173.53/173.44 [2010]~E(x20101,x20102)+E(f736(x20103,x20104,x20101),f736(x20103,x20104,x20102))
% 173.53/173.44 [2011]~E(x20111,x20112)+E(f456(x20111,x20113),f456(x20112,x20113))
% 173.53/173.44 [2012]~E(x20121,x20122)+E(f456(x20123,x20121),f456(x20123,x20122))
% 173.53/173.44 [2013]~E(x20131,x20132)+E(f278(x20131,x20133,x20134,x20135,x20136),f278(x20132,x20133,x20134,x20135,x20136))
% 173.53/173.44 [2014]~E(x20141,x20142)+E(f278(x20143,x20141,x20144,x20145,x20146),f278(x20143,x20142,x20144,x20145,x20146))
% 173.53/173.44 [2015]~E(x20151,x20152)+E(f278(x20153,x20154,x20151,x20155,x20156),f278(x20153,x20154,x20152,x20155,x20156))
% 173.53/173.44 [2016]~E(x20161,x20162)+E(f278(x20163,x20164,x20165,x20161,x20166),f278(x20163,x20164,x20165,x20162,x20166))
% 173.53/173.44 [2017]~E(x20171,x20172)+E(f278(x20173,x20174,x20175,x20176,x20171),f278(x20173,x20174,x20175,x20176,x20172))
% 173.53/173.44 [2018]~E(x20181,x20182)+E(f833(x20181),f833(x20182))
% 173.53/173.44 [2019]~E(x20191,x20192)+E(f392(x20191,x20193),f392(x20192,x20193))
% 173.53/173.44 [2020]~E(x20201,x20202)+E(f392(x20203,x20201),f392(x20203,x20202))
% 173.53/173.44 [2021]~E(x20211,x20212)+E(f261(x20211,x20213),f261(x20212,x20213))
% 173.53/173.44 [2022]~E(x20221,x20222)+E(f261(x20223,x20221),f261(x20223,x20222))
% 173.53/173.44 [2023]~E(x20231,x20232)+E(f363(x20231,x20233),f363(x20232,x20233))
% 173.53/173.44 [2024]~E(x20241,x20242)+E(f363(x20243,x20241),f363(x20243,x20242))
% 173.53/173.44 [2025]~E(x20251,x20252)+E(f379(x20251,x20253),f379(x20252,x20253))
% 173.53/173.44 [2026]~E(x20261,x20262)+E(f379(x20263,x20261),f379(x20263,x20262))
% 173.53/173.44 [2027]~E(x20271,x20272)+E(f718(x20271,x20273,x20274),f718(x20272,x20273,x20274))
% 173.53/173.44 [2028]~E(x20281,x20282)+E(f718(x20283,x20281,x20284),f718(x20283,x20282,x20284))
% 173.53/173.44 [2029]~E(x20291,x20292)+E(f718(x20293,x20294,x20291),f718(x20293,x20294,x20292))
% 173.53/173.44 [2030]~E(x20301,x20302)+E(f548(x20301,x20303,x20304,x20305,x20306),f548(x20302,x20303,x20304,x20305,x20306))
% 173.53/173.44 [2031]~E(x20311,x20312)+E(f548(x20313,x20311,x20314,x20315,x20316),f548(x20313,x20312,x20314,x20315,x20316))
% 173.53/173.44 [2032]~E(x20321,x20322)+E(f548(x20323,x20324,x20321,x20325,x20326),f548(x20323,x20324,x20322,x20325,x20326))
% 173.53/173.44 [2033]~E(x20331,x20332)+E(f548(x20333,x20334,x20335,x20331,x20336),f548(x20333,x20334,x20335,x20332,x20336))
% 173.53/173.44 [2034]~E(x20341,x20342)+E(f548(x20343,x20344,x20345,x20346,x20341),f548(x20343,x20344,x20345,x20346,x20342))
% 173.53/173.44 [2035]~E(x20351,x20352)+E(f767(x20351,x20353,x20354,x20355,x20356),f767(x20352,x20353,x20354,x20355,x20356))
% 173.53/173.44 [2036]~E(x20361,x20362)+E(f767(x20363,x20361,x20364,x20365,x20366),f767(x20363,x20362,x20364,x20365,x20366))
% 173.53/173.44 [2037]~E(x20371,x20372)+E(f767(x20373,x20374,x20371,x20375,x20376),f767(x20373,x20374,x20372,x20375,x20376))
% 173.53/173.44 [2038]~E(x20381,x20382)+E(f767(x20383,x20384,x20385,x20381,x20386),f767(x20383,x20384,x20385,x20382,x20386))
% 173.53/173.44 [2039]~E(x20391,x20392)+E(f767(x20393,x20394,x20395,x20396,x20391),f767(x20393,x20394,x20395,x20396,x20392))
% 173.53/173.44 [2040]~E(x20401,x20402)+E(f215(x20401,x20403,x20404,x20405,x20406),f215(x20402,x20403,x20404,x20405,x20406))
% 173.53/173.44 [2041]~E(x20411,x20412)+E(f215(x20413,x20411,x20414,x20415,x20416),f215(x20413,x20412,x20414,x20415,x20416))
% 173.53/173.44 [2042]~E(x20421,x20422)+E(f215(x20423,x20424,x20421,x20425,x20426),f215(x20423,x20424,x20422,x20425,x20426))
% 173.53/173.44 [2043]~E(x20431,x20432)+E(f215(x20433,x20434,x20435,x20431,x20436),f215(x20433,x20434,x20435,x20432,x20436))
% 173.53/173.44 [2044]~E(x20441,x20442)+E(f215(x20443,x20444,x20445,x20446,x20441),f215(x20443,x20444,x20445,x20446,x20442))
% 173.53/173.44 [2045]~E(x20451,x20452)+E(f645(x20451,x20453,x20454),f645(x20452,x20453,x20454))
% 173.53/173.44 [2046]~E(x20461,x20462)+E(f645(x20463,x20461,x20464),f645(x20463,x20462,x20464))
% 173.53/173.44 [2047]~E(x20471,x20472)+E(f645(x20473,x20474,x20471),f645(x20473,x20474,x20472))
% 173.53/173.44 [2048]~E(x20481,x20482)+E(f545(x20481,x20483),f545(x20482,x20483))
% 173.53/173.44 [2049]~E(x20491,x20492)+E(f545(x20493,x20491),f545(x20493,x20492))
% 173.53/173.44 [2050]~E(x20501,x20502)+E(f306(x20501,x20503,x20504),f306(x20502,x20503,x20504))
% 173.53/173.44 [2051]~E(x20511,x20512)+E(f306(x20513,x20511,x20514),f306(x20513,x20512,x20514))
% 173.53/173.44 [2052]~E(x20521,x20522)+E(f306(x20523,x20524,x20521),f306(x20523,x20524,x20522))
% 173.53/173.44 [2053]~E(x20531,x20532)+E(f242(x20531,x20533,x20534),f242(x20532,x20533,x20534))
% 173.53/173.44 [2054]~E(x20541,x20542)+E(f242(x20543,x20541,x20544),f242(x20543,x20542,x20544))
% 173.53/173.44 [2055]~E(x20551,x20552)+E(f242(x20553,x20554,x20551),f242(x20553,x20554,x20552))
% 173.53/173.44 [2056]~E(x20561,x20562)+E(f525(x20561,x20563,x20564,x20565),f525(x20562,x20563,x20564,x20565))
% 173.53/173.44 [2057]~E(x20571,x20572)+E(f525(x20573,x20571,x20574,x20575),f525(x20573,x20572,x20574,x20575))
% 173.53/173.44 [2058]~E(x20581,x20582)+E(f525(x20583,x20584,x20581,x20585),f525(x20583,x20584,x20582,x20585))
% 173.53/173.44 [2059]~E(x20591,x20592)+E(f525(x20593,x20594,x20595,x20591),f525(x20593,x20594,x20595,x20592))
% 173.53/173.44 [2060]~E(x20601,x20602)+E(f104(x20601,x20603,x20604,x20605),f104(x20602,x20603,x20604,x20605))
% 173.53/173.44 [2061]~E(x20611,x20612)+E(f104(x20613,x20611,x20614,x20615),f104(x20613,x20612,x20614,x20615))
% 173.53/173.44 [2062]~E(x20621,x20622)+E(f104(x20623,x20624,x20621,x20625),f104(x20623,x20624,x20622,x20625))
% 173.53/173.44 [2063]~E(x20631,x20632)+E(f104(x20633,x20634,x20635,x20631),f104(x20633,x20634,x20635,x20632))
% 173.53/173.44 [2064]~E(x20641,x20642)+E(f491(x20641,x20643,x20644,x20645),f491(x20642,x20643,x20644,x20645))
% 173.53/173.44 [2065]~E(x20651,x20652)+E(f491(x20653,x20651,x20654,x20655),f491(x20653,x20652,x20654,x20655))
% 173.53/173.44 [2066]~E(x20661,x20662)+E(f491(x20663,x20664,x20661,x20665),f491(x20663,x20664,x20662,x20665))
% 173.53/173.44 [2067]~E(x20671,x20672)+E(f491(x20673,x20674,x20675,x20671),f491(x20673,x20674,x20675,x20672))
% 173.53/173.44 [2068]~E(x20681,x20682)+E(f270(x20681,x20683),f270(x20682,x20683))
% 173.53/173.44 [2069]~E(x20691,x20692)+E(f270(x20693,x20691),f270(x20693,x20692))
% 173.53/173.44 [2070]~E(x20701,x20702)+E(f610(x20701,x20703),f610(x20702,x20703))
% 173.53/173.44 [2071]~E(x20711,x20712)+E(f610(x20713,x20711),f610(x20713,x20712))
% 173.53/173.44 [2072]~E(x20721,x20722)+E(f658(x20721,x20723),f658(x20722,x20723))
% 173.53/173.44 [2073]~E(x20731,x20732)+E(f658(x20733,x20731),f658(x20733,x20732))
% 173.53/173.44 [2074]~E(x20741,x20742)+E(f216(x20741,x20743,x20744,x20745),f216(x20742,x20743,x20744,x20745))
% 173.53/173.44 [2075]~E(x20751,x20752)+E(f216(x20753,x20751,x20754,x20755),f216(x20753,x20752,x20754,x20755))
% 173.53/173.44 [2076]~E(x20761,x20762)+E(f216(x20763,x20764,x20761,x20765),f216(x20763,x20764,x20762,x20765))
% 173.53/173.44 [2077]~E(x20771,x20772)+E(f216(x20773,x20774,x20775,x20771),f216(x20773,x20774,x20775,x20772))
% 173.53/173.44 [2078]~E(x20781,x20782)+E(f647(x20781,x20783,x20784),f647(x20782,x20783,x20784))
% 173.53/173.44 [2079]~E(x20791,x20792)+E(f647(x20793,x20791,x20794),f647(x20793,x20792,x20794))
% 173.53/173.44 [2080]~E(x20801,x20802)+E(f647(x20803,x20804,x20801),f647(x20803,x20804,x20802))
% 173.53/173.44 [2081]~E(x20811,x20812)+E(f501(x20811,x20813,x20814,x20815,x20816),f501(x20812,x20813,x20814,x20815,x20816))
% 173.53/173.44 [2082]~E(x20821,x20822)+E(f501(x20823,x20821,x20824,x20825,x20826),f501(x20823,x20822,x20824,x20825,x20826))
% 173.53/173.44 [2083]~E(x20831,x20832)+E(f501(x20833,x20834,x20831,x20835,x20836),f501(x20833,x20834,x20832,x20835,x20836))
% 173.53/173.44 [2084]~E(x20841,x20842)+E(f501(x20843,x20844,x20845,x20841,x20846),f501(x20843,x20844,x20845,x20842,x20846))
% 173.53/173.44 [2085]~E(x20851,x20852)+E(f501(x20853,x20854,x20855,x20856,x20851),f501(x20853,x20854,x20855,x20856,x20852))
% 173.53/173.44 [2086]~E(x20861,x20862)+E(f468(x20861,x20863,x20864,x20865),f468(x20862,x20863,x20864,x20865))
% 173.53/173.44 [2087]~E(x20871,x20872)+E(f468(x20873,x20871,x20874,x20875),f468(x20873,x20872,x20874,x20875))
% 173.53/173.44 [2088]~E(x20881,x20882)+E(f468(x20883,x20884,x20881,x20885),f468(x20883,x20884,x20882,x20885))
% 173.53/173.44 [2089]~E(x20891,x20892)+E(f468(x20893,x20894,x20895,x20891),f468(x20893,x20894,x20895,x20892))
% 173.53/173.44 [2090]~E(x20901,x20902)+E(f560(x20901,x20903,x20904,x20905),f560(x20902,x20903,x20904,x20905))
% 173.53/173.44 [2091]~E(x20911,x20912)+E(f560(x20913,x20911,x20914,x20915),f560(x20913,x20912,x20914,x20915))
% 173.53/173.44 [2092]~E(x20921,x20922)+E(f560(x20923,x20924,x20921,x20925),f560(x20923,x20924,x20922,x20925))
% 173.53/173.44 [2093]~E(x20931,x20932)+E(f560(x20933,x20934,x20935,x20931),f560(x20933,x20934,x20935,x20932))
% 173.53/173.44 [2094]~E(x20941,x20942)+E(f295(x20941,x20943,x20944),f295(x20942,x20943,x20944))
% 173.53/173.44 [2095]~E(x20951,x20952)+E(f295(x20953,x20951,x20954),f295(x20953,x20952,x20954))
% 173.53/173.44 [2096]~E(x20961,x20962)+E(f295(x20963,x20964,x20961),f295(x20963,x20964,x20962))
% 173.53/173.44 [2097]~E(x20971,x20972)+E(f455(x20971,x20973),f455(x20972,x20973))
% 173.53/173.44 [2098]~E(x20981,x20982)+E(f455(x20983,x20981),f455(x20983,x20982))
% 173.53/173.44 [2099]~E(x20991,x20992)+E(f397(x20991,x20993,x20994),f397(x20992,x20993,x20994))
% 173.53/173.44 [2100]~E(x21001,x21002)+E(f397(x21003,x21001,x21004),f397(x21003,x21002,x21004))
% 173.53/173.44 [2101]~E(x21011,x21012)+E(f397(x21013,x21014,x21011),f397(x21013,x21014,x21012))
% 173.53/173.44 [2102]~E(x21021,x21022)+E(f570(x21021,x21023),f570(x21022,x21023))
% 173.53/173.44 [2103]~E(x21031,x21032)+E(f570(x21033,x21031),f570(x21033,x21032))
% 173.53/173.44 [2104]~E(x21041,x21042)+E(f400(x21041,x21043,x21044),f400(x21042,x21043,x21044))
% 173.53/173.44 [2105]~E(x21051,x21052)+E(f400(x21053,x21051,x21054),f400(x21053,x21052,x21054))
% 173.53/173.44 [2106]~E(x21061,x21062)+E(f400(x21063,x21064,x21061),f400(x21063,x21064,x21062))
% 173.53/173.44 [2107]~E(x21071,x21072)+E(f207(x21071,x21073),f207(x21072,x21073))
% 173.53/173.44 [2108]~E(x21081,x21082)+E(f207(x21083,x21081),f207(x21083,x21082))
% 173.53/173.44 [2109]~E(x21091,x21092)+E(f534(x21091,x21093,x21094,x21095,x21096,x21097,x21098,x21099),f534(x21092,x21093,x21094,x21095,x21096,x21097,x21098,x21099))
% 173.53/173.44 [2110]~E(x21101,x21102)+E(f534(x21103,x21101,x21104,x21105,x21106,x21107,x21108,x21109),f534(x21103,x21102,x21104,x21105,x21106,x21107,x21108,x21109))
% 173.53/173.44 [2111]~E(x21111,x21112)+E(f534(x21113,x21114,x21111,x21115,x21116,x21117,x21118,x21119),f534(x21113,x21114,x21112,x21115,x21116,x21117,x21118,x21119))
% 173.53/173.44 [2112]~E(x21121,x21122)+E(f534(x21123,x21124,x21125,x21121,x21126,x21127,x21128,x21129),f534(x21123,x21124,x21125,x21122,x21126,x21127,x21128,x21129))
% 173.53/173.44 [2113]~E(x21131,x21132)+E(f534(x21133,x21134,x21135,x21136,x21131,x21137,x21138,x21139),f534(x21133,x21134,x21135,x21136,x21132,x21137,x21138,x21139))
% 173.53/173.44 [2114]~E(x21141,x21142)+E(f534(x21143,x21144,x21145,x21146,x21147,x21141,x21148,x21149),f534(x21143,x21144,x21145,x21146,x21147,x21142,x21148,x21149))
% 173.53/173.44 [2115]~E(x21151,x21152)+E(f534(x21153,x21154,x21155,x21156,x21157,x21158,x21151,x21159),f534(x21153,x21154,x21155,x21156,x21157,x21158,x21152,x21159))
% 173.53/173.44 [2116]~E(x21161,x21162)+E(f534(x21163,x21164,x21165,x21166,x21167,x21168,x21169,x21161),f534(x21163,x21164,x21165,x21166,x21167,x21168,x21169,x21162))
% 173.53/173.44 [2117]~E(x21171,x21172)+E(f479(x21171,x21173,x21174,x21175),f479(x21172,x21173,x21174,x21175))
% 173.53/173.44 [2118]~E(x21181,x21182)+E(f479(x21183,x21181,x21184,x21185),f479(x21183,x21182,x21184,x21185))
% 173.53/173.44 [2119]~E(x21191,x21192)+E(f479(x21193,x21194,x21191,x21195),f479(x21193,x21194,x21192,x21195))
% 173.53/173.44 [2120]~E(x21201,x21202)+E(f479(x21203,x21204,x21205,x21201),f479(x21203,x21204,x21205,x21202))
% 173.53/173.44 [2121]~E(x21211,x21212)+E(f514(x21211,x21213,x21214,x21215,x21216),f514(x21212,x21213,x21214,x21215,x21216))
% 173.53/173.44 [2122]~E(x21221,x21222)+E(f514(x21223,x21221,x21224,x21225,x21226),f514(x21223,x21222,x21224,x21225,x21226))
% 173.53/173.44 [2123]~E(x21231,x21232)+E(f514(x21233,x21234,x21231,x21235,x21236),f514(x21233,x21234,x21232,x21235,x21236))
% 173.53/173.44 [2124]~E(x21241,x21242)+E(f514(x21243,x21244,x21245,x21241,x21246),f514(x21243,x21244,x21245,x21242,x21246))
% 173.53/173.44 [2125]~E(x21251,x21252)+E(f514(x21253,x21254,x21255,x21256,x21251),f514(x21253,x21254,x21255,x21256,x21252))
% 173.53/173.44 [2126]~E(x21261,x21262)+E(f401(x21261,x21263,x21264,x21265,x21266),f401(x21262,x21263,x21264,x21265,x21266))
% 173.53/173.44 [2127]~E(x21271,x21272)+E(f401(x21273,x21271,x21274,x21275,x21276),f401(x21273,x21272,x21274,x21275,x21276))
% 173.53/173.44 [2128]~E(x21281,x21282)+E(f401(x21283,x21284,x21281,x21285,x21286),f401(x21283,x21284,x21282,x21285,x21286))
% 173.53/173.44 [2129]~E(x21291,x21292)+E(f401(x21293,x21294,x21295,x21291,x21296),f401(x21293,x21294,x21295,x21292,x21296))
% 173.53/173.44 [2130]~E(x21301,x21302)+E(f401(x21303,x21304,x21305,x21306,x21301),f401(x21303,x21304,x21305,x21306,x21302))
% 173.53/173.44 [2131]~E(x21311,x21312)+E(f435(x21311,x21313,x21314),f435(x21312,x21313,x21314))
% 173.53/173.44 [2132]~E(x21321,x21322)+E(f435(x21323,x21321,x21324),f435(x21323,x21322,x21324))
% 173.53/173.44 [2133]~E(x21331,x21332)+E(f435(x21333,x21334,x21331),f435(x21333,x21334,x21332))
% 173.53/173.44 [2134]~E(x21341,x21342)+E(f829(x21341,x21343,x21344,x21345),f829(x21342,x21343,x21344,x21345))
% 173.53/173.44 [2135]~E(x21351,x21352)+E(f829(x21353,x21351,x21354,x21355),f829(x21353,x21352,x21354,x21355))
% 173.53/173.44 [2136]~E(x21361,x21362)+E(f829(x21363,x21364,x21361,x21365),f829(x21363,x21364,x21362,x21365))
% 173.53/173.44 [2137]~E(x21371,x21372)+E(f829(x21373,x21374,x21375,x21371),f829(x21373,x21374,x21375,x21372))
% 173.53/173.44 [2138]~E(x21381,x21382)+E(f197(x21381,x21383),f197(x21382,x21383))
% 173.53/173.44 [2139]~E(x21391,x21392)+E(f197(x21393,x21391),f197(x21393,x21392))
% 173.53/173.44 [2140]~E(x21401,x21402)+E(f463(x21401,x21403),f463(x21402,x21403))
% 173.53/173.44 [2141]~E(x21411,x21412)+E(f463(x21413,x21411),f463(x21413,x21412))
% 173.53/173.44 [2142]~E(x21421,x21422)+E(f506(x21421,x21423,x21424,x21425),f506(x21422,x21423,x21424,x21425))
% 173.53/173.44 [2143]~E(x21431,x21432)+E(f506(x21433,x21431,x21434,x21435),f506(x21433,x21432,x21434,x21435))
% 173.53/173.44 [2144]~E(x21441,x21442)+E(f506(x21443,x21444,x21441,x21445),f506(x21443,x21444,x21442,x21445))
% 173.53/173.44 [2145]~E(x21451,x21452)+E(f506(x21453,x21454,x21455,x21451),f506(x21453,x21454,x21455,x21452))
% 173.53/173.44 [2146]~E(x21461,x21462)+E(f582(x21461,x21463),f582(x21462,x21463))
% 173.53/173.44 [2147]~E(x21471,x21472)+E(f582(x21473,x21471),f582(x21473,x21472))
% 173.53/173.44 [2148]~E(x21481,x21482)+E(f828(x21481,x21483,x21484,x21485),f828(x21482,x21483,x21484,x21485))
% 173.53/173.44 [2149]~E(x21491,x21492)+E(f828(x21493,x21491,x21494,x21495),f828(x21493,x21492,x21494,x21495))
% 173.53/173.44 [2150]~E(x21501,x21502)+E(f828(x21503,x21504,x21501,x21505),f828(x21503,x21504,x21502,x21505))
% 173.53/173.44 [2151]~E(x21511,x21512)+E(f828(x21513,x21514,x21515,x21511),f828(x21513,x21514,x21515,x21512))
% 173.53/173.44 [2152]~E(x21521,x21522)+E(f518(x21521,x21523,x21524,x21525,x21526),f518(x21522,x21523,x21524,x21525,x21526))
% 173.53/173.44 [2153]~E(x21531,x21532)+E(f518(x21533,x21531,x21534,x21535,x21536),f518(x21533,x21532,x21534,x21535,x21536))
% 173.53/173.44 [2154]~E(x21541,x21542)+E(f518(x21543,x21544,x21541,x21545,x21546),f518(x21543,x21544,x21542,x21545,x21546))
% 173.53/173.44 [2155]~E(x21551,x21552)+E(f518(x21553,x21554,x21555,x21551,x21556),f518(x21553,x21554,x21555,x21552,x21556))
% 173.53/173.44 [2156]~E(x21561,x21562)+E(f518(x21563,x21564,x21565,x21566,x21561),f518(x21563,x21564,x21565,x21566,x21562))
% 173.53/173.44 [2157]~E(x21571,x21572)+E(f622(x21571,x21573,x21574,x21575,x21576),f622(x21572,x21573,x21574,x21575,x21576))
% 173.53/173.44 [2158]~E(x21581,x21582)+E(f622(x21583,x21581,x21584,x21585,x21586),f622(x21583,x21582,x21584,x21585,x21586))
% 173.53/173.44 [2159]~E(x21591,x21592)+E(f622(x21593,x21594,x21591,x21595,x21596),f622(x21593,x21594,x21592,x21595,x21596))
% 173.53/173.44 [2160]~E(x21601,x21602)+E(f622(x21603,x21604,x21605,x21601,x21606),f622(x21603,x21604,x21605,x21602,x21606))
% 173.53/173.44 [2161]~E(x21611,x21612)+E(f622(x21613,x21614,x21615,x21616,x21611),f622(x21613,x21614,x21615,x21616,x21612))
% 173.53/173.44 [2162]~E(x21621,x21622)+E(f398(x21621,x21623,x21624),f398(x21622,x21623,x21624))
% 173.53/173.44 [2163]~E(x21631,x21632)+E(f398(x21633,x21631,x21634),f398(x21633,x21632,x21634))
% 173.53/173.44 [2164]~E(x21641,x21642)+E(f398(x21643,x21644,x21641),f398(x21643,x21644,x21642))
% 173.53/173.44 [2165]~E(x21651,x21652)+E(f733(x21651,x21653,x21654,x21655,x21656,x21657,x21658),f733(x21652,x21653,x21654,x21655,x21656,x21657,x21658))
% 173.53/173.44 [2166]~E(x21661,x21662)+E(f733(x21663,x21661,x21664,x21665,x21666,x21667,x21668),f733(x21663,x21662,x21664,x21665,x21666,x21667,x21668))
% 173.53/173.44 [2167]~E(x21671,x21672)+E(f733(x21673,x21674,x21671,x21675,x21676,x21677,x21678),f733(x21673,x21674,x21672,x21675,x21676,x21677,x21678))
% 173.53/173.44 [2168]~E(x21681,x21682)+E(f733(x21683,x21684,x21685,x21681,x21686,x21687,x21688),f733(x21683,x21684,x21685,x21682,x21686,x21687,x21688))
% 173.53/173.44 [2169]~E(x21691,x21692)+E(f733(x21693,x21694,x21695,x21696,x21691,x21697,x21698),f733(x21693,x21694,x21695,x21696,x21692,x21697,x21698))
% 173.53/173.44 [2170]~E(x21701,x21702)+E(f733(x21703,x21704,x21705,x21706,x21707,x21701,x21708),f733(x21703,x21704,x21705,x21706,x21707,x21702,x21708))
% 173.53/173.44 [2171]~E(x21711,x21712)+E(f733(x21713,x21714,x21715,x21716,x21717,x21718,x21711),f733(x21713,x21714,x21715,x21716,x21717,x21718,x21712))
% 173.53/173.44 [2172]~E(x21721,x21722)+E(f639(x21721,x21723,x21724,x21725,x21726),f639(x21722,x21723,x21724,x21725,x21726))
% 173.53/173.44 [2173]~E(x21731,x21732)+E(f639(x21733,x21731,x21734,x21735,x21736),f639(x21733,x21732,x21734,x21735,x21736))
% 173.53/173.44 [2174]~E(x21741,x21742)+E(f639(x21743,x21744,x21741,x21745,x21746),f639(x21743,x21744,x21742,x21745,x21746))
% 173.53/173.44 [2175]~E(x21751,x21752)+E(f639(x21753,x21754,x21755,x21751,x21756),f639(x21753,x21754,x21755,x21752,x21756))
% 173.53/173.44 [2176]~E(x21761,x21762)+E(f639(x21763,x21764,x21765,x21766,x21761),f639(x21763,x21764,x21765,x21766,x21762))
% 173.53/173.44 [2177]~E(x21771,x21772)+E(f628(x21771,x21773,x21774,x21775,x21776),f628(x21772,x21773,x21774,x21775,x21776))
% 173.53/173.44 [2178]~E(x21781,x21782)+E(f628(x21783,x21781,x21784,x21785,x21786),f628(x21783,x21782,x21784,x21785,x21786))
% 173.53/173.44 [2179]~E(x21791,x21792)+E(f628(x21793,x21794,x21791,x21795,x21796),f628(x21793,x21794,x21792,x21795,x21796))
% 173.53/173.44 [2180]~E(x21801,x21802)+E(f628(x21803,x21804,x21805,x21801,x21806),f628(x21803,x21804,x21805,x21802,x21806))
% 173.53/173.44 [2181]~E(x21811,x21812)+E(f628(x21813,x21814,x21815,x21816,x21811),f628(x21813,x21814,x21815,x21816,x21812))
% 173.53/173.44 [2182]~E(x21821,x21822)+E(f432(x21821,x21823,x21824),f432(x21822,x21823,x21824))
% 173.53/173.44 [2183]~E(x21831,x21832)+E(f432(x21833,x21831,x21834),f432(x21833,x21832,x21834))
% 173.53/173.44 [2184]~E(x21841,x21842)+E(f432(x21843,x21844,x21841),f432(x21843,x21844,x21842))
% 173.53/173.44 [2185]~E(x21851,x21852)+E(f674(x21851,x21853),f674(x21852,x21853))
% 173.53/173.44 [2186]~E(x21861,x21862)+E(f674(x21863,x21861),f674(x21863,x21862))
% 173.53/173.44 [2187]~E(x21871,x21872)+E(f521(x21871,x21873,x21874,x21875,x21876),f521(x21872,x21873,x21874,x21875,x21876))
% 173.53/173.44 [2188]~E(x21881,x21882)+E(f521(x21883,x21881,x21884,x21885,x21886),f521(x21883,x21882,x21884,x21885,x21886))
% 173.53/173.44 [2189]~E(x21891,x21892)+E(f521(x21893,x21894,x21891,x21895,x21896),f521(x21893,x21894,x21892,x21895,x21896))
% 173.53/173.44 [2190]~E(x21901,x21902)+E(f521(x21903,x21904,x21905,x21901,x21906),f521(x21903,x21904,x21905,x21902,x21906))
% 173.53/173.44 [2191]~E(x21911,x21912)+E(f521(x21913,x21914,x21915,x21916,x21911),f521(x21913,x21914,x21915,x21916,x21912))
% 173.53/173.44 [2192]~E(x21921,x21922)+E(f764(x21921,x21923,x21924),f764(x21922,x21923,x21924))
% 173.53/173.44 [2193]~E(x21931,x21932)+E(f764(x21933,x21931,x21934),f764(x21933,x21932,x21934))
% 173.53/173.44 [2194]~E(x21941,x21942)+E(f764(x21943,x21944,x21941),f764(x21943,x21944,x21942))
% 173.53/173.44 [2195]~E(x21951,x21952)+E(f374(x21951,x21953),f374(x21952,x21953))
% 173.53/173.44 [2196]~E(x21961,x21962)+E(f374(x21963,x21961),f374(x21963,x21962))
% 173.53/173.44 [2197]~E(x21971,x21972)+E(f784(x21971,x21973),f784(x21972,x21973))
% 173.53/173.44 [2198]~E(x21981,x21982)+E(f784(x21983,x21981),f784(x21983,x21982))
% 173.53/173.44 [2199]~E(x21991,x21992)+E(f651(x21991,x21993),f651(x21992,x21993))
% 173.53/173.44 [2200]~E(x22001,x22002)+E(f651(x22003,x22001),f651(x22003,x22002))
% 173.53/173.44 [2201]~E(x22011,x22012)+E(f448(x22011,x22013,x22014,x22015),f448(x22012,x22013,x22014,x22015))
% 173.53/173.44 [2202]~E(x22021,x22022)+E(f448(x22023,x22021,x22024,x22025),f448(x22023,x22022,x22024,x22025))
% 173.53/173.44 [2203]~E(x22031,x22032)+E(f448(x22033,x22034,x22031,x22035),f448(x22033,x22034,x22032,x22035))
% 173.53/173.44 [2204]~E(x22041,x22042)+E(f448(x22043,x22044,x22045,x22041),f448(x22043,x22044,x22045,x22042))
% 173.53/173.44 [2205]~E(x22051,x22052)+E(f841(x22051,x22053,x22054),f841(x22052,x22053,x22054))
% 173.53/173.44 [2206]~E(x22061,x22062)+E(f841(x22063,x22061,x22064),f841(x22063,x22062,x22064))
% 173.53/173.44 [2207]~E(x22071,x22072)+E(f841(x22073,x22074,x22071),f841(x22073,x22074,x22072))
% 173.53/173.44 [2208]~E(x22081,x22082)+E(f509(x22081,x22083,x22084,x22085,x22086),f509(x22082,x22083,x22084,x22085,x22086))
% 173.53/173.44 [2209]~E(x22091,x22092)+E(f509(x22093,x22091,x22094,x22095,x22096),f509(x22093,x22092,x22094,x22095,x22096))
% 173.53/173.44 [2210]~E(x22101,x22102)+E(f509(x22103,x22104,x22101,x22105,x22106),f509(x22103,x22104,x22102,x22105,x22106))
% 173.53/173.44 [2211]~E(x22111,x22112)+E(f509(x22113,x22114,x22115,x22111,x22116),f509(x22113,x22114,x22115,x22112,x22116))
% 173.53/173.44 [2212]~E(x22121,x22122)+E(f509(x22123,x22124,x22125,x22126,x22121),f509(x22123,x22124,x22125,x22126,x22122))
% 173.53/173.44 [2213]~E(x22131,x22132)+E(f457(x22131,x22133,x22134),f457(x22132,x22133,x22134))
% 173.53/173.44 [2214]~E(x22141,x22142)+E(f457(x22143,x22141,x22144),f457(x22143,x22142,x22144))
% 173.53/173.44 [2215]~E(x22151,x22152)+E(f457(x22153,x22154,x22151),f457(x22153,x22154,x22152))
% 173.53/173.44 [2216]~E(x22161,x22162)+E(f336(x22161,x22163,x22164),f336(x22162,x22163,x22164))
% 173.53/173.44 [2217]~E(x22171,x22172)+E(f336(x22173,x22171,x22174),f336(x22173,x22172,x22174))
% 173.53/173.44 [2218]~E(x22181,x22182)+E(f336(x22183,x22184,x22181),f336(x22183,x22184,x22182))
% 173.53/173.44 [2219]~E(x22191,x22192)+E(f384(x22191,x22193,x22194,x22195),f384(x22192,x22193,x22194,x22195))
% 173.53/173.44 [2220]~E(x22201,x22202)+E(f384(x22203,x22201,x22204,x22205),f384(x22203,x22202,x22204,x22205))
% 173.53/173.44 [2221]~E(x22211,x22212)+E(f384(x22213,x22214,x22211,x22215),f384(x22213,x22214,x22212,x22215))
% 173.53/173.44 [2222]~E(x22221,x22222)+E(f384(x22223,x22224,x22225,x22221),f384(x22223,x22224,x22225,x22222))
% 173.53/173.44 [2223]~E(x22231,x22232)+E(f550(x22231,x22233),f550(x22232,x22233))
% 173.53/173.44 [2224]~E(x22241,x22242)+E(f550(x22243,x22241),f550(x22243,x22242))
% 173.53/173.44 [2225]~E(x22251,x22252)+E(f839(x22251,x22253,x22254),f839(x22252,x22253,x22254))
% 173.53/173.44 [2226]~E(x22261,x22262)+E(f839(x22263,x22261,x22264),f839(x22263,x22262,x22264))
% 173.53/173.44 [2227]~E(x22271,x22272)+E(f839(x22273,x22274,x22271),f839(x22273,x22274,x22272))
% 173.53/173.44 [2228]~E(x22281,x22282)+E(f338(x22281,x22283,x22284),f338(x22282,x22283,x22284))
% 173.53/173.44 [2229]~E(x22291,x22292)+E(f338(x22293,x22291,x22294),f338(x22293,x22292,x22294))
% 173.53/173.44 [2230]~E(x22301,x22302)+E(f338(x22303,x22304,x22301),f338(x22303,x22304,x22302))
% 173.53/173.44 [2231]~E(x22311,x22312)+E(f482(x22311,x22313,x22314,x22315),f482(x22312,x22313,x22314,x22315))
% 173.53/173.44 [2232]~E(x22321,x22322)+E(f482(x22323,x22321,x22324,x22325),f482(x22323,x22322,x22324,x22325))
% 173.53/173.44 [2233]~E(x22331,x22332)+E(f482(x22333,x22334,x22331,x22335),f482(x22333,x22334,x22332,x22335))
% 173.53/173.44 [2234]~E(x22341,x22342)+E(f482(x22343,x22344,x22345,x22341),f482(x22343,x22344,x22345,x22342))
% 173.53/173.44 [2235]~E(x22351,x22352)+E(f530(x22351,x22353,x22354,x22355,x22356,x22357),f530(x22352,x22353,x22354,x22355,x22356,x22357))
% 173.53/173.44 [2236]~E(x22361,x22362)+E(f530(x22363,x22361,x22364,x22365,x22366,x22367),f530(x22363,x22362,x22364,x22365,x22366,x22367))
% 173.53/173.44 [2237]~E(x22371,x22372)+E(f530(x22373,x22374,x22371,x22375,x22376,x22377),f530(x22373,x22374,x22372,x22375,x22376,x22377))
% 173.53/173.44 [2238]~E(x22381,x22382)+E(f530(x22383,x22384,x22385,x22381,x22386,x22387),f530(x22383,x22384,x22385,x22382,x22386,x22387))
% 173.53/173.44 [2239]~E(x22391,x22392)+E(f530(x22393,x22394,x22395,x22396,x22391,x22397),f530(x22393,x22394,x22395,x22396,x22392,x22397))
% 173.53/173.44 [2240]~E(x22401,x22402)+E(f530(x22403,x22404,x22405,x22406,x22407,x22401),f530(x22403,x22404,x22405,x22406,x22407,x22402))
% 173.53/173.44 [2241]~E(x22411,x22412)+E(f663(x22411,x22413,x22414),f663(x22412,x22413,x22414))
% 173.53/173.44 [2242]~E(x22421,x22422)+E(f663(x22423,x22421,x22424),f663(x22423,x22422,x22424))
% 173.53/173.44 [2243]~E(x22431,x22432)+E(f663(x22433,x22434,x22431),f663(x22433,x22434,x22432))
% 173.53/173.44 [2244]~E(x22441,x22442)+E(f838(x22441,x22443),f838(x22442,x22443))
% 173.53/173.44 [2245]~E(x22451,x22452)+E(f838(x22453,x22451),f838(x22453,x22452))
% 173.53/173.44 [2246]~E(x22461,x22462)+E(f404(x22461,x22463,x22464,x22465,x22466),f404(x22462,x22463,x22464,x22465,x22466))
% 173.53/173.44 [2247]~E(x22471,x22472)+E(f404(x22473,x22471,x22474,x22475,x22476),f404(x22473,x22472,x22474,x22475,x22476))
% 173.53/173.44 [2248]~E(x22481,x22482)+E(f404(x22483,x22484,x22481,x22485,x22486),f404(x22483,x22484,x22482,x22485,x22486))
% 173.53/173.44 [2249]~E(x22491,x22492)+E(f404(x22493,x22494,x22495,x22491,x22496),f404(x22493,x22494,x22495,x22492,x22496))
% 173.53/173.44 [2250]~E(x22501,x22502)+E(f404(x22503,x22504,x22505,x22506,x22501),f404(x22503,x22504,x22505,x22506,x22502))
% 173.53/173.44 [2251]~E(x22511,x22512)+E(f655(x22511,x22513),f655(x22512,x22513))
% 173.53/173.44 [2252]~E(x22521,x22522)+E(f655(x22523,x22521),f655(x22523,x22522))
% 173.53/173.44 [2253]~E(x22531,x22532)+E(f350(x22531,x22533,x22534,x22535),f350(x22532,x22533,x22534,x22535))
% 173.53/173.44 [2254]~E(x22541,x22542)+E(f350(x22543,x22541,x22544,x22545),f350(x22543,x22542,x22544,x22545))
% 173.53/173.44 [2255]~E(x22551,x22552)+E(f350(x22553,x22554,x22551,x22555),f350(x22553,x22554,x22552,x22555))
% 173.53/173.44 [2256]~E(x22561,x22562)+E(f350(x22563,x22564,x22565,x22561),f350(x22563,x22564,x22565,x22562))
% 173.53/173.44 [2257]~E(x22571,x22572)+E(f561(x22571,x22573,x22574,x22575,x22576,x22577),f561(x22572,x22573,x22574,x22575,x22576,x22577))
% 173.53/173.44 [2258]~E(x22581,x22582)+E(f561(x22583,x22581,x22584,x22585,x22586,x22587),f561(x22583,x22582,x22584,x22585,x22586,x22587))
% 173.53/173.44 [2259]~E(x22591,x22592)+E(f561(x22593,x22594,x22591,x22595,x22596,x22597),f561(x22593,x22594,x22592,x22595,x22596,x22597))
% 173.53/173.44 [2260]~E(x22601,x22602)+E(f561(x22603,x22604,x22605,x22601,x22606,x22607),f561(x22603,x22604,x22605,x22602,x22606,x22607))
% 173.53/173.44 [2261]~E(x22611,x22612)+E(f561(x22613,x22614,x22615,x22616,x22611,x22617),f561(x22613,x22614,x22615,x22616,x22612,x22617))
% 173.53/173.44 [2262]~E(x22621,x22622)+E(f561(x22623,x22624,x22625,x22626,x22627,x22621),f561(x22623,x22624,x22625,x22626,x22627,x22622))
% 173.53/173.44 [2263]~E(x22631,x22632)+E(f399(x22631,x22633,x22634,x22635),f399(x22632,x22633,x22634,x22635))
% 173.53/173.44 [2264]~E(x22641,x22642)+E(f399(x22643,x22641,x22644,x22645),f399(x22643,x22642,x22644,x22645))
% 173.53/173.44 [2265]~E(x22651,x22652)+E(f399(x22653,x22654,x22651,x22655),f399(x22653,x22654,x22652,x22655))
% 173.53/173.44 [2266]~E(x22661,x22662)+E(f399(x22663,x22664,x22665,x22661),f399(x22663,x22664,x22665,x22662))
% 173.53/173.44 [2267]~E(x22671,x22672)+E(f500(x22671,x22673,x22674,x22675,x22676),f500(x22672,x22673,x22674,x22675,x22676))
% 173.53/173.44 [2268]~E(x22681,x22682)+E(f500(x22683,x22681,x22684,x22685,x22686),f500(x22683,x22682,x22684,x22685,x22686))
% 173.53/173.44 [2269]~E(x22691,x22692)+E(f500(x22693,x22694,x22691,x22695,x22696),f500(x22693,x22694,x22692,x22695,x22696))
% 173.53/173.44 [2270]~E(x22701,x22702)+E(f500(x22703,x22704,x22705,x22701,x22706),f500(x22703,x22704,x22705,x22702,x22706))
% 173.53/173.44 [2271]~E(x22711,x22712)+E(f500(x22713,x22714,x22715,x22716,x22711),f500(x22713,x22714,x22715,x22716,x22712))
% 173.53/173.44 [2272]~E(x22721,x22722)+E(f637(x22721,x22723,x22724,x22725,x22726),f637(x22722,x22723,x22724,x22725,x22726))
% 173.53/173.44 [2273]~E(x22731,x22732)+E(f637(x22733,x22731,x22734,x22735,x22736),f637(x22733,x22732,x22734,x22735,x22736))
% 173.53/173.44 [2274]~E(x22741,x22742)+E(f637(x22743,x22744,x22741,x22745,x22746),f637(x22743,x22744,x22742,x22745,x22746))
% 173.53/173.44 [2275]~E(x22751,x22752)+E(f637(x22753,x22754,x22755,x22751,x22756),f637(x22753,x22754,x22755,x22752,x22756))
% 173.53/173.44 [2276]~E(x22761,x22762)+E(f637(x22763,x22764,x22765,x22766,x22761),f637(x22763,x22764,x22765,x22766,x22762))
% 173.53/173.44 [2277]~E(x22771,x22772)+E(f371(x22771,x22773),f371(x22772,x22773))
% 173.53/173.44 [2278]~E(x22781,x22782)+E(f371(x22783,x22781),f371(x22783,x22782))
% 173.53/173.44 [2279]~E(x22791,x22792)+E(f102(x22791),f102(x22792))
% 173.53/173.44 [2280]~E(x22801,x22802)+E(f606(x22801,x22803,x22804,x22805),f606(x22802,x22803,x22804,x22805))
% 173.53/173.44 [2281]~E(x22811,x22812)+E(f606(x22813,x22811,x22814,x22815),f606(x22813,x22812,x22814,x22815))
% 173.53/173.44 [2282]~E(x22821,x22822)+E(f606(x22823,x22824,x22821,x22825),f606(x22823,x22824,x22822,x22825))
% 173.53/173.44 [2283]~E(x22831,x22832)+E(f606(x22833,x22834,x22835,x22831),f606(x22833,x22834,x22835,x22832))
% 173.53/173.44 [2284]~E(x22841,x22842)+E(f390(x22841,x22843),f390(x22842,x22843))
% 173.53/173.44 [2285]~E(x22851,x22852)+E(f390(x22853,x22851),f390(x22853,x22852))
% 173.53/173.44 [2286]~E(x22861,x22862)+E(f652(x22861,x22863),f652(x22862,x22863))
% 173.53/173.44 [2287]~E(x22871,x22872)+E(f652(x22873,x22871),f652(x22873,x22872))
% 173.53/173.44 [2288]~E(x22881,x22882)+E(f746(x22881,x22883,x22884,x22885,x22886,x22887),f746(x22882,x22883,x22884,x22885,x22886,x22887))
% 173.53/173.44 [2289]~E(x22891,x22892)+E(f746(x22893,x22891,x22894,x22895,x22896,x22897),f746(x22893,x22892,x22894,x22895,x22896,x22897))
% 173.53/173.44 [2290]~E(x22901,x22902)+E(f746(x22903,x22904,x22901,x22905,x22906,x22907),f746(x22903,x22904,x22902,x22905,x22906,x22907))
% 173.53/173.44 [2291]~E(x22911,x22912)+E(f746(x22913,x22914,x22915,x22911,x22916,x22917),f746(x22913,x22914,x22915,x22912,x22916,x22917))
% 173.53/173.44 [2292]~E(x22921,x22922)+E(f746(x22923,x22924,x22925,x22926,x22921,x22927),f746(x22923,x22924,x22925,x22926,x22922,x22927))
% 173.53/173.44 [2293]~E(x22931,x22932)+E(f746(x22933,x22934,x22935,x22936,x22937,x22931),f746(x22933,x22934,x22935,x22936,x22937,x22932))
% 173.53/173.44 [2294]~E(x22941,x22942)+E(f450(x22941,x22943,x22944,x22945),f450(x22942,x22943,x22944,x22945))
% 173.53/173.44 [2295]~E(x22951,x22952)+E(f450(x22953,x22951,x22954,x22955),f450(x22953,x22952,x22954,x22955))
% 173.53/173.44 [2296]~E(x22961,x22962)+E(f450(x22963,x22964,x22961,x22965),f450(x22963,x22964,x22962,x22965))
% 173.53/173.44 [2297]~E(x22971,x22972)+E(f450(x22973,x22974,x22975,x22971),f450(x22973,x22974,x22975,x22972))
% 173.53/173.44 [2298]~E(x22981,x22982)+E(f830(x22981,x22983,x22984,x22985,x22986),f830(x22982,x22983,x22984,x22985,x22986))
% 173.53/173.44 [2299]~E(x22991,x22992)+E(f830(x22993,x22991,x22994,x22995,x22996),f830(x22993,x22992,x22994,x22995,x22996))
% 173.53/173.44 [2300]~E(x23001,x23002)+E(f830(x23003,x23004,x23001,x23005,x23006),f830(x23003,x23004,x23002,x23005,x23006))
% 173.53/173.44 [2301]~E(x23011,x23012)+E(f830(x23013,x23014,x23015,x23011,x23016),f830(x23013,x23014,x23015,x23012,x23016))
% 173.53/173.44 [2302]~E(x23021,x23022)+E(f830(x23023,x23024,x23025,x23026,x23021),f830(x23023,x23024,x23025,x23026,x23022))
% 173.53/173.44 [2303]~E(x23031,x23032)+E(f811(x23031,x23033,x23034),f811(x23032,x23033,x23034))
% 173.53/173.44 [2304]~E(x23041,x23042)+E(f811(x23043,x23041,x23044),f811(x23043,x23042,x23044))
% 173.53/173.44 [2305]~E(x23051,x23052)+E(f811(x23053,x23054,x23051),f811(x23053,x23054,x23052))
% 173.53/173.44 [2306]~E(x23061,x23062)+E(f650(x23061,x23063),f650(x23062,x23063))
% 173.53/173.44 [2307]~E(x23071,x23072)+E(f650(x23073,x23071),f650(x23073,x23072))
% 173.53/173.44 [2308]~E(x23081,x23082)+E(f474(x23081,x23083,x23084,x23085),f474(x23082,x23083,x23084,x23085))
% 173.53/173.44 [2309]~E(x23091,x23092)+E(f474(x23093,x23091,x23094,x23095),f474(x23093,x23092,x23094,x23095))
% 173.53/173.44 [2310]~E(x23101,x23102)+E(f474(x23103,x23104,x23101,x23105),f474(x23103,x23104,x23102,x23105))
% 173.53/173.44 [2311]~E(x23111,x23112)+E(f474(x23113,x23114,x23115,x23111),f474(x23113,x23114,x23115,x23112))
% 173.53/173.44 [2312]~E(x23121,x23122)+E(f594(x23121,x23123,x23124,x23125,x23126),f594(x23122,x23123,x23124,x23125,x23126))
% 173.53/173.44 [2313]~E(x23131,x23132)+E(f594(x23133,x23131,x23134,x23135,x23136),f594(x23133,x23132,x23134,x23135,x23136))
% 173.53/173.44 [2314]~E(x23141,x23142)+E(f594(x23143,x23144,x23141,x23145,x23146),f594(x23143,x23144,x23142,x23145,x23146))
% 173.53/173.44 [2315]~E(x23151,x23152)+E(f594(x23153,x23154,x23155,x23151,x23156),f594(x23153,x23154,x23155,x23152,x23156))
% 173.53/173.44 [2316]~E(x23161,x23162)+E(f594(x23163,x23164,x23165,x23166,x23161),f594(x23163,x23164,x23165,x23166,x23162))
% 173.53/173.44 [2317]~E(x23171,x23172)+E(f754(x23171,x23173,x23174,x23175,x23176),f754(x23172,x23173,x23174,x23175,x23176))
% 173.53/173.44 [2318]~E(x23181,x23182)+E(f754(x23183,x23181,x23184,x23185,x23186),f754(x23183,x23182,x23184,x23185,x23186))
% 173.53/173.44 [2319]~E(x23191,x23192)+E(f754(x23193,x23194,x23191,x23195,x23196),f754(x23193,x23194,x23192,x23195,x23196))
% 173.53/173.44 [2320]~E(x23201,x23202)+E(f754(x23203,x23204,x23205,x23201,x23206),f754(x23203,x23204,x23205,x23202,x23206))
% 173.53/173.44 [2321]~E(x23211,x23212)+E(f754(x23213,x23214,x23215,x23216,x23211),f754(x23213,x23214,x23215,x23216,x23212))
% 173.53/173.44 [2322]~E(x23221,x23222)+E(f493(x23221,x23223,x23224,x23225),f493(x23222,x23223,x23224,x23225))
% 173.53/173.44 [2323]~E(x23231,x23232)+E(f493(x23233,x23231,x23234,x23235),f493(x23233,x23232,x23234,x23235))
% 173.53/173.44 [2324]~E(x23241,x23242)+E(f493(x23243,x23244,x23241,x23245),f493(x23243,x23244,x23242,x23245))
% 173.53/173.44 [2325]~E(x23251,x23252)+E(f493(x23253,x23254,x23255,x23251),f493(x23253,x23254,x23255,x23252))
% 173.53/173.44 [2326]~E(x23261,x23262)+E(f753(x23261,x23263,x23264),f753(x23262,x23263,x23264))
% 173.53/173.44 [2327]~E(x23271,x23272)+E(f753(x23273,x23271,x23274),f753(x23273,x23272,x23274))
% 173.53/173.44 [2328]~E(x23281,x23282)+E(f753(x23283,x23284,x23281),f753(x23283,x23284,x23282))
% 173.53/173.44 [2329]~E(x23291,x23292)+E(f749(x23291,x23293),f749(x23292,x23293))
% 173.53/173.44 [2330]~E(x23301,x23302)+E(f749(x23303,x23301),f749(x23303,x23302))
% 173.53/173.44 [2331]~E(x23311,x23312)+E(f678(x23311,x23313,x23314),f678(x23312,x23313,x23314))
% 173.53/173.44 [2332]~E(x23321,x23322)+E(f678(x23323,x23321,x23324),f678(x23323,x23322,x23324))
% 173.53/173.44 [2333]~E(x23331,x23332)+E(f678(x23333,x23334,x23331),f678(x23333,x23334,x23332))
% 173.53/173.44 [2334]~E(x23341,x23342)+E(f672(x23341,x23343,x23344,x23345,x23346),f672(x23342,x23343,x23344,x23345,x23346))
% 173.53/173.44 [2335]~E(x23351,x23352)+E(f672(x23353,x23351,x23354,x23355,x23356),f672(x23353,x23352,x23354,x23355,x23356))
% 173.53/173.44 [2336]~E(x23361,x23362)+E(f672(x23363,x23364,x23361,x23365,x23366),f672(x23363,x23364,x23362,x23365,x23366))
% 173.53/173.44 [2337]~E(x23371,x23372)+E(f672(x23373,x23374,x23375,x23371,x23376),f672(x23373,x23374,x23375,x23372,x23376))
% 173.53/173.44 [2338]~E(x23381,x23382)+E(f672(x23383,x23384,x23385,x23386,x23381),f672(x23383,x23384,x23385,x23386,x23382))
% 173.53/173.44 [2339]~E(x23391,x23392)+E(f505(x23391,x23393,x23394),f505(x23392,x23393,x23394))
% 173.53/173.44 [2340]~E(x23401,x23402)+E(f505(x23403,x23401,x23404),f505(x23403,x23402,x23404))
% 173.53/173.44 [2341]~E(x23411,x23412)+E(f505(x23413,x23414,x23411),f505(x23413,x23414,x23412))
% 173.53/173.44 [2342]~E(x23421,x23422)+E(f772(x23421,x23423,x23424,x23425,x23426),f772(x23422,x23423,x23424,x23425,x23426))
% 173.53/173.44 [2343]~E(x23431,x23432)+E(f772(x23433,x23431,x23434,x23435,x23436),f772(x23433,x23432,x23434,x23435,x23436))
% 173.53/173.44 [2344]~E(x23441,x23442)+E(f772(x23443,x23444,x23441,x23445,x23446),f772(x23443,x23444,x23442,x23445,x23446))
% 173.53/173.44 [2345]~E(x23451,x23452)+E(f772(x23453,x23454,x23455,x23451,x23456),f772(x23453,x23454,x23455,x23452,x23456))
% 173.53/173.44 [2346]~E(x23461,x23462)+E(f772(x23463,x23464,x23465,x23466,x23461),f772(x23463,x23464,x23465,x23466,x23462))
% 173.53/173.44 [2347]~E(x23471,x23472)+E(f489(x23471,x23473,x23474),f489(x23472,x23473,x23474))
% 173.53/173.44 [2348]~E(x23481,x23482)+E(f489(x23483,x23481,x23484),f489(x23483,x23482,x23484))
% 173.53/173.44 [2349]~E(x23491,x23492)+E(f489(x23493,x23494,x23491),f489(x23493,x23494,x23492))
% 173.53/173.44 [2350]~E(x23501,x23502)+E(f555(x23501,x23503),f555(x23502,x23503))
% 173.53/173.44 [2351]~E(x23511,x23512)+E(f555(x23513,x23511),f555(x23513,x23512))
% 173.53/173.44 [2352]~E(x23521,x23522)+E(f76(x23521,x23523,x23524),f76(x23522,x23523,x23524))
% 173.53/173.44 [2353]~E(x23531,x23532)+E(f76(x23533,x23531,x23534),f76(x23533,x23532,x23534))
% 173.53/173.44 [2354]~E(x23541,x23542)+E(f76(x23543,x23544,x23541),f76(x23543,x23544,x23542))
% 173.53/173.44 [2355]~E(x23551,x23552)+E(f649(x23551,x23553),f649(x23552,x23553))
% 173.53/173.44 [2356]~E(x23561,x23562)+E(f649(x23563,x23561),f649(x23563,x23562))
% 173.53/173.44 [2357]~E(x23571,x23572)+E(f745(x23571,x23573,x23574),f745(x23572,x23573,x23574))
% 173.53/173.44 [2358]~E(x23581,x23582)+E(f745(x23583,x23581,x23584),f745(x23583,x23582,x23584))
% 173.53/173.44 [2359]~E(x23591,x23592)+E(f745(x23593,x23594,x23591),f745(x23593,x23594,x23592))
% 173.53/173.44 [2360]~E(x23601,x23602)+E(f272(x23601,x23603,x23604),f272(x23602,x23603,x23604))
% 173.53/173.44 [2361]~E(x23611,x23612)+E(f272(x23613,x23611,x23614),f272(x23613,x23612,x23614))
% 173.53/173.44 [2362]~E(x23621,x23622)+E(f272(x23623,x23624,x23621),f272(x23623,x23624,x23622))
% 173.53/173.44 [2363]~E(x23631,x23632)+E(f797(x23631,x23633,x23634,x23635),f797(x23632,x23633,x23634,x23635))
% 173.53/173.44 [2364]~E(x23641,x23642)+E(f797(x23643,x23641,x23644,x23645),f797(x23643,x23642,x23644,x23645))
% 173.53/173.44 [2365]~E(x23651,x23652)+E(f797(x23653,x23654,x23651,x23655),f797(x23653,x23654,x23652,x23655))
% 173.53/173.44 [2366]~E(x23661,x23662)+E(f797(x23663,x23664,x23665,x23661),f797(x23663,x23664,x23665,x23662))
% 173.53/173.44 [2367]~E(x23671,x23672)+E(f460(x23671,x23673,x23674,x23675),f460(x23672,x23673,x23674,x23675))
% 173.53/173.44 [2368]~E(x23681,x23682)+E(f460(x23683,x23681,x23684,x23685),f460(x23683,x23682,x23684,x23685))
% 173.53/173.44 [2369]~E(x23691,x23692)+E(f460(x23693,x23694,x23691,x23695),f460(x23693,x23694,x23692,x23695))
% 173.53/173.44 [2370]~E(x23701,x23702)+E(f460(x23703,x23704,x23705,x23701),f460(x23703,x23704,x23705,x23702))
% 173.53/173.44 [2371]~E(x23711,x23712)+E(f381(x23711,x23713),f381(x23712,x23713))
% 173.53/173.44 [2372]~E(x23721,x23722)+E(f381(x23723,x23721),f381(x23723,x23722))
% 173.53/173.44 [2373]~E(x23731,x23732)+E(f819(x23731),f819(x23732))
% 173.53/173.44 [2374]~E(x23741,x23742)+E(f760(x23741,x23743),f760(x23742,x23743))
% 173.53/173.44 [2375]~E(x23751,x23752)+E(f760(x23753,x23751),f760(x23753,x23752))
% 173.53/173.44 [2376]~E(x23761,x23762)+E(f564(x23761,x23763,x23764,x23765,x23766,x23767),f564(x23762,x23763,x23764,x23765,x23766,x23767))
% 173.53/173.44 [2377]~E(x23771,x23772)+E(f564(x23773,x23771,x23774,x23775,x23776,x23777),f564(x23773,x23772,x23774,x23775,x23776,x23777))
% 173.53/173.44 [2378]~E(x23781,x23782)+E(f564(x23783,x23784,x23781,x23785,x23786,x23787),f564(x23783,x23784,x23782,x23785,x23786,x23787))
% 173.53/173.44 [2379]~E(x23791,x23792)+E(f564(x23793,x23794,x23795,x23791,x23796,x23797),f564(x23793,x23794,x23795,x23792,x23796,x23797))
% 173.53/173.44 [2380]~E(x23801,x23802)+E(f564(x23803,x23804,x23805,x23806,x23801,x23807),f564(x23803,x23804,x23805,x23806,x23802,x23807))
% 173.53/173.44 [2381]~E(x23811,x23812)+E(f564(x23813,x23814,x23815,x23816,x23817,x23811),f564(x23813,x23814,x23815,x23816,x23817,x23812))
% 173.53/173.44 [2382]~E(x23821,x23822)+E(f375(x23821,x23823),f375(x23822,x23823))
% 173.53/173.44 [2383]~E(x23831,x23832)+E(f375(x23833,x23831),f375(x23833,x23832))
% 173.53/173.44 [2384]~E(x23841,x23842)+E(f591(x23841,x23843,x23844,x23845,x23846),f591(x23842,x23843,x23844,x23845,x23846))
% 173.53/173.44 [2385]~E(x23851,x23852)+E(f591(x23853,x23851,x23854,x23855,x23856),f591(x23853,x23852,x23854,x23855,x23856))
% 173.53/173.44 [2386]~E(x23861,x23862)+E(f591(x23863,x23864,x23861,x23865,x23866),f591(x23863,x23864,x23862,x23865,x23866))
% 173.53/173.44 [2387]~E(x23871,x23872)+E(f591(x23873,x23874,x23875,x23871,x23876),f591(x23873,x23874,x23875,x23872,x23876))
% 173.53/173.44 [2388]~E(x23881,x23882)+E(f591(x23883,x23884,x23885,x23886,x23881),f591(x23883,x23884,x23885,x23886,x23882))
% 173.53/173.44 [2389]~E(x23891,x23892)+E(f406(x23891,x23893,x23894,x23895,x23896),f406(x23892,x23893,x23894,x23895,x23896))
% 173.53/173.44 [2390]~E(x23901,x23902)+E(f406(x23903,x23901,x23904,x23905,x23906),f406(x23903,x23902,x23904,x23905,x23906))
% 173.53/173.44 [2391]~E(x23911,x23912)+E(f406(x23913,x23914,x23911,x23915,x23916),f406(x23913,x23914,x23912,x23915,x23916))
% 173.53/173.44 [2392]~E(x23921,x23922)+E(f406(x23923,x23924,x23925,x23921,x23926),f406(x23923,x23924,x23925,x23922,x23926))
% 173.53/173.44 [2393]~E(x23931,x23932)+E(f406(x23933,x23934,x23935,x23936,x23931),f406(x23933,x23934,x23935,x23936,x23932))
% 173.53/173.44 [2394]~E(x23941,x23942)+E(f411(x23941,x23943,x23944,x23945,x23946),f411(x23942,x23943,x23944,x23945,x23946))
% 173.53/173.44 [2395]~E(x23951,x23952)+E(f411(x23953,x23951,x23954,x23955,x23956),f411(x23953,x23952,x23954,x23955,x23956))
% 173.53/173.44 [2396]~E(x23961,x23962)+E(f411(x23963,x23964,x23961,x23965,x23966),f411(x23963,x23964,x23962,x23965,x23966))
% 173.53/173.44 [2397]~E(x23971,x23972)+E(f411(x23973,x23974,x23975,x23971,x23976),f411(x23973,x23974,x23975,x23972,x23976))
% 173.53/173.44 [2398]~E(x23981,x23982)+E(f411(x23983,x23984,x23985,x23986,x23981),f411(x23983,x23984,x23985,x23986,x23982))
% 173.53/173.44 [2399]~E(x23991,x23992)+E(f494(x23991,x23993),f494(x23992,x23993))
% 173.53/173.44 [2400]~E(x24001,x24002)+E(f494(x24003,x24001),f494(x24003,x24002))
% 173.53/173.44 [2401]~E(x24011,x24012)+E(f362(x24011),f362(x24012))
% 173.53/173.44 [2402]~E(x24021,x24022)+E(f253(x24021,x24023,x24024,x24025,x24026),f253(x24022,x24023,x24024,x24025,x24026))
% 173.53/173.44 [2403]~E(x24031,x24032)+E(f253(x24033,x24031,x24034,x24035,x24036),f253(x24033,x24032,x24034,x24035,x24036))
% 173.53/173.44 [2404]~E(x24041,x24042)+E(f253(x24043,x24044,x24041,x24045,x24046),f253(x24043,x24044,x24042,x24045,x24046))
% 173.53/173.44 [2405]~E(x24051,x24052)+E(f253(x24053,x24054,x24055,x24051,x24056),f253(x24053,x24054,x24055,x24052,x24056))
% 173.53/173.44 [2406]~E(x24061,x24062)+E(f253(x24063,x24064,x24065,x24066,x24061),f253(x24063,x24064,x24065,x24066,x24062))
% 173.53/173.44 [2407]~E(x24071,x24072)+E(f759(x24071),f759(x24072))
% 173.53/173.44 [2408]~E(x24081,x24082)+E(f633(x24081,x24083,x24084,x24085),f633(x24082,x24083,x24084,x24085))
% 173.53/173.44 [2409]~E(x24091,x24092)+E(f633(x24093,x24091,x24094,x24095),f633(x24093,x24092,x24094,x24095))
% 173.53/173.44 [2410]~E(x24101,x24102)+E(f633(x24103,x24104,x24101,x24105),f633(x24103,x24104,x24102,x24105))
% 173.53/173.44 [2411]~E(x24111,x24112)+E(f633(x24113,x24114,x24115,x24111),f633(x24113,x24114,x24115,x24112))
% 173.53/173.44 [2412]~E(x24121,x24122)+E(f271(x24121,x24123,x24124),f271(x24122,x24123,x24124))
% 173.53/173.44 [2413]~E(x24131,x24132)+E(f271(x24133,x24131,x24134),f271(x24133,x24132,x24134))
% 173.53/173.44 [2414]~E(x24141,x24142)+E(f271(x24143,x24144,x24141),f271(x24143,x24144,x24142))
% 173.53/173.44 [2415]~E(x24151,x24152)+E(f696(x24151,x24153,x24154,x24155,x24156,x24157),f696(x24152,x24153,x24154,x24155,x24156,x24157))
% 173.53/173.44 [2416]~E(x24161,x24162)+E(f696(x24163,x24161,x24164,x24165,x24166,x24167),f696(x24163,x24162,x24164,x24165,x24166,x24167))
% 173.53/173.44 [2417]~E(x24171,x24172)+E(f696(x24173,x24174,x24171,x24175,x24176,x24177),f696(x24173,x24174,x24172,x24175,x24176,x24177))
% 173.53/173.44 [2418]~E(x24181,x24182)+E(f696(x24183,x24184,x24185,x24181,x24186,x24187),f696(x24183,x24184,x24185,x24182,x24186,x24187))
% 173.53/173.44 [2419]~E(x24191,x24192)+E(f696(x24193,x24194,x24195,x24196,x24191,x24197),f696(x24193,x24194,x24195,x24196,x24192,x24197))
% 173.53/173.44 [2420]~E(x24201,x24202)+E(f696(x24203,x24204,x24205,x24206,x24207,x24201),f696(x24203,x24204,x24205,x24206,x24207,x24202))
% 173.53/173.44 [2421]~E(x24211,x24212)+E(f709(x24211,x24213,x24214,x24215,x24216,x24217),f709(x24212,x24213,x24214,x24215,x24216,x24217))
% 173.53/173.44 [2422]~E(x24221,x24222)+E(f709(x24223,x24221,x24224,x24225,x24226,x24227),f709(x24223,x24222,x24224,x24225,x24226,x24227))
% 173.53/173.44 [2423]~E(x24231,x24232)+E(f709(x24233,x24234,x24231,x24235,x24236,x24237),f709(x24233,x24234,x24232,x24235,x24236,x24237))
% 173.53/173.44 [2424]~E(x24241,x24242)+E(f709(x24243,x24244,x24245,x24241,x24246,x24247),f709(x24243,x24244,x24245,x24242,x24246,x24247))
% 173.53/173.44 [2425]~E(x24251,x24252)+E(f709(x24253,x24254,x24255,x24256,x24251,x24257),f709(x24253,x24254,x24255,x24256,x24252,x24257))
% 173.53/173.44 [2426]~E(x24261,x24262)+E(f709(x24263,x24264,x24265,x24266,x24267,x24261),f709(x24263,x24264,x24265,x24266,x24267,x24262))
% 173.53/173.44 [2427]~E(x24271,x24272)+E(f599(x24271,x24273,x24274),f599(x24272,x24273,x24274))
% 173.53/173.44 [2428]~E(x24281,x24282)+E(f599(x24283,x24281,x24284),f599(x24283,x24282,x24284))
% 173.53/173.44 [2429]~E(x24291,x24292)+E(f599(x24293,x24294,x24291),f599(x24293,x24294,x24292))
% 173.53/173.44 [2430]~E(x24301,x24302)+E(f641(x24301,x24303,x24304,x24305,x24306,x24307,x24308),f641(x24302,x24303,x24304,x24305,x24306,x24307,x24308))
% 173.53/173.44 [2431]~E(x24311,x24312)+E(f641(x24313,x24311,x24314,x24315,x24316,x24317,x24318),f641(x24313,x24312,x24314,x24315,x24316,x24317,x24318))
% 173.53/173.44 [2432]~E(x24321,x24322)+E(f641(x24323,x24324,x24321,x24325,x24326,x24327,x24328),f641(x24323,x24324,x24322,x24325,x24326,x24327,x24328))
% 173.53/173.44 [2433]~E(x24331,x24332)+E(f641(x24333,x24334,x24335,x24331,x24336,x24337,x24338),f641(x24333,x24334,x24335,x24332,x24336,x24337,x24338))
% 173.53/173.44 [2434]~E(x24341,x24342)+E(f641(x24343,x24344,x24345,x24346,x24341,x24347,x24348),f641(x24343,x24344,x24345,x24346,x24342,x24347,x24348))
% 173.53/173.44 [2435]~E(x24351,x24352)+E(f641(x24353,x24354,x24355,x24356,x24357,x24351,x24358),f641(x24353,x24354,x24355,x24356,x24357,x24352,x24358))
% 173.53/173.44 [2436]~E(x24361,x24362)+E(f641(x24363,x24364,x24365,x24366,x24367,x24368,x24361),f641(x24363,x24364,x24365,x24366,x24367,x24368,x24362))
% 173.53/173.44 [2437]~E(x24371,x24372)+E(f719(x24371,x24373,x24374,x24375),f719(x24372,x24373,x24374,x24375))
% 173.53/173.44 [2438]~E(x24381,x24382)+E(f719(x24383,x24381,x24384,x24385),f719(x24383,x24382,x24384,x24385))
% 173.53/173.44 [2439]~E(x24391,x24392)+E(f719(x24393,x24394,x24391,x24395),f719(x24393,x24394,x24392,x24395))
% 173.53/173.44 [2440]~E(x24401,x24402)+E(f719(x24403,x24404,x24405,x24401),f719(x24403,x24404,x24405,x24402))
% 173.53/173.44 [2441]~E(x24411,x24412)+E(f549(x24411,x24413,x24414,x24415,x24416),f549(x24412,x24413,x24414,x24415,x24416))
% 173.53/173.44 [2442]~E(x24421,x24422)+E(f549(x24423,x24421,x24424,x24425,x24426),f549(x24423,x24422,x24424,x24425,x24426))
% 173.53/173.44 [2443]~E(x24431,x24432)+E(f549(x24433,x24434,x24431,x24435,x24436),f549(x24433,x24434,x24432,x24435,x24436))
% 173.53/173.44 [2444]~E(x24441,x24442)+E(f549(x24443,x24444,x24445,x24441,x24446),f549(x24443,x24444,x24445,x24442,x24446))
% 173.53/173.44 [2445]~E(x24451,x24452)+E(f549(x24453,x24454,x24455,x24456,x24451),f549(x24453,x24454,x24455,x24456,x24452))
% 173.53/173.44 [2446]~E(x24461,x24462)+E(f713(x24461,x24463,x24464,x24465,x24466,x24467),f713(x24462,x24463,x24464,x24465,x24466,x24467))
% 173.53/173.44 [2447]~E(x24471,x24472)+E(f713(x24473,x24471,x24474,x24475,x24476,x24477),f713(x24473,x24472,x24474,x24475,x24476,x24477))
% 173.53/173.44 [2448]~E(x24481,x24482)+E(f713(x24483,x24484,x24481,x24485,x24486,x24487),f713(x24483,x24484,x24482,x24485,x24486,x24487))
% 173.53/173.44 [2449]~E(x24491,x24492)+E(f713(x24493,x24494,x24495,x24491,x24496,x24497),f713(x24493,x24494,x24495,x24492,x24496,x24497))
% 173.53/173.44 [2450]~E(x24501,x24502)+E(f713(x24503,x24504,x24505,x24506,x24501,x24507),f713(x24503,x24504,x24505,x24506,x24502,x24507))
% 173.53/173.44 [2451]~E(x24511,x24512)+E(f713(x24513,x24514,x24515,x24516,x24517,x24511),f713(x24513,x24514,x24515,x24516,x24517,x24512))
% 173.53/173.44 [2452]~E(x24521,x24522)+E(f510(x24521,x24523,x24524,x24525,x24526),f510(x24522,x24523,x24524,x24525,x24526))
% 173.53/173.44 [2453]~E(x24531,x24532)+E(f510(x24533,x24531,x24534,x24535,x24536),f510(x24533,x24532,x24534,x24535,x24536))
% 173.53/173.44 [2454]~E(x24541,x24542)+E(f510(x24543,x24544,x24541,x24545,x24546),f510(x24543,x24544,x24542,x24545,x24546))
% 173.53/173.44 [2455]~E(x24551,x24552)+E(f510(x24553,x24554,x24555,x24551,x24556),f510(x24553,x24554,x24555,x24552,x24556))
% 173.53/173.44 [2456]~E(x24561,x24562)+E(f510(x24563,x24564,x24565,x24566,x24561),f510(x24563,x24564,x24565,x24566,x24562))
% 173.53/173.44 [2457]~E(x24571,x24572)+E(f214(x24571,x24573,x24574,x24575,x24576),f214(x24572,x24573,x24574,x24575,x24576))
% 173.53/173.44 [2458]~E(x24581,x24582)+E(f214(x24583,x24581,x24584,x24585,x24586),f214(x24583,x24582,x24584,x24585,x24586))
% 173.53/173.44 [2459]~E(x24591,x24592)+E(f214(x24593,x24594,x24591,x24595,x24596),f214(x24593,x24594,x24592,x24595,x24596))
% 173.53/173.44 [2460]~E(x24601,x24602)+E(f214(x24603,x24604,x24605,x24601,x24606),f214(x24603,x24604,x24605,x24602,x24606))
% 173.53/173.44 [2461]~E(x24611,x24612)+E(f214(x24613,x24614,x24615,x24616,x24611),f214(x24613,x24614,x24615,x24616,x24612))
% 173.53/173.44 [2462]~E(x24621,x24622)+E(f708(x24621,x24623,x24624,x24625,x24626,x24627,x24628,x24629),f708(x24622,x24623,x24624,x24625,x24626,x24627,x24628,x24629))
% 173.53/173.44 [2463]~E(x24631,x24632)+E(f708(x24633,x24631,x24634,x24635,x24636,x24637,x24638,x24639),f708(x24633,x24632,x24634,x24635,x24636,x24637,x24638,x24639))
% 173.53/173.44 [2464]~E(x24641,x24642)+E(f708(x24643,x24644,x24641,x24645,x24646,x24647,x24648,x24649),f708(x24643,x24644,x24642,x24645,x24646,x24647,x24648,x24649))
% 173.53/173.44 [2465]~E(x24651,x24652)+E(f708(x24653,x24654,x24655,x24651,x24656,x24657,x24658,x24659),f708(x24653,x24654,x24655,x24652,x24656,x24657,x24658,x24659))
% 173.53/173.44 [2466]~E(x24661,x24662)+E(f708(x24663,x24664,x24665,x24666,x24661,x24667,x24668,x24669),f708(x24663,x24664,x24665,x24666,x24662,x24667,x24668,x24669))
% 173.53/173.44 [2467]~E(x24671,x24672)+E(f708(x24673,x24674,x24675,x24676,x24677,x24671,x24678,x24679),f708(x24673,x24674,x24675,x24676,x24677,x24672,x24678,x24679))
% 173.53/173.44 [2468]~E(x24681,x24682)+E(f708(x24683,x24684,x24685,x24686,x24687,x24688,x24681,x24689),f708(x24683,x24684,x24685,x24686,x24687,x24688,x24682,x24689))
% 173.53/173.44 [2469]~E(x24691,x24692)+E(f708(x24693,x24694,x24695,x24696,x24697,x24698,x24699,x24691),f708(x24693,x24694,x24695,x24696,x24697,x24698,x24699,x24692))
% 173.53/173.44 [2470]~E(x24701,x24702)+E(f662(x24701,x24703,x24704),f662(x24702,x24703,x24704))
% 173.53/173.44 [2471]~E(x24711,x24712)+E(f662(x24713,x24711,x24714),f662(x24713,x24712,x24714))
% 173.53/173.44 [2472]~E(x24721,x24722)+E(f662(x24723,x24724,x24721),f662(x24723,x24724,x24722))
% 173.53/173.44 [2473]~E(x24731,x24732)+E(f557(x24731,x24733),f557(x24732,x24733))
% 173.53/173.44 [2474]~E(x24741,x24742)+E(f557(x24743,x24741),f557(x24743,x24742))
% 173.53/173.44 [2475]~E(x24751,x24752)+E(f640(x24751,x24753,x24754,x24755,x24756),f640(x24752,x24753,x24754,x24755,x24756))
% 173.53/173.44 [2476]~E(x24761,x24762)+E(f640(x24763,x24761,x24764,x24765,x24766),f640(x24763,x24762,x24764,x24765,x24766))
% 173.53/173.44 [2477]~E(x24771,x24772)+E(f640(x24773,x24774,x24771,x24775,x24776),f640(x24773,x24774,x24772,x24775,x24776))
% 173.53/173.44 [2478]~E(x24781,x24782)+E(f640(x24783,x24784,x24785,x24781,x24786),f640(x24783,x24784,x24785,x24782,x24786))
% 173.53/173.44 [2479]~E(x24791,x24792)+E(f640(x24793,x24794,x24795,x24796,x24791),f640(x24793,x24794,x24795,x24796,x24792))
% 173.53/173.44 [2480]~E(x24801,x24802)+E(f666(x24801,x24803,x24804),f666(x24802,x24803,x24804))
% 173.53/173.44 [2481]~E(x24811,x24812)+E(f666(x24813,x24811,x24814),f666(x24813,x24812,x24814))
% 173.53/173.44 [2482]~E(x24821,x24822)+E(f666(x24823,x24824,x24821),f666(x24823,x24824,x24822))
% 173.53/173.44 [2483]~E(x24831,x24832)+E(f540(x24831,x24833,x24834),f540(x24832,x24833,x24834))
% 173.53/173.44 [2484]~E(x24841,x24842)+E(f540(x24843,x24841,x24844),f540(x24843,x24842,x24844))
% 173.53/173.44 [2485]~E(x24851,x24852)+E(f540(x24853,x24854,x24851),f540(x24853,x24854,x24852))
% 173.53/173.44 [2486]~E(x24861,x24862)+E(f783(x24861,x24863,x24864),f783(x24862,x24863,x24864))
% 173.53/173.44 [2487]~E(x24871,x24872)+E(f783(x24873,x24871,x24874),f783(x24873,x24872,x24874))
% 173.53/173.44 [2488]~E(x24881,x24882)+E(f783(x24883,x24884,x24881),f783(x24883,x24884,x24882))
% 173.53/173.44 [2489]~E(x24891,x24892)+E(f130(x24891),f130(x24892))
% 173.53/173.44 [2490]~E(x24901,x24902)+E(f631(x24901,x24903,x24904),f631(x24902,x24903,x24904))
% 173.53/173.44 [2491]~E(x24911,x24912)+E(f631(x24913,x24911,x24914),f631(x24913,x24912,x24914))
% 173.53/173.44 [2492]~E(x24921,x24922)+E(f631(x24923,x24924,x24921),f631(x24923,x24924,x24922))
% 173.53/173.44 [2493]~E(x24931,x24932)+E(f328(x24931),f328(x24932))
% 173.53/173.44 [2494]~E(x24941,x24942)+E(f762(x24941,x24943,x24944,x24945),f762(x24942,x24943,x24944,x24945))
% 173.53/173.44 [2495]~E(x24951,x24952)+E(f762(x24953,x24951,x24954,x24955),f762(x24953,x24952,x24954,x24955))
% 173.53/173.44 [2496]~E(x24961,x24962)+E(f762(x24963,x24964,x24961,x24965),f762(x24963,x24964,x24962,x24965))
% 173.53/173.44 [2497]~E(x24971,x24972)+E(f762(x24973,x24974,x24975,x24971),f762(x24973,x24974,x24975,x24972))
% 173.53/173.44 [2498]~E(x24981,x24982)+E(f487(x24981,x24983,x24984,x24985,x24986),f487(x24982,x24983,x24984,x24985,x24986))
% 173.53/173.44 [2499]~E(x24991,x24992)+E(f487(x24993,x24991,x24994,x24995,x24996),f487(x24993,x24992,x24994,x24995,x24996))
% 173.53/173.44 [2500]~E(x25001,x25002)+E(f487(x25003,x25004,x25001,x25005,x25006),f487(x25003,x25004,x25002,x25005,x25006))
% 173.53/173.44 [2501]~E(x25011,x25012)+E(f487(x25013,x25014,x25015,x25011,x25016),f487(x25013,x25014,x25015,x25012,x25016))
% 173.53/173.44 [2502]~E(x25021,x25022)+E(f487(x25023,x25024,x25025,x25026,x25021),f487(x25023,x25024,x25025,x25026,x25022))
% 173.53/173.44 [2503]~E(x25031,x25032)+E(f593(x25031,x25033,x25034,x25035,x25036),f593(x25032,x25033,x25034,x25035,x25036))
% 173.53/173.44 [2504]~E(x25041,x25042)+E(f593(x25043,x25041,x25044,x25045,x25046),f593(x25043,x25042,x25044,x25045,x25046))
% 173.53/173.44 [2505]~E(x25051,x25052)+E(f593(x25053,x25054,x25051,x25055,x25056),f593(x25053,x25054,x25052,x25055,x25056))
% 173.53/173.44 [2506]~E(x25061,x25062)+E(f593(x25063,x25064,x25065,x25061,x25066),f593(x25063,x25064,x25065,x25062,x25066))
% 173.53/173.44 [2507]~E(x25071,x25072)+E(f593(x25073,x25074,x25075,x25076,x25071),f593(x25073,x25074,x25075,x25076,x25072))
% 173.53/173.44 [2508]~E(x25081,x25082)+E(f441(x25081,x25083,x25084),f441(x25082,x25083,x25084))
% 173.53/173.44 [2509]~E(x25091,x25092)+E(f441(x25093,x25091,x25094),f441(x25093,x25092,x25094))
% 173.53/173.44 [2510]~E(x25101,x25102)+E(f441(x25103,x25104,x25101),f441(x25103,x25104,x25102))
% 173.53/173.44 [2511]~E(x25111,x25112)+E(f832(x25111,x25113),f832(x25112,x25113))
% 173.53/173.44 [2512]~E(x25121,x25122)+E(f832(x25123,x25121),f832(x25123,x25122))
% 173.53/173.44 [2513]~E(x25131,x25132)+E(f782(x25131,x25133,x25134),f782(x25132,x25133,x25134))
% 173.53/173.44 [2514]~E(x25141,x25142)+E(f782(x25143,x25141,x25144),f782(x25143,x25142,x25144))
% 173.53/173.44 [2515]~E(x25151,x25152)+E(f782(x25153,x25154,x25151),f782(x25153,x25154,x25152))
% 173.53/173.44 [2516]~E(x25161,x25162)+E(f734(x25161,x25163,x25164),f734(x25162,x25163,x25164))
% 173.53/173.44 [2517]~E(x25171,x25172)+E(f734(x25173,x25171,x25174),f734(x25173,x25172,x25174))
% 173.53/173.44 [2518]~E(x25181,x25182)+E(f734(x25183,x25184,x25181),f734(x25183,x25184,x25182))
% 173.53/173.44 [2519]~E(x25191,x25192)+E(f643(x25191,x25193,x25194),f643(x25192,x25193,x25194))
% 173.53/173.44 [2520]~E(x25201,x25202)+E(f643(x25203,x25201,x25204),f643(x25203,x25202,x25204))
% 173.53/173.44 [2521]~E(x25211,x25212)+E(f643(x25213,x25214,x25211),f643(x25213,x25214,x25212))
% 173.53/173.44 [2522]~E(x25221,x25222)+E(f632(x25221,x25223,x25224),f632(x25222,x25223,x25224))
% 173.53/173.44 [2523]~E(x25231,x25232)+E(f632(x25233,x25231,x25234),f632(x25233,x25232,x25234))
% 173.53/173.44 [2524]~E(x25241,x25242)+E(f632(x25243,x25244,x25241),f632(x25243,x25244,x25242))
% 173.53/173.44 [2525]~E(x25251,x25252)+E(f576(x25251,x25253,x25254,x25255),f576(x25252,x25253,x25254,x25255))
% 173.53/173.44 [2526]~E(x25261,x25262)+E(f576(x25263,x25261,x25264,x25265),f576(x25263,x25262,x25264,x25265))
% 173.53/173.44 [2527]~E(x25271,x25272)+E(f576(x25273,x25274,x25271,x25275),f576(x25273,x25274,x25272,x25275))
% 173.53/173.44 [2528]~E(x25281,x25282)+E(f576(x25283,x25284,x25285,x25281),f576(x25283,x25284,x25285,x25282))
% 173.53/173.44 [2529]~E(x25291,x25292)+E(f344(x25291,x25293,x25294),f344(x25292,x25293,x25294))
% 173.53/173.44 [2530]~E(x25301,x25302)+E(f344(x25303,x25301,x25304),f344(x25303,x25302,x25304))
% 173.53/173.44 [2531]~E(x25311,x25312)+E(f344(x25313,x25314,x25311),f344(x25313,x25314,x25312))
% 173.53/173.44 [2532]~E(x25321,x25322)+E(f442(x25321,x25323,x25324),f442(x25322,x25323,x25324))
% 173.53/173.44 [2533]~E(x25331,x25332)+E(f442(x25333,x25331,x25334),f442(x25333,x25332,x25334))
% 173.53/173.44 [2534]~E(x25341,x25342)+E(f442(x25343,x25344,x25341),f442(x25343,x25344,x25342))
% 173.53/173.44 [2535]~E(x25351,x25352)+E(f424(x25351,x25353,x25354,x25355,x25356,x25357,x25358),f424(x25352,x25353,x25354,x25355,x25356,x25357,x25358))
% 173.53/173.44 [2536]~E(x25361,x25362)+E(f424(x25363,x25361,x25364,x25365,x25366,x25367,x25368),f424(x25363,x25362,x25364,x25365,x25366,x25367,x25368))
% 173.53/173.44 [2537]~E(x25371,x25372)+E(f424(x25373,x25374,x25371,x25375,x25376,x25377,x25378),f424(x25373,x25374,x25372,x25375,x25376,x25377,x25378))
% 173.53/173.44 [2538]~E(x25381,x25382)+E(f424(x25383,x25384,x25385,x25381,x25386,x25387,x25388),f424(x25383,x25384,x25385,x25382,x25386,x25387,x25388))
% 173.53/173.44 [2539]~E(x25391,x25392)+E(f424(x25393,x25394,x25395,x25396,x25391,x25397,x25398),f424(x25393,x25394,x25395,x25396,x25392,x25397,x25398))
% 173.53/173.44 [2540]~E(x25401,x25402)+E(f424(x25403,x25404,x25405,x25406,x25407,x25401,x25408),f424(x25403,x25404,x25405,x25406,x25407,x25402,x25408))
% 173.53/173.44 [2541]~E(x25411,x25412)+E(f424(x25413,x25414,x25415,x25416,x25417,x25418,x25411),f424(x25413,x25414,x25415,x25416,x25417,x25418,x25412))
% 173.53/173.44 [2542]~E(x25421,x25422)+E(f835(x25421),f835(x25422))
% 173.53/173.44 [2543]~E(x25431,x25432)+E(f325(x25431,x25433),f325(x25432,x25433))
% 173.53/173.44 [2544]~E(x25441,x25442)+E(f325(x25443,x25441),f325(x25443,x25442))
% 173.53/173.44 [2545]~E(x25451,x25452)+E(f368(x25451),f368(x25452))
% 173.53/173.44 [2546]~E(x25461,x25462)+E(f106(x25461,x25463,x25464,x25465),f106(x25462,x25463,x25464,x25465))
% 173.53/173.44 [2547]~E(x25471,x25472)+E(f106(x25473,x25471,x25474,x25475),f106(x25473,x25472,x25474,x25475))
% 173.53/173.44 [2548]~E(x25481,x25482)+E(f106(x25483,x25484,x25481,x25485),f106(x25483,x25484,x25482,x25485))
% 173.53/173.44 [2549]~E(x25491,x25492)+E(f106(x25493,x25494,x25495,x25491),f106(x25493,x25494,x25495,x25492))
% 173.53/173.44 [2550]~E(x25501,x25502)+E(f317(x25501),f317(x25502))
% 173.53/173.44 [2551]~E(x25511,x25512)+E(f294(x25511,x25513,x25514),f294(x25512,x25513,x25514))
% 173.53/173.44 [2552]~E(x25521,x25522)+E(f294(x25523,x25521,x25524),f294(x25523,x25522,x25524))
% 173.53/173.44 [2553]~E(x25531,x25532)+E(f294(x25533,x25534,x25531),f294(x25533,x25534,x25532))
% 173.53/173.44 [2554]~E(x25541,x25542)+E(f329(x25541,x25543,x25544),f329(x25542,x25543,x25544))
% 173.53/173.44 [2555]~E(x25551,x25552)+E(f329(x25553,x25551,x25554),f329(x25553,x25552,x25554))
% 173.53/173.44 [2556]~E(x25561,x25562)+E(f329(x25563,x25564,x25561),f329(x25563,x25564,x25562))
% 173.53/173.44 [2557]~P1(x25571)+P1(x25572)+~E(x25571,x25572)
% 173.53/173.44 [2558]~P22(x25581)+P22(x25582)+~E(x25581,x25582)
% 173.53/173.44 [2559]~P23(x25591)+P23(x25592)+~E(x25591,x25592)
% 173.53/173.44 [2560]~P103(x25601)+P103(x25602)+~E(x25601,x25602)
% 173.53/173.44 [2561]P33(x25612,x25613)+~E(x25611,x25612)+~P33(x25611,x25613)
% 173.53/173.44 [2562]P33(x25623,x25622)+~E(x25621,x25622)+~P33(x25623,x25621)
% 173.53/173.44 [2563]~P24(x25631)+P24(x25632)+~E(x25631,x25632)
% 173.53/173.44 [2564]~P112(x25641)+P112(x25642)+~E(x25641,x25642)
% 173.53/173.44 [2565]~P101(x25651)+P101(x25652)+~E(x25651,x25652)
% 173.53/173.44 [2566]~P25(x25661)+P25(x25662)+~E(x25661,x25662)
% 173.53/173.44 [2567]~P90(x25671)+P90(x25672)+~E(x25671,x25672)
% 173.53/173.44 [2568]~P26(x25681)+P26(x25682)+~E(x25681,x25682)
% 173.53/173.44 [2569]~P107(x25691)+P107(x25692)+~E(x25691,x25692)
% 173.53/173.44 [2570]~P118(x25701)+P118(x25702)+~E(x25701,x25702)
% 173.53/173.44 [2571]~P32(x25711)+P32(x25712)+~E(x25711,x25712)
% 173.53/173.44 [2572]~P60(x25721)+P60(x25722)+~E(x25721,x25722)
% 173.53/173.44 [2573]P13(x25732,x25733,x25734)+~E(x25731,x25732)+~P13(x25731,x25733,x25734)
% 173.53/173.44 [2574]P13(x25743,x25742,x25744)+~E(x25741,x25742)+~P13(x25743,x25741,x25744)
% 173.53/173.44 [2575]P13(x25753,x25754,x25752)+~E(x25751,x25752)+~P13(x25753,x25754,x25751)
% 173.53/173.44 [2576]P139(x25762,x25763,x25764)+~E(x25761,x25762)+~P139(x25761,x25763,x25764)
% 173.53/173.44 [2577]P139(x25773,x25772,x25774)+~E(x25771,x25772)+~P139(x25773,x25771,x25774)
% 173.53/173.44 [2578]P139(x25783,x25784,x25782)+~E(x25781,x25782)+~P139(x25783,x25784,x25781)
% 173.53/173.44 [2579]~P70(x25791)+P70(x25792)+~E(x25791,x25792)
% 173.53/173.44 [2580]~P136(x25801)+P136(x25802)+~E(x25801,x25802)
% 173.53/173.44 [2581]P41(x25812,x25813)+~E(x25811,x25812)+~P41(x25811,x25813)
% 173.53/173.44 [2582]P41(x25823,x25822)+~E(x25821,x25822)+~P41(x25823,x25821)
% 173.53/173.44 [2583]~P75(x25831)+P75(x25832)+~E(x25831,x25832)
% 173.53/173.44 [2584]P58(x25842,x25843,x25844,x25845)+~E(x25841,x25842)+~P58(x25841,x25843,x25844,x25845)
% 173.53/173.44 [2585]P58(x25853,x25852,x25854,x25855)+~E(x25851,x25852)+~P58(x25853,x25851,x25854,x25855)
% 173.53/173.44 [2586]P58(x25863,x25864,x25862,x25865)+~E(x25861,x25862)+~P58(x25863,x25864,x25861,x25865)
% 173.53/173.44 [2587]P58(x25873,x25874,x25875,x25872)+~E(x25871,x25872)+~P58(x25873,x25874,x25875,x25871)
% 173.53/173.44 [2588]P140(x25882,x25883,x25884)+~E(x25881,x25882)+~P140(x25881,x25883,x25884)
% 173.53/173.44 [2589]P140(x25893,x25892,x25894)+~E(x25891,x25892)+~P140(x25893,x25891,x25894)
% 173.53/173.44 [2590]P140(x25903,x25904,x25902)+~E(x25901,x25902)+~P140(x25903,x25904,x25901)
% 173.53/173.44 [2591]~P27(x25911)+P27(x25912)+~E(x25911,x25912)
% 173.53/173.44 [2592]~P105(x25921)+P105(x25922)+~E(x25921,x25922)
% 173.53/173.44 [2593]P48(x25932,x25933)+~E(x25931,x25932)+~P48(x25931,x25933)
% 173.53/173.44 [2594]P48(x25943,x25942)+~E(x25941,x25942)+~P48(x25943,x25941)
% 173.53/173.44 [2595]~P28(x25951)+P28(x25952)+~E(x25951,x25952)
% 173.53/173.44 [2596]~P104(x25961)+P104(x25962)+~E(x25961,x25962)
% 173.53/173.44 [2597]P19(x25972,x25973,x25974,x25975)+~E(x25971,x25972)+~P19(x25971,x25973,x25974,x25975)
% 173.53/173.44 [2598]P19(x25983,x25982,x25984,x25985)+~E(x25981,x25982)+~P19(x25983,x25981,x25984,x25985)
% 173.53/173.44 [2599]P19(x25993,x25994,x25992,x25995)+~E(x25991,x25992)+~P19(x25993,x25994,x25991,x25995)
% 173.53/173.44 [2600]P19(x26003,x26004,x26005,x26002)+~E(x26001,x26002)+~P19(x26003,x26004,x26005,x26001)
% 173.53/173.44 [2601]~P29(x26011)+P29(x26012)+~E(x26011,x26012)
% 173.53/173.44 [2602]~P66(x26021)+P66(x26022)+~E(x26021,x26022)
% 173.53/173.44 [2603]~P43(x26031)+P43(x26032)+~E(x26031,x26032)
% 173.53/173.44 [2604]~P30(x26041)+P30(x26042)+~E(x26041,x26042)
% 173.53/173.44 [2605]~P71(x26051)+P71(x26052)+~E(x26051,x26052)
% 173.53/173.44 [2606]~P73(x26061)+P73(x26062)+~E(x26061,x26062)
% 173.53/173.44 [2607]~P98(x26071)+P98(x26072)+~E(x26071,x26072)
% 173.53/173.44 [2608]P34(x26082,x26083,x26084)+~E(x26081,x26082)+~P34(x26081,x26083,x26084)
% 173.53/173.44 [2609]P34(x26093,x26092,x26094)+~E(x26091,x26092)+~P34(x26093,x26091,x26094)
% 173.53/173.44 [2610]P34(x26103,x26104,x26102)+~E(x26101,x26102)+~P34(x26103,x26104,x26101)
% 173.53/173.44 [2611]P21(x26112,x26113,x26114)+~E(x26111,x26112)+~P21(x26111,x26113,x26114)
% 173.53/173.44 [2612]P21(x26123,x26122,x26124)+~E(x26121,x26122)+~P21(x26123,x26121,x26124)
% 173.53/173.44 [2613]P21(x26133,x26134,x26132)+~E(x26131,x26132)+~P21(x26133,x26134,x26131)
% 173.53/173.44 [2614]~P76(x26141)+P76(x26142)+~E(x26141,x26142)
% 173.53/173.44 [2615]~P79(x26151)+P79(x26152)+~E(x26151,x26152)
% 173.53/173.44 [2616]~P64(x26161)+P64(x26162)+~E(x26161,x26162)
% 173.53/173.44 [2617]~P87(x26171)+P87(x26172)+~E(x26171,x26172)
% 173.53/173.44 [2618]P55(x26182,x26183,x26184)+~E(x26181,x26182)+~P55(x26181,x26183,x26184)
% 173.53/173.44 [2619]P55(x26193,x26192,x26194)+~E(x26191,x26192)+~P55(x26193,x26191,x26194)
% 173.53/173.44 [2620]P55(x26203,x26204,x26202)+~E(x26201,x26202)+~P55(x26203,x26204,x26201)
% 173.53/173.44 [2621]~P91(x26211)+P91(x26212)+~E(x26211,x26212)
% 173.53/173.44 [2622]~P88(x26221)+P88(x26222)+~E(x26221,x26222)
% 173.53/173.44 [2623]P50(x26232,x26233,x26234)+~E(x26231,x26232)+~P50(x26231,x26233,x26234)
% 173.53/173.44 [2624]P50(x26243,x26242,x26244)+~E(x26241,x26242)+~P50(x26243,x26241,x26244)
% 173.53/173.44 [2625]P50(x26253,x26254,x26252)+~E(x26251,x26252)+~P50(x26253,x26254,x26251)
% 173.53/173.44 [2626]P9(x26262,x26263,x26264,x26265)+~E(x26261,x26262)+~P9(x26261,x26263,x26264,x26265)
% 173.53/173.44 [2627]P9(x26273,x26272,x26274,x26275)+~E(x26271,x26272)+~P9(x26273,x26271,x26274,x26275)
% 173.53/173.44 [2628]P9(x26283,x26284,x26282,x26285)+~E(x26281,x26282)+~P9(x26283,x26284,x26281,x26285)
% 173.53/173.44 [2629]P9(x26293,x26294,x26295,x26292)+~E(x26291,x26292)+~P9(x26293,x26294,x26295,x26291)
% 173.53/173.44 [2630]~P67(x26301)+P67(x26302)+~E(x26301,x26302)
% 173.53/173.44 [2631]~P94(x26311)+P94(x26312)+~E(x26311,x26312)
% 173.53/173.44 [2632]~P108(x26321)+P108(x26322)+~E(x26321,x26322)
% 173.53/173.44 [2633]~P89(x26331)+P89(x26332)+~E(x26331,x26332)
% 173.53/173.44 [2634]~P77(x26341)+P77(x26342)+~E(x26341,x26342)
% 173.53/173.44 [2635]~P72(x26351)+P72(x26352)+~E(x26351,x26352)
% 173.53/173.44 [2636]~P65(x26361)+P65(x26362)+~E(x26361,x26362)
% 173.53/173.44 [2637]~P99(x26371)+P99(x26372)+~E(x26371,x26372)
% 173.53/173.44 [2638]P3(x26382,x26383,x26384)+~E(x26381,x26382)+~P3(x26381,x26383,x26384)
% 173.53/173.44 [2639]P3(x26393,x26392,x26394)+~E(x26391,x26392)+~P3(x26393,x26391,x26394)
% 173.53/173.44 [2640]P3(x26403,x26404,x26402)+~E(x26401,x26402)+~P3(x26403,x26404,x26401)
% 173.53/173.44 [2641]P20(x26412,x26413)+~E(x26411,x26412)+~P20(x26411,x26413)
% 173.53/173.44 [2642]P20(x26423,x26422)+~E(x26421,x26422)+~P20(x26423,x26421)
% 173.53/173.44 [2643]~P111(x26431)+P111(x26432)+~E(x26431,x26432)
% 173.53/173.44 [2644]~P96(x26441)+P96(x26442)+~E(x26441,x26442)
% 173.53/173.44 [2645]P49(x26452,x26453,x26454)+~E(x26451,x26452)+~P49(x26451,x26453,x26454)
% 173.53/173.44 [2646]P49(x26463,x26462,x26464)+~E(x26461,x26462)+~P49(x26463,x26461,x26464)
% 173.53/173.44 [2647]P49(x26473,x26474,x26472)+~E(x26471,x26472)+~P49(x26473,x26474,x26471)
% 173.53/173.44 [2648]~P120(x26481)+P120(x26482)+~E(x26481,x26482)
% 173.53/173.44 [2649]~P137(x26491)+P137(x26492)+~E(x26491,x26492)
% 173.53/173.44 [2650]P39(x26502,x26503,x26504,x26505,x26506)+~E(x26501,x26502)+~P39(x26501,x26503,x26504,x26505,x26506)
% 173.53/173.44 [2651]P39(x26513,x26512,x26514,x26515,x26516)+~E(x26511,x26512)+~P39(x26513,x26511,x26514,x26515,x26516)
% 173.53/173.44 [2652]P39(x26523,x26524,x26522,x26525,x26526)+~E(x26521,x26522)+~P39(x26523,x26524,x26521,x26525,x26526)
% 173.53/173.44 [2653]P39(x26533,x26534,x26535,x26532,x26536)+~E(x26531,x26532)+~P39(x26533,x26534,x26535,x26531,x26536)
% 173.53/173.44 [2654]P39(x26543,x26544,x26545,x26546,x26542)+~E(x26541,x26542)+~P39(x26543,x26544,x26545,x26546,x26541)
% 173.53/173.44 [2655]P57(x26552,x26553)+~E(x26551,x26552)+~P57(x26551,x26553)
% 173.53/173.44 [2656]P57(x26563,x26562)+~E(x26561,x26562)+~P57(x26563,x26561)
% 173.53/173.44 [2657]~P117(x26571)+P117(x26572)+~E(x26571,x26572)
% 173.53/173.44 [2658]~P102(x26581)+P102(x26582)+~E(x26581,x26582)
% 173.53/173.44 [2659]~P63(x26591)+P63(x26592)+~E(x26591,x26592)
% 173.53/173.44 [2660]~P31(x26601)+P31(x26602)+~E(x26601,x26602)
% 173.53/173.44 [2661]P36(x26612,x26613,x26614,x26615)+~E(x26611,x26612)+~P36(x26611,x26613,x26614,x26615)
% 173.53/173.44 [2662]P36(x26623,x26622,x26624,x26625)+~E(x26621,x26622)+~P36(x26623,x26621,x26624,x26625)
% 173.53/173.44 [2663]P36(x26633,x26634,x26632,x26635)+~E(x26631,x26632)+~P36(x26633,x26634,x26631,x26635)
% 173.53/173.44 [2664]P36(x26643,x26644,x26645,x26642)+~E(x26641,x26642)+~P36(x26643,x26644,x26645,x26641)
% 173.53/173.44 [2665]~P84(x26651)+P84(x26652)+~E(x26651,x26652)
% 173.53/173.44 [2666]~P78(x26661)+P78(x26662)+~E(x26661,x26662)
% 173.53/173.44 [2667]P8(x26672,x26673,x26674)+~E(x26671,x26672)+~P8(x26671,x26673,x26674)
% 173.53/173.44 [2668]P8(x26683,x26682,x26684)+~E(x26681,x26682)+~P8(x26683,x26681,x26684)
% 173.53/173.44 [2669]P8(x26693,x26694,x26692)+~E(x26691,x26692)+~P8(x26693,x26694,x26691)
% 173.53/173.44 [2670]~P110(x26701)+P110(x26702)+~E(x26701,x26702)
% 173.53/173.44 [2671]P12(x26712,x26713,x26714)+~E(x26711,x26712)+~P12(x26711,x26713,x26714)
% 173.53/173.44 [2672]P12(x26723,x26722,x26724)+~E(x26721,x26722)+~P12(x26723,x26721,x26724)
% 173.53/173.44 [2673]P12(x26733,x26734,x26732)+~E(x26731,x26732)+~P12(x26733,x26734,x26731)
% 173.53/173.44 [2674]~P109(x26741)+P109(x26742)+~E(x26741,x26742)
% 173.53/173.44 [2675]~P132(x26751)+P132(x26752)+~E(x26751,x26752)
% 173.53/173.44 [2676]~P4(x26761)+P4(x26762)+~E(x26761,x26762)
% 173.53/173.44 [2677]~P81(x26771)+P81(x26772)+~E(x26771,x26772)
% 173.53/173.44 [2678]P38(x26782,x26783,x26784)+~E(x26781,x26782)+~P38(x26781,x26783,x26784)
% 173.53/173.44 [2679]P38(x26793,x26792,x26794)+~E(x26791,x26792)+~P38(x26793,x26791,x26794)
% 173.53/173.44 [2680]P38(x26803,x26804,x26802)+~E(x26801,x26802)+~P38(x26803,x26804,x26801)
% 173.53/173.44 [2681]~P113(x26811)+P113(x26812)+~E(x26811,x26812)
% 173.53/173.44 [2682]~P106(x26821)+P106(x26822)+~E(x26821,x26822)
% 173.53/173.44 [2683]P18(x26832,x26833,x26834)+~E(x26831,x26832)+~P18(x26831,x26833,x26834)
% 173.53/173.44 [2684]P18(x26843,x26842,x26844)+~E(x26841,x26842)+~P18(x26843,x26841,x26844)
% 173.53/173.44 [2685]P18(x26853,x26854,x26852)+~E(x26851,x26852)+~P18(x26853,x26854,x26851)
% 173.53/173.44 [2686]~P128(x26861)+P128(x26862)+~E(x26861,x26862)
% 173.53/173.44 [2687]P7(x26872,x26873,x26874)+~E(x26871,x26872)+~P7(x26871,x26873,x26874)
% 173.53/173.44 [2688]P7(x26883,x26882,x26884)+~E(x26881,x26882)+~P7(x26883,x26881,x26884)
% 173.53/173.44 [2689]P7(x26893,x26894,x26892)+~E(x26891,x26892)+~P7(x26893,x26894,x26891)
% 173.53/173.44 [2690]P11(x26902,x26903,x26904)+~E(x26901,x26902)+~P11(x26901,x26903,x26904)
% 173.53/173.44 [2691]P11(x26913,x26912,x26914)+~E(x26911,x26912)+~P11(x26913,x26911,x26914)
% 173.53/173.44 [2692]P11(x26923,x26924,x26922)+~E(x26921,x26922)+~P11(x26923,x26924,x26921)
% 173.53/173.44 [2693]~P82(x26931)+P82(x26932)+~E(x26931,x26932)
% 173.53/173.44 [2694]~P134(x26941)+P134(x26942)+~E(x26941,x26942)
% 173.53/173.44 [2695]~P133(x26951)+P133(x26952)+~E(x26951,x26952)
% 173.53/173.44 [2696]P35(x26962,x26963)+~E(x26961,x26962)+~P35(x26961,x26963)
% 173.53/173.44 [2697]P35(x26973,x26972)+~E(x26971,x26972)+~P35(x26973,x26971)
% 173.53/173.44 [2698]~P83(x26981)+P83(x26982)+~E(x26981,x26982)
% 173.53/173.44 [2699]~P127(x26991)+P127(x26992)+~E(x26991,x26992)
% 173.53/173.44 [2700]~P131(x27001)+P131(x27002)+~E(x27001,x27002)
% 173.53/173.44 [2701]~P100(x27011)+P100(x27012)+~E(x27011,x27012)
% 173.53/173.44 [2702]P46(x27022,x27023)+~E(x27021,x27022)+~P46(x27021,x27023)
% 173.53/173.44 [2703]P46(x27033,x27032)+~E(x27031,x27032)+~P46(x27033,x27031)
% 173.53/173.44 [2704]~P93(x27041)+P93(x27042)+~E(x27041,x27042)
% 173.53/173.44 [2705]~P121(x27051)+P121(x27052)+~E(x27051,x27052)
% 173.53/173.44 [2706]~P114(x27061)+P114(x27062)+~E(x27061,x27062)
% 173.53/173.44 [2707]~P80(x27071)+P80(x27072)+~E(x27071,x27072)
% 173.53/173.44 [2708]P37(x27082,x27083,x27084,x27085)+~E(x27081,x27082)+~P37(x27081,x27083,x27084,x27085)
% 173.53/173.44 [2709]P37(x27093,x27092,x27094,x27095)+~E(x27091,x27092)+~P37(x27093,x27091,x27094,x27095)
% 173.53/173.44 [2710]P37(x27103,x27104,x27102,x27105)+~E(x27101,x27102)+~P37(x27103,x27104,x27101,x27105)
% 173.53/173.44 [2711]P37(x27113,x27114,x27115,x27112)+~E(x27111,x27112)+~P37(x27113,x27114,x27115,x27111)
% 173.53/173.44 [2712]~P122(x27121)+P122(x27122)+~E(x27121,x27122)
% 173.53/173.44 [2713]~P68(x27131)+P68(x27132)+~E(x27131,x27132)
% 173.53/173.44 [2714]P14(x27142,x27143,x27144,x27145)+~E(x27141,x27142)+~P14(x27141,x27143,x27144,x27145)
% 173.53/173.44 [2715]P14(x27153,x27152,x27154,x27155)+~E(x27151,x27152)+~P14(x27153,x27151,x27154,x27155)
% 173.53/173.44 [2716]P14(x27163,x27164,x27162,x27165)+~E(x27161,x27162)+~P14(x27163,x27164,x27161,x27165)
% 173.53/173.44 [2717]P14(x27173,x27174,x27175,x27172)+~E(x27171,x27172)+~P14(x27173,x27174,x27175,x27171)
% 173.53/173.44 [2718]~P123(x27181)+P123(x27182)+~E(x27181,x27182)
% 173.53/173.44 [2719]~P129(x27191)+P129(x27192)+~E(x27191,x27192)
% 173.53/173.44 [2720]P54(x27202,x27203,x27204)+~E(x27201,x27202)+~P54(x27201,x27203,x27204)
% 173.53/173.44 [2721]P54(x27213,x27212,x27214)+~E(x27211,x27212)+~P54(x27213,x27211,x27214)
% 173.53/173.44 [2722]P54(x27223,x27224,x27222)+~E(x27221,x27222)+~P54(x27223,x27224,x27221)
% 173.53/173.44 [2723]~P130(x27231)+P130(x27232)+~E(x27231,x27232)
% 173.53/173.44 [2724]P59(x27242,x27243)+~E(x27241,x27242)+~P59(x27241,x27243)
% 173.53/173.44 [2725]P59(x27253,x27252)+~E(x27251,x27252)+~P59(x27253,x27251)
% 173.53/173.44 [2726]~P97(x27261)+P97(x27262)+~E(x27261,x27262)
% 173.53/173.44 [2727]~P62(x27271)+P62(x27272)+~E(x27271,x27272)
% 173.53/173.44 [2728]P51(x27282,x27283)+~E(x27281,x27282)+~P51(x27281,x27283)
% 173.53/173.44 [2729]P51(x27293,x27292)+~E(x27291,x27292)+~P51(x27293,x27291)
% 173.53/173.44 [2730]~P61(x27301)+P61(x27302)+~E(x27301,x27302)
% 173.53/173.44 [2731]P45(x27312,x27313,x27314,x27315,x27316,x27317)+~E(x27311,x27312)+~P45(x27311,x27313,x27314,x27315,x27316,x27317)
% 173.53/173.44 [2732]P45(x27323,x27322,x27324,x27325,x27326,x27327)+~E(x27321,x27322)+~P45(x27323,x27321,x27324,x27325,x27326,x27327)
% 173.53/173.44 [2733]P45(x27333,x27334,x27332,x27335,x27336,x27337)+~E(x27331,x27332)+~P45(x27333,x27334,x27331,x27335,x27336,x27337)
% 173.53/173.44 [2734]P45(x27343,x27344,x27345,x27342,x27346,x27347)+~E(x27341,x27342)+~P45(x27343,x27344,x27345,x27341,x27346,x27347)
% 173.53/173.44 [2735]P45(x27353,x27354,x27355,x27356,x27352,x27357)+~E(x27351,x27352)+~P45(x27353,x27354,x27355,x27356,x27351,x27357)
% 173.53/173.44 [2736]P45(x27363,x27364,x27365,x27366,x27367,x27362)+~E(x27361,x27362)+~P45(x27363,x27364,x27365,x27366,x27367,x27361)
% 173.53/173.44 [2737]~P116(x27371)+P116(x27372)+~E(x27371,x27372)
% 173.53/173.44 [2738]P42(x27382,x27383)+~E(x27381,x27382)+~P42(x27381,x27383)
% 173.53/173.44 [2739]P42(x27393,x27392)+~E(x27391,x27392)+~P42(x27393,x27391)
% 173.53/173.44 [2740]P52(x27402,x27403)+~E(x27401,x27402)+~P52(x27401,x27403)
% 173.53/173.44 [2741]P52(x27413,x27412)+~E(x27411,x27412)+~P52(x27413,x27411)
% 173.53/173.44 [2742]~P119(x27421)+P119(x27422)+~E(x27421,x27422)
% 173.53/173.44 [2743]~P40(x27431)+P40(x27432)+~E(x27431,x27432)
% 173.53/173.44 [2744]~P95(x27441)+P95(x27442)+~E(x27441,x27442)
% 173.53/173.44 [2745]P56(x27452,x27453,x27454,x27455,x27456)+~E(x27451,x27452)+~P56(x27451,x27453,x27454,x27455,x27456)
% 173.53/173.44 [2746]P56(x27463,x27462,x27464,x27465,x27466)+~E(x27461,x27462)+~P56(x27463,x27461,x27464,x27465,x27466)
% 173.53/173.44 [2747]P56(x27473,x27474,x27472,x27475,x27476)+~E(x27471,x27472)+~P56(x27473,x27474,x27471,x27475,x27476)
% 173.53/173.44 [2748]P56(x27483,x27484,x27485,x27482,x27486)+~E(x27481,x27482)+~P56(x27483,x27484,x27485,x27481,x27486)
% 173.53/173.44 [2749]P56(x27493,x27494,x27495,x27496,x27492)+~E(x27491,x27492)+~P56(x27493,x27494,x27495,x27496,x27491)
% 173.53/173.44 [2750]~P115(x27501)+P115(x27502)+~E(x27501,x27502)
% 173.53/173.44 [2751]P17(x27512,x27513,x27514,x27515,x27516,x27517)+~E(x27511,x27512)+~P17(x27511,x27513,x27514,x27515,x27516,x27517)
% 173.53/173.44 [2752]P17(x27523,x27522,x27524,x27525,x27526,x27527)+~E(x27521,x27522)+~P17(x27523,x27521,x27524,x27525,x27526,x27527)
% 173.53/173.44 [2753]P17(x27533,x27534,x27532,x27535,x27536,x27537)+~E(x27531,x27532)+~P17(x27533,x27534,x27531,x27535,x27536,x27537)
% 173.53/173.44 [2754]P17(x27543,x27544,x27545,x27542,x27546,x27547)+~E(x27541,x27542)+~P17(x27543,x27544,x27545,x27541,x27546,x27547)
% 173.53/173.44 [2755]P17(x27553,x27554,x27555,x27556,x27552,x27557)+~E(x27551,x27552)+~P17(x27553,x27554,x27555,x27556,x27551,x27557)
% 173.53/173.44 [2756]P17(x27563,x27564,x27565,x27566,x27567,x27562)+~E(x27561,x27562)+~P17(x27563,x27564,x27565,x27566,x27567,x27561)
% 173.53/173.44 [2757]~P74(x27571)+P74(x27572)+~E(x27571,x27572)
% 173.53/173.44 [2758]~P126(x27581)+P126(x27582)+~E(x27581,x27582)
% 173.53/173.44 [2759]P10(x27592,x27593,x27594,x27595,x27596,x27597)+~E(x27591,x27592)+~P10(x27591,x27593,x27594,x27595,x27596,x27597)
% 173.53/173.44 [2760]P10(x27603,x27602,x27604,x27605,x27606,x27607)+~E(x27601,x27602)+~P10(x27603,x27601,x27604,x27605,x27606,x27607)
% 173.53/173.44 [2761]P10(x27613,x27614,x27612,x27615,x27616,x27617)+~E(x27611,x27612)+~P10(x27613,x27614,x27611,x27615,x27616,x27617)
% 173.53/173.44 [2762]P10(x27623,x27624,x27625,x27622,x27626,x27627)+~E(x27621,x27622)+~P10(x27623,x27624,x27625,x27621,x27626,x27627)
% 173.53/173.44 [2763]P10(x27633,x27634,x27635,x27636,x27632,x27637)+~E(x27631,x27632)+~P10(x27633,x27634,x27635,x27636,x27631,x27637)
% 173.53/173.44 [2764]P10(x27643,x27644,x27645,x27646,x27647,x27642)+~E(x27641,x27642)+~P10(x27643,x27644,x27645,x27646,x27647,x27641)
% 173.53/173.44 [2765]~P85(x27651)+P85(x27652)+~E(x27651,x27652)
% 173.53/173.44 [2766]P2(x27662,x27663)+~E(x27661,x27662)+~P2(x27661,x27663)
% 173.53/173.44 [2767]P2(x27673,x27672)+~E(x27671,x27672)+~P2(x27673,x27671)
% 173.53/173.44 [2768]P15(x27682,x27683,x27684,x27685)+~E(x27681,x27682)+~P15(x27681,x27683,x27684,x27685)
% 173.53/173.44 [2769]P15(x27693,x27692,x27694,x27695)+~E(x27691,x27692)+~P15(x27693,x27691,x27694,x27695)
% 173.53/173.44 [2770]P15(x27703,x27704,x27702,x27705)+~E(x27701,x27702)+~P15(x27703,x27704,x27701,x27705)
% 173.53/173.44 [2771]P15(x27713,x27714,x27715,x27712)+~E(x27711,x27712)+~P15(x27713,x27714,x27715,x27711)
% 173.53/173.44 [2772]~P135(x27721)+P135(x27722)+~E(x27721,x27722)
% 173.53/173.44 [2773]P6(x27732,x27733,x27734,x27735,x27736)+~E(x27731,x27732)+~P6(x27731,x27733,x27734,x27735,x27736)
% 173.53/173.44 [2774]P6(x27743,x27742,x27744,x27745,x27746)+~E(x27741,x27742)+~P6(x27743,x27741,x27744,x27745,x27746)
% 173.53/173.44 [2775]P6(x27753,x27754,x27752,x27755,x27756)+~E(x27751,x27752)+~P6(x27753,x27754,x27751,x27755,x27756)
% 173.53/173.44 [2776]P6(x27763,x27764,x27765,x27762,x27766)+~E(x27761,x27762)+~P6(x27763,x27764,x27765,x27761,x27766)
% 173.53/173.44 [2777]P6(x27773,x27774,x27775,x27776,x27772)+~E(x27771,x27772)+~P6(x27773,x27774,x27775,x27776,x27771)
% 173.53/173.44 [2778]~P124(x27781)+P124(x27782)+~E(x27781,x27782)
% 173.53/173.44 [2779]P53(x27792,x27793,x27794,x27795,x27796,x27797,x27798)+~E(x27791,x27792)+~P53(x27791,x27793,x27794,x27795,x27796,x27797,x27798)
% 173.53/173.44 [2780]P53(x27803,x27802,x27804,x27805,x27806,x27807,x27808)+~E(x27801,x27802)+~P53(x27803,x27801,x27804,x27805,x27806,x27807,x27808)
% 173.53/173.44 [2781]P53(x27813,x27814,x27812,x27815,x27816,x27817,x27818)+~E(x27811,x27812)+~P53(x27813,x27814,x27811,x27815,x27816,x27817,x27818)
% 173.53/173.44 [2782]P53(x27823,x27824,x27825,x27822,x27826,x27827,x27828)+~E(x27821,x27822)+~P53(x27823,x27824,x27825,x27821,x27826,x27827,x27828)
% 173.53/173.44 [2783]P53(x27833,x27834,x27835,x27836,x27832,x27837,x27838)+~E(x27831,x27832)+~P53(x27833,x27834,x27835,x27836,x27831,x27837,x27838)
% 173.53/173.44 [2784]P53(x27843,x27844,x27845,x27846,x27847,x27842,x27848)+~E(x27841,x27842)+~P53(x27843,x27844,x27845,x27846,x27847,x27841,x27848)
% 173.53/173.44 [2785]P53(x27853,x27854,x27855,x27856,x27857,x27858,x27852)+~E(x27851,x27852)+~P53(x27853,x27854,x27855,x27856,x27857,x27858,x27851)
% 173.53/173.44 [2786]~P92(x27861)+P92(x27862)+~E(x27861,x27862)
% 173.53/173.44 [2787]~P69(x27871)+P69(x27872)+~E(x27871,x27872)
% 173.53/173.44 [2788]~P125(x27881)+P125(x27882)+~E(x27881,x27882)
% 173.53/173.44 [2789]~P86(x27891)+P86(x27892)+~E(x27891,x27892)
% 173.53/173.44 [2790]P16(x27902,x27903,x27904,x27905,x27906)+~E(x27901,x27902)+~P16(x27901,x27903,x27904,x27905,x27906)
% 173.53/173.44 [2791]P16(x27913,x27912,x27914,x27915,x27916)+~E(x27911,x27912)+~P16(x27913,x27911,x27914,x27915,x27916)
% 173.53/173.44 [2792]P16(x27923,x27924,x27922,x27925,x27926)+~E(x27921,x27922)+~P16(x27923,x27924,x27921,x27925,x27926)
% 173.53/173.44 [2793]P16(x27933,x27934,x27935,x27932,x27936)+~E(x27931,x27932)+~P16(x27933,x27934,x27935,x27931,x27936)
% 173.53/173.44 [2794]P16(x27943,x27944,x27945,x27946,x27942)+~E(x27941,x27942)+~P16(x27943,x27944,x27945,x27946,x27941)
% 173.53/173.44 [2795]~P47(x27951)+P47(x27952)+~E(x27951,x27952)
% 173.53/173.44 [2796]~P138(x27961)+P138(x27962)+~E(x27961,x27962)
% 173.53/173.44 [2797]P44(x27972,x27973,x27974,x27975)+~E(x27971,x27972)+~P44(x27971,x27973,x27974,x27975)
% 173.53/173.44 [2798]P44(x27983,x27982,x27984,x27985)+~E(x27981,x27982)+~P44(x27983,x27981,x27984,x27985)
% 173.53/173.44 [2799]P44(x27993,x27994,x27992,x27995)+~E(x27991,x27992)+~P44(x27993,x27994,x27991,x27995)
% 173.53/173.44 [2800]P44(x28003,x28004,x28005,x28002)+~E(x28001,x28002)+~P44(x28003,x28004,x28005,x28001)
% 173.53/173.44 [2801]P5(x28012,x28013,x28014)+~E(x28011,x28012)+~P5(x28011,x28013,x28014)
% 173.53/173.44 [2802]P5(x28023,x28022,x28024)+~E(x28021,x28022)+~P5(x28023,x28021,x28024)
% 173.53/173.44 [2803]P5(x28033,x28034,x28032)+~E(x28031,x28032)+~P5(x28033,x28034,x28031)
% 173.53/173.44
% 173.53/173.44 %-------------------------------------------
% 173.53/173.47 cnf(10099,plain,
% 173.53/173.47 (~E(f312(a126,x100991),x100991)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10102,plain,
% 173.53/173.47 (E(f37(x101021,x101022,x101023,x101024,x101025,x101026,x101027,x101028,x101029,a23),x101022)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10105,plain,
% 173.53/173.47 (E(f37(x101051,x101052,x101053,x101054,x101055,x101056,x101057,x101058,x101059,a23),x101052)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10108,plain,
% 173.53/173.47 (~E(f312(a126,x101081),x101081)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10111,plain,
% 173.53/173.47 (~E(f312(a126,x101111),x101111)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10114,plain,
% 173.53/173.47 (E(f37(x101141,x101142,x101143,x101144,x101145,x101146,x101147,x101148,x101149,a23),x101142)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10121,plain,
% 173.53/173.47 (~E(f312(a126,x101211),x101211)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10132,plain,
% 173.53/173.47 (~E(f312(a126,x101321),x101321)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10137,plain,
% 173.53/173.47 (~P22(f312(f71(x101371,x101372,f189(f860(x101371,a845))),x101373))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10140,plain,
% 173.53/173.47 (~P22(f312(f71(x101401,x101402,f189(f860(x101401,a845))),x101403))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10143,plain,
% 173.53/173.47 (~E(f312(a126,x101431),x101431)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10146,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x101461),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10149,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x101491),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10166,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x101661)),x101661))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(10169,plain,
% 173.53/173.47 (~E(f312(f312(f147(x101691),x101692),x101693),x101693)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(10172,plain,
% 173.53/173.47 (E(f312(f117(a1),x101721),f312(f116(a1),x101721))),
% 173.53/173.47 inference(rename_variables,[],[3067])).
% 173.53/173.47 cnf(10175,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x101751),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10178,plain,
% 173.53/173.47 (E(f37(x101781,x101782,x101783,x101784,x101785,x101786,x101787,x101788,x101789,a23),x101782)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10181,plain,
% 173.53/173.47 (E(f37(x101811,x101812,x101813,x101814,x101815,x101816,x101817,x101818,x101819,a23),x101812)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10188,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x101881),x101882)),x101882))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(10191,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x101911),x101912)),x101912))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(10212,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x102121),x102121))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10215,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f54(a852,x102151,x102152)),x102151))),
% 173.53/173.47 inference(rename_variables,[],[3658])).
% 173.53/173.47 cnf(10234,plain,
% 173.53/173.47 (E(f312(f53(a852),f312(f279(a852),x102341)),x102341)),
% 173.53/173.47 inference(rename_variables,[],[3102])).
% 173.53/173.47 cnf(10242,plain,
% 173.53/173.47 (~E(f312(a126,x102421),x102421)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10245,plain,
% 173.53/173.47 (~E(f312(a126,x102451),x102451)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10248,plain,
% 173.53/173.47 (~E(f312(a126,x102481),x102481)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10253,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x102531),f312(a126,x102531)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10264,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x102641),x102641))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(10271,plain,
% 173.53/173.47 (E(f37(x102711,x102712,x102713,x102714,x102715,x102716,x102717,x102718,x102719,a23),x102712)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10274,plain,
% 173.53/173.47 (E(f37(x102741,x102742,x102743,x102744,x102745,x102746,x102747,x102748,x102749,a23),x102742)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10297,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x102971),x102971))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10304,plain,
% 173.53/173.47 (~E(f312(f312(f312(f81(x103041,f856(x103042)),x103043),x103044),f312(f219(x103042),x103045)),f312(f16(f856(x103042),x103041),f192(x103042)))),
% 173.53/173.47 inference(rename_variables,[],[4492])).
% 173.53/173.47 cnf(10329,plain,
% 173.53/173.47 (~E(f312(f312(f147(x103291),x103292),x103293),x103293)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(10332,plain,
% 173.53/173.47 (~E(f312(a27,x103321),f36(x103322,x103323))),
% 173.53/173.47 inference(rename_variables,[],[4404])).
% 173.53/173.47 cnf(10345,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x103451),x103451))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(10348,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x103481),x103481))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10351,plain,
% 173.53/173.47 (~E(f312(a126,x103511),x103511)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10358,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x103581),x103581))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(10369,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x103691),f312(a126,x103691)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10376,plain,
% 173.53/173.47 (E(f312(f312(f129(x103761),f127(x103761)),x103762),x103762)),
% 173.53/173.47 inference(rename_variables,[],[3155])).
% 173.53/173.47 cnf(10394,plain,
% 173.53/173.47 (~P22(f312(f71(x103941,x103942,f189(f860(x103941,a845))),x103943))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10423,plain,
% 173.53/173.47 (~E(f312(a27,x104231),f36(x104232,x104233))),
% 173.53/173.47 inference(rename_variables,[],[4404])).
% 173.53/173.47 cnf(10432,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x104321),x104321))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10437,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x104371),x104371))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(10440,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x104401),f312(a126,x104401)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10443,plain,
% 173.53/173.47 (~P22(f312(f71(x104431,x104432,f189(f860(x104431,a845))),x104433))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10448,plain,
% 173.53/173.47 (~P22(f312(f71(x104481,x104482,f189(f860(x104481,a845))),x104483))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10461,plain,
% 173.53/173.47 (~E(f312(a126,x104611),x104611)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10484,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x104841),f312(a126,x104841)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10487,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x104871),f312(a126,x104871)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10490,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x104901),f312(a126,f312(f312(f89(a852),x104902),x104901))))),
% 173.53/173.47 inference(rename_variables,[],[3651])).
% 173.53/173.47 cnf(10493,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x104931),f312(f312(f90(a852),x104931),x104931)))),
% 173.53/173.47 inference(rename_variables,[],[3478])).
% 173.53/173.47 cnf(10496,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x104961),f312(f312(f90(a852),x104961),x104961)))),
% 173.53/173.47 inference(rename_variables,[],[3478])).
% 173.53/173.47 cnf(10501,plain,
% 173.53/173.47 (P22(f312(f312(f314(x105011),x105012),f235(f860(x105011,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(10516,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x105161),x105162)),x105162))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(10519,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x105191),x105192)),x105192))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(10522,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x105221)),x105221))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(10525,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x105251)),x105251))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(10528,plain,
% 173.53/173.47 (P22(f312(f235(f860(x105281,a845)),x105282))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(10531,plain,
% 173.53/173.47 (E(f312(f53(a852),f312(f279(a852),x105311)),x105311)),
% 173.53/173.47 inference(rename_variables,[],[3102])).
% 173.53/173.47 cnf(10534,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x105341),f312(a126,x105341)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10541,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x105411),x105411))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(10546,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x105461),x105461))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(10555,plain,
% 173.53/173.47 (E(f37(x105551,x105552,x105553,x105554,x105555,x105556,x105557,x105558,x105559,a23),x105552)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10558,plain,
% 173.53/173.47 (P22(f312(f235(f860(x105581,a845)),x105582))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(10561,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x105611),f312(f312(f90(a852),x105611),x105611)))),
% 173.53/173.47 inference(rename_variables,[],[3478])).
% 173.53/173.47 cnf(10565,plain,
% 173.53/173.47 (E(f312(f165(x105651),f37(x105652,f312(f312(f129(x105651),f312(f165(x105651),x105653)),f312(f312(f147(x105651),x105654),f127(x105651))),x105655,x105656,x105657,x105658,x105659,x1056510,x1056511,a23)),f312(f312(f147(x105651),x105654),x105653))),
% 173.53/173.47 inference(scs_inference,[],[4358,10102,10105,10114,10178,10181,10271,10274,10555,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,4404,10332,2804,3038,3106,3067,3046,3135,3155,10376,4492,4420,10169,3102,10234,3984,4501,3119,3568,3510,3272,10253,10369,10440,10484,10487,3653,3187,4472,10146,10149,10175,4488,3640,3416,3790,3230,3232,3205,4469,4414,3907,3202,10264,10358,10437,3203,3204,10345,4468,10212,10297,10348,3361,3266,10528,3297,3718,3658,10215,4481,10166,10522,4028,4480,4459,3180,3181,4461,4464,4495,10137,10140,10394,10443,4500,3478,10493,10496,4498,3679,4496,10188,10191,10516,3651,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267])).
% 173.53/173.47 cnf(10566,plain,
% 173.53/173.47 (E(f37(x105661,x105662,x105663,x105664,x105665,x105666,x105667,x105668,x105669,a23),x105662)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10572,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a113),f312(a3,x105721)),f312(a3,f2(a852))))),
% 173.53/173.47 inference(scs_inference,[],[4358,10102,10105,10114,10178,10181,10271,10274,10555,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,4404,10332,2804,3038,3106,3067,3046,3135,3155,10376,4492,4420,10169,3102,10234,3984,4501,3119,3568,3510,3272,10253,10369,10440,10484,10487,10534,3653,3187,4472,10146,10149,10175,4488,3640,3416,3790,3230,3232,3205,4469,4414,3907,3202,10264,10358,10437,3203,3204,10345,4468,10212,10297,10348,3361,3266,10528,3297,3718,3658,10215,4481,10166,10522,4028,4480,4459,3180,3181,4461,4464,4495,10137,10140,10394,10443,4500,3478,10493,10496,4498,3679,4496,10188,10191,10516,3651,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272])).
% 173.53/173.47 cnf(10578,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,f312(a126,f312(f312(f89(a852),x105781),x105782)))),f312(a126,x105782)))),
% 173.53/173.47 inference(scs_inference,[],[4358,10102,10105,10114,10178,10181,10271,10274,10555,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,4404,10332,2804,3038,3106,3067,3046,3135,3155,10376,4492,4420,10169,3102,10234,3984,4501,3119,3568,3510,3272,10253,10369,10440,10484,10487,10534,3653,3187,4472,10146,10149,10175,4488,3640,3416,3790,3230,3232,3205,4469,4414,3907,3202,10264,10358,10437,3203,3204,10345,4468,10212,10297,10348,3361,3266,10528,3297,3718,3658,10215,4481,10166,10522,4028,4480,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,4500,3478,10493,10496,4498,3679,4496,10188,10191,10516,3651,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275])).
% 173.53/173.47 cnf(10603,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x106031),x106031))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10616,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x106161),f312(a126,x106161)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10619,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x106191,f860(x106192,a845))),x106193),x106194))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(10622,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x106221),x106221))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(10627,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x106271),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10640,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x106401),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10643,plain,
% 173.53/173.47 (~P22(f312(f312(f228(f860(x106431,a845)),x106432),f189(f860(x106431,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4493])).
% 173.53/173.47 cnf(10646,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x106461),x106461))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10649,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x106491),x106491))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10664,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x106641),x106641))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10673,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x106731),x106732),f189(f860(x106731,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10682,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x106821),x106821))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10685,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x106851),x106852),f189(f860(x106851,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10688,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x106881,a845)),f312(f290(x106882,x106881,x106883),f312(f291(x106882,x106881,x106883),x106884))),x106884))),
% 173.53/173.47 inference(rename_variables,[],[4089])).
% 173.53/173.47 cnf(10697,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x106971,a845)),f312(f168(x106971),f312(f132(x106971,x106972),x106973))),f312(f168(x106971),x106973)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(10700,plain,
% 173.53/173.47 (E(f312(f290(x107001,x107001,f5(x107001)),x107002),x107002)),
% 173.53/173.47 inference(rename_variables,[],[3262])).
% 173.53/173.47 cnf(10705,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x107051))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(10708,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x107081),x107081))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10711,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x107111),x107111))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10714,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x107141,f860(x107142,a845))),x107143),x107144))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(10721,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x107211),x107211))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(10732,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x107321),f312(a126,f312(f312(f89(a852),x107322),x107321))))),
% 173.53/173.47 inference(rename_variables,[],[3651])).
% 173.53/173.47 cnf(10735,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x107351),f312(f312(f90(a852),x107351),x107351)))),
% 173.53/173.47 inference(rename_variables,[],[3478])).
% 173.53/173.47 cnf(10745,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x107451),x107451))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10748,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x107481),x107481))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(10751,plain,
% 173.53/173.47 (~E(f312(a126,x107511),x107511)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10756,plain,
% 173.53/173.47 (P22(f312(f312(f314(x107561),x107562),f235(f860(x107561,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(10761,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x107611),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(10776,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x107761))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(10783,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x107831),x107831))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10792,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x107921),x107922),f189(f860(x107921,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10800,plain,
% 173.53/173.47 (P22(f312(f312(f314(x108001),x108002),f235(f860(x108001,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(10803,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x108031),f853(x108031))),f312(f312(f239(f853(x108031),f853(x108031)),x108032),f127(x108031))),f141(x108031,x108033)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(10809,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(x108091,x108091)),x108092),f237(x108091,f189(f860(x108091,a845)))))),
% 173.53/173.47 inference(scs_inference,[],[4460,4358,10102,10105,10114,10178,10181,10271,10274,10555,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,4404,10332,2804,3038,3106,3067,3046,3262,3135,3155,10376,4492,4420,10169,3102,10234,3984,3840,4501,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,3653,3187,4472,10146,10149,10175,10627,10640,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3569,3907,4493,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,4484,10673,10685,10792,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,4500,3478,10493,10496,10561,10735,4498,4499,10619,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798])).
% 173.53/173.47 cnf(10810,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x108101),x108102),f189(f860(x108101,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10812,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x108121),x108122),f312(f291(x108121,x108123,x108124),f189(f860(x108123,a845)))))),
% 173.53/173.47 inference(scs_inference,[],[4460,4358,10102,10105,10114,10178,10181,10271,10274,10555,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,4404,10332,2804,3038,3106,3067,3046,3262,3135,3155,10376,4492,4420,10169,3102,10234,3984,3840,4501,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,3653,3187,4472,10146,10149,10175,10627,10640,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3569,3907,4493,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,4484,10673,10685,10792,10810,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,4500,3478,10493,10496,10561,10735,4498,4499,10619,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828])).
% 173.53/173.47 cnf(10813,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x108131),x108132),f189(f860(x108131,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10816,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x108161,a845)),x108162),f312(f312(f289(x108161),x108163),x108162)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(10819,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x108191),x108191))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(10822,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x108221,a845)),x108222),f312(f312(f289(x108221),x108223),x108222)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(10825,plain,
% 173.53/173.47 (E(f37(x108251,x108252,x108253,x108254,x108255,x108256,x108257,x108258,x108259,a23),x108252)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10828,plain,
% 173.53/173.47 (E(f37(x108281,x108282,x108283,x108284,x108285,x108286,x108287,x108288,x108289,a23),x108282)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(10839,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x108391,a845)),x108392),f312(f312(f289(x108391),x108393),x108392)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(10842,plain,
% 173.53/173.47 (P36(x108421,x108422,x108423,f180(x108421,x108422,x108424,x108423))),
% 173.53/173.47 inference(rename_variables,[],[3766])).
% 173.53/173.47 cnf(10850,plain,
% 173.53/173.47 (~P22(f312(f71(x108501,x108502,f189(f860(x108501,a845))),x108503))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(10854,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(a852,a852)),f312(f312(f239(a852,a852),f312(a126,x108541)),x108541)),f287(a852,a302)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,4404,10332,2804,3930,3038,3106,3067,3046,3262,3135,3155,10376,4492,4420,10169,3102,10234,3984,3840,4501,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,3653,3187,4472,10146,10149,10175,10627,10640,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3569,3907,4493,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,4484,10673,10685,10792,10810,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,4500,3807,3647,10816,10822,3478,10493,10496,10561,10735,4498,4499,10619,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264])).
% 173.53/173.47 cnf(10865,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x108651),f312(a126,x108651)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(10875,plain,
% 173.53/173.47 (~E(f312(f290(x108751,f860(x108751,a845),x108752),x108753),f312(f288(x108751),x108753))),
% 173.53/173.47 inference(rename_variables,[],[4482])).
% 173.53/173.47 cnf(10878,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x108781),x108782),f189(f860(x108781,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10881,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x108811,x108811)),f312(f312(f239(x108811,x108811),x108812),x108812)),f287(x108811,x108813)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(10884,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x108841,a845)),x108842),f235(f860(x108841,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(10887,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x108871,a845)),f312(f168(x108871),f166(x108871,x108872,x108873))),f312(f168(x108871),x108873)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(10903,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x109031,a845)),f189(f860(x109031,a845))),x109032))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(10917,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x109171),f853(x109171))),f312(f312(f239(f853(x109171),f853(x109171)),x109172),f127(x109171))),f143(x109171,x109173)))),
% 173.53/173.47 inference(rename_variables,[],[4502])).
% 173.53/173.47 cnf(10928,plain,
% 173.53/173.47 (~E(f312(a126,x109281),x109281)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10931,plain,
% 173.53/173.47 (~E(f312(a126,x109311),x109311)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(10943,plain,
% 173.53/173.47 (P19(x109431,x109431,f5(x109431),x109432)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(10948,plain,
% 173.53/173.47 (~E(f312(f290(x109481,f860(x109481,a845),x109482),x109483),f312(f288(x109481),x109483))),
% 173.53/173.47 inference(rename_variables,[],[4482])).
% 173.53/173.47 cnf(10953,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x109531,a845)),x109532),f235(f860(x109531,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(10967,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x109671),x109672),f189(f860(x109671,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10970,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x109701)),x109701))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(10975,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x109751),x109752),f189(f860(x109751,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(10987,plain,
% 173.53/173.47 (~P22(f312(f312(f314(a852),f312(a126,f312(f138(a852,a852,f89(a852),f2(a852)),x109871))),f312(f168(a852),x109871)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,4404,10332,10423,2804,3930,3661,3038,3106,3067,10172,3046,3262,3135,3155,10376,4492,3838,4420,10169,4482,10875,3310,3102,10234,3984,3840,10881,4501,10803,4502,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3901,3569,3907,3585,10884,4493,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,4484,10673,10685,10792,10810,10813,10878,10967,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,10970,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,4500,3807,3647,10816,10822,3649,3478,10493,10496,10561,10735,4498,4499,10619,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717])).
% 173.53/173.47 cnf(10988,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x109881)),x109881))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(10991,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x109911),x109912),f189(f860(x109911,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11001,plain,
% 173.53/173.47 (E(f312(x110011,f739(f312(x110011,x110012),f312(f219(x110013),x110012),x110011,x110014,x110013)),f312(x110011,x110012))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,4404,10332,10423,2804,3930,3661,3038,3106,3067,10172,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,4482,10875,3310,3102,10234,3984,3840,10881,4501,10803,4502,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3901,3569,3907,3585,10884,4493,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,4484,10673,10685,10792,10810,10813,10878,10967,10975,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,10970,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,4500,3807,3647,10816,10822,3649,3478,10493,10496,10561,10735,4498,4499,10619,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789])).
% 173.53/173.47 cnf(11010,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x110101,x110101)),f312(f312(f239(x110101,x110101),x110102),x110102)),f287(x110101,x110103)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(11015,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x110151),f853(x110151))),f312(f312(f239(f853(x110151),f853(x110151)),x110152),f127(x110151))),f141(x110151,x110153)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(11018,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x110181),f853(x110181))),f312(f312(f239(f853(x110181),f853(x110181)),x110182),f127(x110181))),f143(x110181,x110183)))),
% 173.53/173.47 inference(rename_variables,[],[4502])).
% 173.53/173.47 cnf(11021,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x110211),f853(x110211))),f312(f312(f239(f853(x110211),f853(x110211)),x110212),f127(x110211))),f153(x110211,x110213)))),
% 173.53/173.47 inference(rename_variables,[],[4503])).
% 173.53/173.47 cnf(11026,plain,
% 173.53/173.47 (~P22(f312(f312(f228(f860(x110261,a845)),x110262),f189(f860(x110261,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4493])).
% 173.53/173.47 cnf(11029,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x110291),x110292),f189(f860(x110291,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11034,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110341,a845)),x110342),f235(f860(x110341,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(11037,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x110371,f860(x110372,a845))),x110373),x110374))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(11041,plain,
% 173.53/173.47 (~P57(f853(x110411),f154(x110411,x110412))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,4404,10332,10423,2804,3930,3661,3038,3106,3067,10172,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,4482,10875,3310,3102,10234,3984,3840,10881,4501,10803,11015,4502,10917,4503,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,10761,4488,3640,3416,3790,3230,3232,3205,4469,4414,3947,3850,10697,3901,3569,3907,3585,10884,10953,4493,10643,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,3266,10528,3297,3718,3658,10215,4481,10166,10522,10525,10970,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,4500,3807,3647,10816,10822,3649,3478,10493,10496,10561,10735,4498,4499,10619,10714,4089,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059])).
% 173.53/173.47 cnf(11046,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x110461),x110462),f189(f860(x110461,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11049,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(x110491,x110491)),f312(f312(f239(x110491,x110491),x110492),x110493)),f149(x110491,f127(f860(x110491,a852)))))),
% 173.53/173.47 inference(rename_variables,[],[4500])).
% 173.53/173.47 cnf(11052,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110521,a845)),x110522),x110522))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(11055,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x110551),x110552),f189(f860(x110551,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11058,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110581,a845)),f189(f860(x110581,a845))),x110582))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(11061,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x110611,x110611)),f312(f312(f239(x110611,x110611),x110612),x110612)),f287(x110611,x110613)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(11072,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x110721),f853(x110721))),f312(f312(f239(f853(x110721),f853(x110721)),x110722),f127(x110721))),f153(x110721,x110723)))),
% 173.53/173.47 inference(rename_variables,[],[4503])).
% 173.53/173.47 cnf(11075,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x110751),f853(x110751))),f312(f312(f239(f853(x110751),f853(x110751)),f127(x110751)),x110752)),f141(x110751,x110753)))),
% 173.53/173.47 inference(rename_variables,[],[4504])).
% 173.53/173.47 cnf(11083,plain,
% 173.53/173.47 (P22(f312(f312(f314(x110831),x110832),f235(f860(x110831,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(11088,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110881,a845)),f189(f860(x110881,a845))),x110882))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(11091,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x110911),x110912),f189(f860(x110911,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11094,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110941,a845)),x110942),f235(f860(x110941,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(11099,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x110991,a845)),f189(f860(x110991,a845))),x110992))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(11112,plain,
% 173.53/173.47 (P22(f312(f235(f860(x111121,a845)),x111122))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(11120,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x111201),f853(x111201))),f312(f312(f239(f853(x111201),f853(x111201)),x111202),f127(x111201))),f141(x111201,x111203)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(11123,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x111231),f853(x111231))),f312(f312(f239(f853(x111231),f853(x111231)),x111232),f127(x111231))),f143(x111231,x111233)))),
% 173.53/173.47 inference(rename_variables,[],[4502])).
% 173.53/173.47 cnf(11126,plain,
% 173.53/173.47 (~E(f312(a126,x111261),x111261)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11129,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x111291),x111292),f189(f860(x111291,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11134,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(f853(x111341),f853(x111341))),f312(f312(f239(f853(x111341),f853(x111341)),x111342),x111342)),f154(x111341,f287(x111341,x111343))))),
% 173.53/173.47 inference(rename_variables,[],[3978])).
% 173.53/173.47 cnf(11139,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x111391),f853(x111391))),f312(f312(f239(f853(x111391),f853(x111391)),x111392),f127(x111391))),f141(x111391,x111393)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(11148,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x111481),x111482),f181(x111483,x111481,f183(x111483,x111481,x111484,f189(f860(x111483,a845))))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,4404,10332,10423,2804,3930,3661,3038,3106,3067,10172,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,4482,10875,3310,3102,10234,3984,3840,10881,11010,4501,10803,11015,11120,4502,10917,11018,4503,11021,4504,11075,4505,3119,3408,3568,3510,3714,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,10761,4488,3640,3416,3790,3230,3232,3205,4469,4414,3978,11134,3947,3850,10697,3901,3569,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,3266,10528,10558,3297,3718,3658,10215,4481,10166,10522,10525,10970,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,4500,3807,3647,10816,10822,3506,3649,10903,11058,11088,3478,10493,10496,10561,10735,4498,4499,10619,10714,4089,3989,3679,4496,10188,10191,10516,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632])).
% 173.53/173.47 cnf(11149,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x111491),x111492),f189(f860(x111491,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11152,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x111521),x111522),f189(f860(x111521,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11155,plain,
% 173.53/173.47 (P22(f312(f312(f314(x111551),x111552),f235(f860(x111551,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(11160,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(x111601,x111601)),f312(f312(f239(x111601,x111601),x111602),x111603)),f149(x111601,f127(f860(x111601,a852)))))),
% 173.53/173.47 inference(rename_variables,[],[4500])).
% 173.53/173.47 cnf(11163,plain,
% 173.53/173.47 (~E(f312(f290(x111631,f860(x111631,a845),x111632),x111633),f312(f288(x111631),x111633))),
% 173.53/173.47 inference(rename_variables,[],[4482])).
% 173.53/173.47 cnf(11166,plain,
% 173.53/173.47 (~E(f312(f290(x111661,f860(x111661,a845),x111662),x111663),f312(f288(x111661),x111663))),
% 173.53/173.47 inference(rename_variables,[],[4482])).
% 173.53/173.47 cnf(11169,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x111691),f853(x111691))),f312(f312(f239(f853(x111691),f853(x111691)),x111692),f127(x111691))),f141(x111691,x111693)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(11175,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x111751),f853(x111751))),f312(f312(f239(f853(x111751),f853(x111751)),x111752),f127(x111751))),f141(x111751,x111753)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(11178,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x111781),x111782),f189(f860(x111781,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11181,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x111811,f860(x111812,a845))),x111813),x111814))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(11184,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x111841),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11191,plain,
% 173.53/173.47 (P22(f312(f312(f314(x111911),f312(x111912,x111913)),f312(f290(x111914,x111911,x111912),f235(f860(x111914,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(11194,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(x111941,x111941)),f312(f312(f239(x111941,x111941),x111942),x111943)),f149(x111941,f127(f860(x111941,a852)))))),
% 173.53/173.47 inference(rename_variables,[],[4500])).
% 173.53/173.47 cnf(11200,plain,
% 173.53/173.47 (E(f37(x112001,x112002,x112003,x112004,x112005,x112006,x112007,x112008,x112009,a23),x112002)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11203,plain,
% 173.53/173.47 (E(f37(x112031,x112032,x112033,x112034,x112035,x112036,x112037,x112038,x112039,a23),x112032)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11206,plain,
% 173.53/173.47 (~E(f312(a126,x112061),x112061)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11213,plain,
% 173.53/173.47 (~E(f312(a126,x112131),x112131)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11218,plain,
% 173.53/173.47 (E(f37(x112181,x112182,x112183,x112184,x112185,x112186,x112187,x112188,x112189,a23),x112182)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11219,plain,
% 173.53/173.47 (E(f38(x112191,x112192,x112193,x112194,x112195,x112196,x112197,x112198,x112199,a23),x112192)),
% 173.53/173.47 inference(rename_variables,[],[4359])).
% 173.53/173.47 cnf(11222,plain,
% 173.53/173.47 (E(f37(x112221,x112222,x112223,x112224,x112225,x112226,x112227,x112228,x112229,a23),x112222)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11229,plain,
% 173.53/173.47 (~E(f312(a126,x112291),x112291)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11234,plain,
% 173.53/173.47 (~E(f312(f312(f89(a1),x112341),x112341),a111)),
% 173.53/173.47 inference(rename_variables,[],[4417])).
% 173.53/173.47 cnf(11243,plain,
% 173.53/173.47 (E(f312(f312(f21(a852),f2(a852)),x112431),f2(a852))),
% 173.53/173.47 inference(rename_variables,[],[3120])).
% 173.53/173.47 cnf(11246,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x112461),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11253,plain,
% 173.53/173.47 (E(f312(f312(f89(a1),f312(f312(f90(a1),x112531),f312(f47(a1,x112532),x112531))),f54(a1,x112532,x112531)),x112532)),
% 173.53/173.47 inference(rename_variables,[],[3722])).
% 173.53/173.47 cnf(11267,plain,
% 173.53/173.47 (E(f37(x112671,x112672,x112673,x112674,x112675,x112676,x112677,x112678,x112679,a23),x112672)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11270,plain,
% 173.53/173.47 (E(f37(x112701,x112702,x112703,x112704,x112705,x112706,x112707,x112708,x112709,a23),x112702)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11273,plain,
% 173.53/173.47 (E(f37(x112731,x112732,x112733,x112734,x112735,x112736,x112737,x112738,x112739,a23),x112732)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11276,plain,
% 173.53/173.47 (E(f37(x112761,x112762,x112763,x112764,x112765,x112766,x112767,x112768,x112769,a23),x112762)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11279,plain,
% 173.53/173.47 (~E(f312(a126,x112791),x112791)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11282,plain,
% 173.53/173.47 (~E(f312(a126,x112821),x112821)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11286,plain,
% 173.53/173.47 (E(f37(x112861,x112862,x112863,x112864,x112865,x112866,x112867,x112868,x112869,a23),x112862)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11305,plain,
% 173.53/173.47 (~E(f312(a126,x113051),x113051)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11308,plain,
% 173.53/173.47 (~E(f312(f312(f147(x113081),x113082),x113083),x113083)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(11315,plain,
% 173.53/173.47 (~P22(f312(f71(x113151,x113152,f189(f860(x113151,a845))),x113153))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(11318,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x113181,f860(x113182,a845))),x113183),x113184))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(11321,plain,
% 173.53/173.47 (P22(f312(f312(f314(x113211),x113212),f235(f860(x113211,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(11329,plain,
% 173.53/173.47 (E(f37(x113291,x113292,x113293,x113294,x113295,x113296,x113297,x113298,x113299,a23),x113292)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11336,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x113361),x113361))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11343,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x113431),x113431))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11344,plain,
% 173.53/173.47 (E(f37(x113441,x113442,x113443,x113444,x113445,x113446,x113447,x113448,x113449,a23),x113442)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11357,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x113571),x113572)),x113572))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(11360,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x113601)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(11371,plain,
% 173.53/173.47 (E(f37(x113711,x113712,x113713,x113714,x113715,x113716,x113717,x113718,x113719,a23),x113712)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11374,plain,
% 173.53/173.47 (E(f37(x113741,x113742,x113743,x113744,x113745,x113746,x113747,x113748,x113749,a23),x113742)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11385,plain,
% 173.53/173.47 (E(f37(x113851,x113852,x113853,x113854,x113855,x113856,x113857,x113858,x113859,a23),x113852)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11390,plain,
% 173.53/173.47 (E(f37(x113901,x113902,x113903,x113904,x113905,x113906,x113907,x113908,x113909,a23),x113902)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11393,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x113931)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(11396,plain,
% 173.53/173.47 (E(f37(x113961,x113962,x113963,x113964,x113965,x113966,x113967,x113968,x113969,a23),x113962)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11399,plain,
% 173.53/173.47 (~E(f312(a126,x113991),x113991)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11402,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x114021),x114021))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11404,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f2(a1)),a92))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,4404,10332,10423,2804,2809,2821,2824,2825,2826,2830,2831,2840,2848,2852,2861,2864,2871,2874,2888,2889,2895,2897,2950,2958,2963,2984,3098,4380,3930,3661,3038,3722,11253,3106,3067,10172,3061,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,10329,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,3568,4417,3510,3714,4105,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,10761,11184,11246,4488,11360,11393,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3947,3850,10697,3901,3569,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,10541,11336,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,10748,4468,10212,10297,10348,10432,10664,10711,3361,10501,10756,10800,11083,11155,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,3266,10528,10558,3305,3297,3718,3658,10215,4481,10166,10522,10525,10970,10988,3224,10705,4028,4480,3726,4459,4462,3180,3181,4461,4464,4495,10137,10140,10394,10443,10448,10850,4500,11049,11160,3807,3647,10816,10822,3506,3649,10903,11058,11088,3478,10493,10496,10561,10735,4498,4499,10619,10714,11037,11181,4089,3989,3679,4496,10188,10191,10516,10519,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383])).
% 173.53/173.47 cnf(11409,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x114091),x114091))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11430,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x114301)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(11443,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x114431),x114431))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11446,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x114461)),x114461))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11447,plain,
% 173.53/173.47 (~E(f312(a126,x114471),x114471)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11453,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x114531)),x114531))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11454,plain,
% 173.53/173.47 (E(f37(x114541,x114542,x114543,x114544,x114545,x114546,x114547,x114548,x114549,a23),x114542)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11461,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x114611),x114612)),x114611))),
% 173.53/173.47 inference(rename_variables,[],[4497])).
% 173.53/173.47 cnf(11464,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x114641)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(11467,plain,
% 173.53/173.47 (~E(f312(a126,x114671),x114671)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11480,plain,
% 173.53/173.47 (P22(f312(f312(f314(x114801),x114802),f312(f312(f289(x114801),x114802),x114803)))),
% 173.53/173.47 inference(rename_variables,[],[3519])).
% 173.53/173.47 cnf(11481,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a1),f2(a1)),f312(f88(a1),f312(f114(a1),f312(a126,x114811)))))),
% 173.53/173.47 inference(rename_variables,[],[4498])).
% 173.53/173.47 cnf(11484,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),f312(f312(f21(a852),x114841),x114842)),f312(a126,x114841)))),
% 173.53/173.47 inference(rename_variables,[],[3653])).
% 173.53/173.47 cnf(11487,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f54(a852,x114871,x114872)),x114871))),
% 173.53/173.47 inference(rename_variables,[],[3658])).
% 173.53/173.47 cnf(11493,plain,
% 173.53/173.47 (E(f312(f312(f129(x114931),x114932),f127(x114931)),x114932)),
% 173.53/173.47 inference(rename_variables,[],[3136])).
% 173.53/173.47 cnf(11496,plain,
% 173.53/173.47 (E(f37(x114961,x114962,x114963,x114964,x114965,x114966,x114967,x114968,x114969,a23),x114962)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11499,plain,
% 173.53/173.47 (E(f37(x114991,x114992,x114993,x114994,x114995,x114996,x114997,x114998,x114999,a23),x114992)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11502,plain,
% 173.53/173.47 (E(f37(x115021,x115022,x115023,x115024,x115025,x115026,x115027,x115028,x115029,a23),x115022)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11511,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x115111),x115111))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11512,plain,
% 173.53/173.47 (E(f37(x115121,x115122,x115123,x115124,x115125,x115126,x115127,x115128,x115129,a23),x115122)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11515,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f54(a852,x115151,x115152)),x115151))),
% 173.53/173.47 inference(rename_variables,[],[3658])).
% 173.53/173.47 cnf(11516,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x115161))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(11518,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a1),f87(a1)),f2(a1)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,4404,10332,10423,2804,2809,2821,2824,2825,2826,2830,2831,2840,2848,2852,2854,2861,2863,2864,2871,2872,2874,2888,2889,2895,2897,2950,2956,2958,2963,2984,3098,4380,3245,3930,3136,11493,3661,3038,3722,11253,3106,3067,10172,3061,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,10329,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,3568,4266,4267,4417,3510,3714,4105,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,3187,4472,10146,10149,10175,10627,10640,10761,11184,11246,4488,11360,11393,11430,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3947,3850,10697,3901,3569,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,10541,11336,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,10748,11402,4468,10212,10297,10348,10432,10664,10711,10721,11409,3361,10501,10756,10800,11083,11155,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,3266,10528,10558,3305,3297,3718,3658,10215,11487,4481,10166,10522,10525,10970,10988,11446,3224,10705,10776,4028,4480,3726,4459,4462,3180,3181,4461,4464,3519,4495,10137,10140,10394,10443,10448,10850,4500,11049,11160,3807,3647,10816,10822,3506,3649,10903,11058,11088,3478,10493,10496,10561,10735,4498,4499,10619,10714,11037,11181,4089,3989,3679,4496,10188,10191,10516,10519,4497,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724])).
% 173.53/173.47 cnf(11531,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x115311),x115311))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11534,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x115341),x115341))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11537,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x115371),x115371))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11540,plain,
% 173.53/173.47 (P22(f312(f312(f314(x115401),f312(x115402,x115403)),f312(f290(x115404,x115401,x115402),f235(f860(x115404,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(11541,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x115411),x115412)),x115412))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(11544,plain,
% 173.53/173.47 (P22(f312(f312(f314(x115441),f312(x115442,x115443)),f312(f290(x115444,x115441,x115442),f235(f860(x115444,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(11545,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x115451)),x115451))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11550,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x115501),x115501))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11551,plain,
% 173.53/173.47 (E(f37(x115511,x115512,x115513,x115514,x115515,x115516,x115517,x115518,x115519,a23),x115512)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11554,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x115541),x115542)),x115541))),
% 173.53/173.47 inference(rename_variables,[],[4497])).
% 173.53/173.47 cnf(11557,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x115571),x115571))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11560,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x115601),x115601))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11566,plain,
% 173.53/173.47 (P22(f312(f312(f314(x115661),x115662),f312(f312(f289(x115661),x115662),x115663)))),
% 173.53/173.47 inference(rename_variables,[],[3519])).
% 173.53/173.47 cnf(11569,plain,
% 173.53/173.47 (~P22(f312(f71(x115691,x115692,f189(f860(x115691,a845))),x115693))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(11572,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x115721),x115721))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11585,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x115851),x115852),f189(f860(x115851,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11588,plain,
% 173.53/173.47 (E(f312(f312(f16(x115881,x115882),x115883),x115884),x115883)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(11591,plain,
% 173.53/173.47 (E(f312(f312(f16(x115911,x115912),x115913),x115914),x115913)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(11600,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f312(f47(a852,x116001),x116002)),x116001))),
% 173.53/173.47 inference(rename_variables,[],[3578])).
% 173.53/173.47 cnf(11601,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),f2(a852)),f312(a126,x116011)))),
% 173.53/173.47 inference(rename_variables,[],[3284])).
% 173.53/173.47 cnf(11604,plain,
% 173.53/173.47 (P22(f312(f312(f314(x116041),f312(x116042,x116043)),f312(f290(x116044,x116041,x116042),f235(f860(x116044,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(11607,plain,
% 173.53/173.47 (P22(f312(f70(x116071),f312(f168(x116071),x116072)))),
% 173.53/173.47 inference(rename_variables,[],[3244])).
% 173.53/173.47 cnf(11610,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x116101))),f312(f114(a1),x116102)))),
% 173.53/173.47 inference(rename_variables,[],[3680])).
% 173.53/173.47 cnf(11613,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x116131),x116132),f189(f860(x116131,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11623,plain,
% 173.53/173.47 (~P22(f312(f312(f314(a852),f2(a852)),f312(f280(a852),x116231)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4430,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,4404,10332,10423,2804,2809,2821,2824,2825,2826,2830,2831,2840,2848,2852,2854,2861,2863,2864,2871,2872,2874,2888,2889,2891,2895,2897,2950,2956,2958,2963,2984,3098,4380,3245,3930,3136,11493,3661,3038,3722,11253,3106,3067,10172,3061,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,10329,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,3568,4266,4267,4417,3510,3714,4105,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,11484,3187,3284,4472,10146,10149,10175,10627,10640,10761,11184,11246,4488,11360,11393,11430,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3244,3947,3850,10697,3901,3569,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,10748,11402,3280,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,3361,10501,10756,10800,11083,11155,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,3266,10528,10558,3305,3297,3718,3658,10215,11487,4481,10166,10522,10525,10970,10988,11446,11453,3224,10705,10776,3680,4028,4480,3726,4459,4462,3180,3181,4461,4464,3519,11480,4495,10137,10140,10394,10443,10448,10850,11315,4500,11049,11160,3913,3807,11191,11540,11544,3647,10816,10822,3506,3649,10903,11058,11088,3578,3478,10493,10496,10561,10735,4498,4499,10619,10714,11037,11181,4089,3989,3679,4496,10188,10191,10516,10519,11357,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048])).
% 173.53/173.47 cnf(11625,plain,
% 173.53/173.47 (~P22(f312(f312(f314(a852),x116251),f312(f279(a852),f2(a852))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4430,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,4404,10332,10423,2804,2809,2821,2824,2825,2826,2830,2831,2840,2848,2852,2854,2861,2863,2864,2871,2872,2874,2888,2889,2891,2895,2897,2950,2956,2958,2963,2984,3098,4380,3245,3930,3136,11493,3661,3038,3722,11253,3106,3067,10172,3061,3046,3262,3135,3155,10376,3309,4492,3838,4420,10169,10329,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,3568,4266,4267,4417,3510,3714,4105,3272,10253,10369,10440,10484,10487,10534,10616,10865,3653,11484,3187,3284,4472,10146,10149,10175,10627,10640,10761,11184,11246,4488,11360,11393,11430,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3244,3947,3850,10697,3901,3569,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,3203,10603,10646,10649,10682,10708,10745,10783,3204,10345,10546,10622,10748,11402,3280,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,3361,10501,10756,10800,11083,11155,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,3266,10528,10558,3305,3297,3718,3658,10215,11487,4481,10166,10522,10525,10970,10988,11446,11453,3224,10705,10776,3680,4028,4480,3726,4459,4462,3180,3181,4461,4464,3519,11480,4495,10137,10140,10394,10443,10448,10850,11315,4500,11049,11160,3913,3807,11191,11540,11544,3647,10816,10822,3506,3649,10903,11058,11088,3578,3478,10493,10496,10561,10735,4498,4499,10619,10714,11037,11181,4089,3989,3679,4496,10188,10191,10516,10519,11357,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048,6049])).
% 173.53/173.47 cnf(11632,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x116321),x116321))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11633,plain,
% 173.53/173.47 (E(f37(x116331,x116332,x116333,x116334,x116335,x116336,x116337,x116338,x116339,a23),x116332)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11636,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x116361),x116361))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11649,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x116491),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11652,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x116521),x116521))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11657,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x116571),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11662,plain,
% 173.53/173.47 (P22(f312(f235(f860(x116621,a845)),x116622))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(11667,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x116671))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(11668,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x116681)),x116681))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11671,plain,
% 173.53/173.47 (~P22(f312(f71(x116711,x116712,f189(f860(x116711,a845))),x116713))),
% 173.53/173.47 inference(rename_variables,[],[4495])).
% 173.53/173.47 cnf(11693,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x116931),x116931))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11696,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x116961),x116961))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11699,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x116991),x116991))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11702,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x117021),x117021))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11705,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x117051)),x117051))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11708,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x117081)),x117081))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11711,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x117111)),x117111))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11714,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x117141)),x117141))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(11732,plain,
% 173.53/173.47 (E(f312(f190(f853(x117321)),f312(f164(x117321),x117322)),f312(f190(f853(x117321)),x117322))),
% 173.53/173.47 inference(rename_variables,[],[3216])).
% 173.53/173.47 cnf(11735,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x117351),x117351))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11741,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x117411),x117411))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(11742,plain,
% 173.53/173.47 (~E(f312(a126,x117421),x117421)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11745,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x117451),x117451))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11756,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x117561),x117561))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11759,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(f859(f853(x117591),f853(x117591)),a845)),f154(x117591,x117592)),f287(f853(x117591),f153(x117591,x117592))))),
% 173.53/173.47 inference(rename_variables,[],[3906])).
% 173.53/173.47 cnf(11766,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x117661),f312(a126,x117661)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(11769,plain,
% 173.53/173.47 (P22(f312(f312(f314(f860(x117691,a845)),x117692),f312(f288(x117691),x117692)))),
% 173.53/173.47 inference(rename_variables,[],[3569])).
% 173.53/173.47 cnf(11770,plain,
% 173.53/173.47 (~E(f312(a126,x117701),x117701)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11777,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x117771),x117771))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11782,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x117821),x117821))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11789,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x117891),x117891))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11790,plain,
% 173.53/173.47 (~E(f312(a126,x117901),x117901)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11795,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x117951,a845)),x117952),f312(f312(f289(x117951),x117953),x117952)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(11798,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x117981),x117981))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11809,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x118091),x118091))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11810,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x118101),f312(a126,x118101)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(11813,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x118131),x118131))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(11816,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x118161),x118161))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(11819,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x118191),x118191))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(11822,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x118221),x118221))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(11825,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x118251),x118251))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11828,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x118281),x118281))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11837,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x118371),x118371))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11838,plain,
% 173.53/173.47 (~E(f312(a126,x118381),x118381)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11843,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x118431),x118431))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11858,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x118581),x118581))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11863,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x118631),x118631))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(11868,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x118681))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(11887,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x118871),f312(a126,x118871)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(11890,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x118901),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11893,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x118931),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11896,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x118961),x118962),f189(f860(x118961,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11899,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x118991),x118992),f189(f860(x118991,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11902,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119021),x119021))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11905,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119051),x119051))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11908,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119081),x119081))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11911,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119111),x119111))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11918,plain,
% 173.53/173.47 (P22(f312(f312(f314(f860(x119181,a845)),x119182),f312(f288(x119181),x119182)))),
% 173.53/173.47 inference(rename_variables,[],[3569])).
% 173.53/173.47 cnf(11930,plain,
% 173.53/173.47 (~P22(f312(f312(f314(a852),f312(a126,f312(f138(a852,a852,f89(a852),f2(a852)),x119301))),f312(f168(a852),f312(f132(a852,x119302),x119301))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,3766,4430,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,4404,10332,10423,3415,2804,2809,2821,2824,2825,2826,2830,2831,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2888,2889,2891,2895,2897,2950,2956,2958,2959,2963,2984,3098,4380,3245,3930,3136,11493,3145,3257,3661,3971,3038,3722,11253,3106,3067,10172,3061,3046,3216,3262,3135,3155,10376,3309,4492,3838,4420,10169,10329,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,3568,4266,4267,4417,3510,3714,4105,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,3653,11484,3187,3284,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,4488,11360,11393,11430,11464,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3244,3947,3906,3850,10697,3901,3569,11769,3907,3585,10884,10953,11034,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,3280,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,3361,10501,10756,10800,11083,11155,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,3266,10528,10558,11112,3305,3297,3718,3658,10215,11487,11515,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,3224,10705,10776,11516,11667,3680,4028,4480,3689,3726,4459,4462,3180,3181,4461,4464,3697,3519,11480,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,3913,3807,11191,11540,11544,3647,10816,10822,10839,3506,3649,10903,11058,11088,3578,3478,10493,10496,10561,10735,4498,11481,4499,10619,10714,11037,11181,4089,3989,3679,4496,10188,10191,10516,10519,11357,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048,6049,6050,6051,6086,6102,6140,6157,6193,6194,6196,6216,6217,6219,6222,6223,6233,6242,6260,6279,6280,6286,6296,6306,6330,6335,6337,6351,6352,6355,6356,6358,6360,6361,6362,6364,6366,6369,6375,6376,6377,6378,6384,6386,6391,6426,6429,6442,6445,6446,6447,6448,6482,6487,6489,6494,6495,6503,6507,6520,6544,6545,6546,6547,6559,6563,6576,6583,6587,6589,6638,6639,6640,6645,6648,6679,6681,6683,6685,6688,6693,6706,6715,6748,6751,6752,6765,6766,6767,6768,6784,6785,6801,6822,6823,6829,6850,6863,6865,6866,6868,6870,6871,6878,6896,6910,6911,6916,6917,6918,6919,6921,6923,6956,6957,6969,6976,6978,6979,6980,7009,7018])).
% 173.53/173.47 cnf(11931,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x119311,a845)),f312(f168(x119311),f312(f132(x119311,x119312),x119313))),f312(f168(x119311),x119313)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(11936,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x119361),x119362),f189(f860(x119361,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11941,plain,
% 173.53/173.47 (E(f312(f190(f853(x119411)),f312(f164(x119411),x119412)),f312(f190(f853(x119411)),x119412))),
% 173.53/173.47 inference(rename_variables,[],[3216])).
% 173.53/173.47 cnf(11948,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x119481),f312(a126,x119481)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(11951,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x119511,a845)),x119512),f235(f860(x119511,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(11952,plain,
% 173.53/173.47 (~E(f312(a126,x119521),x119521)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11955,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x119551,a845)),f312(f168(x119551),f312(f132(x119551,x119552),x119553))),f312(f168(x119551),x119553)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(11967,plain,
% 173.53/173.47 (E(f37(x119671,x119672,x119673,x119674,x119675,x119676,x119677,x119678,x119679,a23),x119672)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(11970,plain,
% 173.53/173.47 (~E(f312(a126,x119701),x119701)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(11974,plain,
% 173.53/173.47 (P22(f312(f70(x119741),f189(f860(x119741,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(11975,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x119751),x119752),f189(f860(x119751,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(11980,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119801),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(11981,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x119811),x119811))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(11986,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x119861,a845)),f312(f168(x119861),f166(x119861,x119862,x119863))),f312(f168(x119861),x119863)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(11989,plain,
% 173.53/173.47 (P19(x119891,x119891,f5(x119891),x119892)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(11994,plain,
% 173.53/173.47 (P22(f312(f312(f314(f860(x119941,a845)),x119942),f312(f288(x119941),x119942)))),
% 173.53/173.47 inference(rename_variables,[],[3569])).
% 173.53/173.47 cnf(12005,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x120051),x120051))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(12008,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x120081),x120082),f189(f860(x120081,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12011,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x120111,a845)),x120112),f312(f312(f289(x120111),x120113),x120112)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(12012,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x120121,a845)),x120122),f235(f860(x120121,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12019,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x120191),f312(a126,x120191)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12022,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x120221),f312(a126,x120221)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12025,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x120251),x120251))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12028,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x120281),x120281))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12031,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x120311),x120311))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12034,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x120341),x120341))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12037,plain,
% 173.53/173.47 (~E(f312(a126,x120371),x120371)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12044,plain,
% 173.53/173.47 (P22(f312(f312(f314(f860(x120441,a845)),x120442),f312(f288(x120441),x120442)))),
% 173.53/173.47 inference(rename_variables,[],[3569])).
% 173.53/173.47 cnf(12053,plain,
% 173.53/173.47 (~E(f312(a126,x120531),x120531)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12054,plain,
% 173.53/173.47 (E(f312(f290(x120541,x120541,f5(x120541)),x120542),x120542)),
% 173.53/173.47 inference(rename_variables,[],[3262])).
% 173.53/173.47 cnf(12057,plain,
% 173.53/173.47 (P37(x120571,x120572,f127(x120571),f127(x120571))),
% 173.53/173.47 inference(rename_variables,[],[3453])).
% 173.53/173.47 cnf(12060,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x120601,a845)),f312(f168(x120601),f166(x120601,x120602,x120603))),f312(f168(x120601),x120603)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(12061,plain,
% 173.53/173.47 (P22(f312(f70(x120611),f312(f168(x120611),x120612)))),
% 173.53/173.47 inference(rename_variables,[],[3244])).
% 173.53/173.47 cnf(12068,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x120681),x120681))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12071,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x120711),x120711))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12076,plain,
% 173.53/173.47 (E(f312(f190(f853(x120761)),f312(f164(x120761),x120762)),f312(f190(f853(x120761)),x120762))),
% 173.53/173.47 inference(rename_variables,[],[3216])).
% 173.53/173.47 cnf(12079,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x120791,f860(x120792,a845))),x120793),x120794))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(12086,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x120861,f860(x120862,a845))),x120863),x120864))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(12089,plain,
% 173.53/173.47 (P33(a852,f312(f165(a852),f312(f312(f150(f853(x120891),a852),f190(f853(x120891))),f175(x120891,x120892))))),
% 173.53/173.47 inference(rename_variables,[],[3760])).
% 173.53/173.47 cnf(12092,plain,
% 173.53/173.47 (P19(x120921,x120921,f5(x120921),x120922)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12095,plain,
% 173.53/173.47 (P22(f312(f312(f314(f853(x120951)),f127(x120951)),f157(x120951,x120952)))),
% 173.53/173.47 inference(rename_variables,[],[3408])).
% 173.53/173.47 cnf(12100,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x121001),x121001))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12101,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x121011))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(12104,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(f859(f853(x121041),f853(x121041)),a845)),f154(x121041,x121042)),f287(f853(x121041),f153(x121041,x121042))))),
% 173.53/173.47 inference(rename_variables,[],[3906])).
% 173.53/173.47 cnf(12110,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121101,a845)),f189(f860(x121101,a845))),x121102))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(12113,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121131,a845)),f312(f290(x121132,x121131,x121133),f312(f291(x121132,x121131,x121133),x121134))),x121134))),
% 173.53/173.47 inference(rename_variables,[],[4089])).
% 173.53/173.47 cnf(12116,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121161,a845)),f312(f168(x121161),f166(x121161,x121162,x121163))),f312(f168(x121161),x121163)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(12117,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121171,a845)),f312(f168(x121171),f312(f132(x121171,x121172),x121173))),f312(f168(x121171),x121173)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(12120,plain,
% 173.53/173.47 (P19(x121201,f856(x121201),f219(x121201),x121202)),
% 173.53/173.47 inference(rename_variables,[],[3454])).
% 173.53/173.47 cnf(12125,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121251,a845)),f312(f290(x121252,x121251,x121253),f312(f291(x121252,x121251,x121253),x121254))),x121254))),
% 173.53/173.47 inference(rename_variables,[],[4089])).
% 173.53/173.47 cnf(12128,plain,
% 173.53/173.47 (P22(f312(f70(f856(x121281)),f312(f290(x121282,f856(x121281),f312(f173(x121282,x121281),x121283)),f235(f860(x121282,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3913])).
% 173.53/173.47 cnf(12133,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x121331,f860(x121332,a845))),x121333),x121334))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(12136,plain,
% 173.53/173.47 (P22(f312(f312(f314(f853(x121361)),f127(x121361)),f157(x121361,x121362)))),
% 173.53/173.47 inference(rename_variables,[],[3408])).
% 173.53/173.47 cnf(12139,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x121391),f853(x121391))),f312(f312(f239(f853(x121391),f853(x121391)),x121392),f127(x121391))),f141(x121391,x121393)))),
% 173.53/173.47 inference(rename_variables,[],[4501])).
% 173.53/173.47 cnf(12142,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x121421),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12144,plain,
% 173.53/173.47 (~P22(f312(f70(x121441),f235(f860(x121441,a845))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,10943,11989,3453,3454,3766,3173,4430,3076,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,4404,10332,10423,3415,2804,2809,2821,2824,2825,2826,2830,2831,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2888,2889,2891,2892,2895,2897,2941,2950,2956,2958,2959,2963,2984,3098,4380,3245,3930,3136,11493,3145,3257,3661,3971,3038,3722,11253,3106,3067,10172,3061,3046,3051,3082,3216,11732,11941,3262,10700,3135,3155,10376,3309,4492,3838,4420,10169,10329,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,3840,10881,11010,11061,4501,10803,11015,11120,11139,11169,11175,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,12095,12136,3568,4266,4267,4417,3510,3714,4105,3760,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,3653,11484,3187,3284,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,4488,11360,11393,11430,11464,3640,3416,3790,3230,3232,3205,4469,4414,3400,4489,3978,11134,3528,3244,11607,3947,3906,11759,12104,3850,10697,11931,11955,3901,10887,11986,12060,3569,11769,11918,11994,12044,3907,3585,10884,10953,11034,11094,11951,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,3280,11974,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,3361,10501,10756,10800,11083,11155,11321,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,3266,10528,10558,11112,3305,3297,3718,3658,10215,11487,11515,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,3224,10705,10776,11516,11667,11868,3680,4028,4480,3689,3726,4459,4462,3180,3181,4461,4464,3697,3519,11480,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,3913,3807,11191,11540,11544,3647,10816,10822,10839,11795,3506,11052,3649,10903,11058,11088,11099,3578,3478,10493,10496,10561,10735,4498,11481,4499,10619,10714,11037,11181,11318,12079,12086,4089,10688,12113,3989,3679,4496,10188,10191,10516,10519,11357,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,95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% 173.53/173.47 cnf(12145,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121451,a845)),x121452),x121452))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12148,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x121481),x121482),f189(f860(x121481,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12151,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121511,a845)),f312(f290(x121512,x121511,x121513),f312(f291(x121512,x121511,x121513),x121514))),x121514))),
% 173.53/173.47 inference(rename_variables,[],[4089])).
% 173.53/173.47 cnf(12152,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121521,a845)),x121522),x121522))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12157,plain,
% 173.53/173.47 (E(f37(x121571,x121572,x121573,x121574,x121575,x121576,x121577,x121578,x121579,a23),x121572)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12160,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x121601,a845)),f312(f168(x121601),f166(x121601,x121602,x121603))),f312(f168(x121601),x121603)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(12161,plain,
% 173.53/173.47 (P22(f312(f70(x121611),f312(f168(x121611),x121612)))),
% 173.53/173.47 inference(rename_variables,[],[3244])).
% 173.53/173.47 cnf(12164,plain,
% 173.53/173.47 (P22(f312(f312(f195(a23),x121641),x121641))),
% 173.53/173.47 inference(rename_variables,[],[3202])).
% 173.53/173.47 cnf(12167,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x121671),x121671))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12170,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x121701),x121701))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12181,plain,
% 173.53/173.47 (P19(x121811,x121811,f5(x121811),x121812)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12188,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x121881),x121882),f189(f860(x121881,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12191,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x121911,x121911)),f312(f312(f239(x121911,x121911),x121912),x121912)),f287(x121911,x121913)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(12194,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x121941),x121942),f189(f860(x121941,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12197,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x121971,x121971)),f312(f312(f239(x121971,x121971),x121972),x121972)),f287(x121971,x121973)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(12207,plain,
% 173.53/173.47 (~E(f312(f312(f147(x122071),x122072),x122073),x122073)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(12210,plain,
% 173.53/173.47 (P22(f312(f312(f314(x122101),x122102),f235(f860(x122101,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(12211,plain,
% 173.53/173.47 (~E(f312(a126,x122111),x122111)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12214,plain,
% 173.53/173.47 (P22(f312(f312(f314(f853(x122141)),f127(x122141)),f157(x122141,x122142)))),
% 173.53/173.47 inference(rename_variables,[],[3408])).
% 173.53/173.47 cnf(12215,plain,
% 173.53/173.47 (~E(f312(f312(f147(x122151),x122152),x122153),f127(x122151))),
% 173.53/173.47 inference(rename_variables,[],[4429])).
% 173.53/173.47 cnf(12218,plain,
% 173.53/173.47 (P22(f312(f312(f314(x122181),f312(x122182,x122183)),f312(f290(x122184,x122181,x122182),f235(f860(x122184,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12219,plain,
% 173.53/173.47 (P19(x122191,x122191,f5(x122191),x122192)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12222,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122221,a845)),f189(f860(x122221,a845))),x122222))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(12223,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122231,a845)),x122232),x122232))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12226,plain,
% 173.53/173.47 (P22(f312(f312(f314(x122261),f312(x122262,x122263)),f312(f290(x122264,x122261,x122262),f235(f860(x122264,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12227,plain,
% 173.53/173.47 (P19(x122271,x122271,f5(x122271),x122272)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12230,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(f853(x122301),f853(x122301))),f312(f312(f239(f853(x122301),f853(x122301)),f127(x122301)),f127(x122301))),f154(x122301,x122302)))),
% 173.53/173.47 inference(rename_variables,[],[3984])).
% 173.53/173.47 cnf(12233,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x122331),x122331))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12234,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x122341),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12240,plain,
% 173.53/173.47 (P19(x122401,x122401,f5(x122401),x122402)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12243,plain,
% 173.53/173.47 (E(f312(f312(f129(x122431),x122432),f127(x122431)),x122432)),
% 173.53/173.47 inference(rename_variables,[],[3136])).
% 173.53/173.47 cnf(12244,plain,
% 173.53/173.47 (~E(f312(f312(f147(x122441),x122442),x122443),x122443)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(12247,plain,
% 173.53/173.47 (E(f312(f312(f129(x122471),x122472),f127(x122471)),x122472)),
% 173.53/173.47 inference(rename_variables,[],[3136])).
% 173.53/173.47 cnf(12248,plain,
% 173.53/173.47 (~E(f312(f312(f147(x122481),x122482),x122483),x122483)),
% 173.53/173.47 inference(rename_variables,[],[4420])).
% 173.53/173.47 cnf(12251,plain,
% 173.53/173.47 (E(f312(f312(f129(x122511),x122512),f127(x122511)),x122512)),
% 173.53/173.47 inference(rename_variables,[],[3136])).
% 173.53/173.47 cnf(12258,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122581,a845)),x122582),f235(f860(x122581,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12262,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x122621),x122621))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12263,plain,
% 173.53/173.47 (~E(f312(a126,x122631),x122631)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12266,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122661,a845)),f189(f860(x122661,a845))),x122662))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(12269,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x122691),x122691))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12272,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122721,a845)),x122722),x122722))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12277,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122771,a845)),x122772),f312(f312(f289(x122771),x122773),x122772)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(12280,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x122801,a845)),x122802),x122802))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12281,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x122811),x122812),f189(f860(x122811,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12284,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x122841),x122842),f189(f860(x122841,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12289,plain,
% 173.53/173.47 (P19(x122891,x122891,f5(x122891),x122892)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12292,plain,
% 173.53/173.47 (E(f312(f190(f853(x122921)),f312(f164(x122921),x122922)),f312(f190(f853(x122921)),x122922))),
% 173.53/173.47 inference(rename_variables,[],[3216])).
% 173.53/173.47 cnf(12295,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x122951),x122951))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12296,plain,
% 173.53/173.47 (P22(f312(f235(f860(x122961,a845)),x122962))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(12299,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x122991),x122992),f189(f860(x122991,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12302,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123021,a845)),x123022),f312(f312(f289(x123021),x123023),x123022)))),
% 173.53/173.47 inference(rename_variables,[],[3647])).
% 173.53/173.47 cnf(12305,plain,
% 173.53/173.47 (P22(f312(f312(f314(x123051),f312(x123052,x123053)),f312(f290(x123054,x123051,x123052),f235(f860(x123054,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12306,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x123061,x123061)),f312(f312(f239(x123061,x123061),x123062),x123062)),f287(x123061,x123063)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(12309,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x123091,x123091)),f312(f312(f239(x123091,x123091),x123092),x123092)),f287(x123091,x123093)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(12312,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x123121),x123121))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12313,plain,
% 173.53/173.47 (P22(f312(f235(f860(x123131,a845)),x123132))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(12316,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123161,a845)),f189(f860(x123161,a845))),x123162))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(12319,plain,
% 173.53/173.47 (P22(f312(f70(x123191),f312(f168(x123191),x123192)))),
% 173.53/173.47 inference(rename_variables,[],[3244])).
% 173.53/173.47 cnf(12329,plain,
% 173.53/173.47 (~P22(f312(f312(f189(f860(x123291,f860(x123292,a845))),x123293),x123294))),
% 173.53/173.47 inference(rename_variables,[],[4499])).
% 173.53/173.47 cnf(12332,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123321,a845)),x123322),f235(f860(x123321,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12335,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(x123351,x123351)),f312(f312(f239(x123351,x123351),x123352),x123352)),f287(x123351,x123353)))),
% 173.53/173.47 inference(rename_variables,[],[3840])).
% 173.53/173.47 cnf(12338,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),f312(f312(f89(a852),x123381),x123382)),x123382))),
% 173.53/173.47 inference(rename_variables,[],[4496])).
% 173.53/173.47 cnf(12339,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x123391),f312(a126,x123391)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12342,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123421,a845)),f312(f168(x123421),f312(f132(x123421,x123422),x123423))),f312(f168(x123421),x123423)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(12345,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123451,a845)),x123452),f235(f860(x123451,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12348,plain,
% 173.53/173.47 (E(f37(x123481,x123482,x123483,x123484,x123485,x123486,x123487,x123488,x123489,a23),x123482)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12355,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(f859(f853(x123551),f853(x123551)),f859(f853(x123551),f853(x123551)))),f420(f287(f859(f853(x123551),f853(x123551)),x123552),f141(x123551,x123553),f859(f853(x123551),f853(x123551)))),f287(f859(f853(x123551),f853(x123551)),x123552)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,10943,11989,12092,12181,12219,12227,12240,3453,3454,3766,3173,4430,3076,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,11967,12157,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,12053,12211,4404,10332,10423,3261,3415,2804,2809,2821,2824,2825,2826,2830,2831,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2885,2888,2889,2891,2892,2895,2897,2941,2950,2956,2958,2959,2963,2984,3098,4380,3543,3245,3930,3136,11493,12243,12247,12251,3145,3257,3661,3971,3038,4400,3722,11253,3106,3067,10172,3061,3046,3051,3082,3216,11732,11941,12076,3262,10700,12054,3134,3135,3155,10376,3309,4492,3838,4420,10169,10329,11308,12207,12244,4429,12215,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,12230,3840,10881,11010,11061,12191,12197,12306,12309,12335,4501,10803,11015,11120,11139,11169,11175,12139,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,12095,12136,12214,3568,4266,4267,4417,11234,3510,3714,4105,3760,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,12022,3653,11484,3187,3284,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,12142,4488,11360,11393,11430,11464,3640,3416,3790,3230,3232,3205,4469,4414,3594,4120,3400,4489,3978,11134,3528,3244,11607,12061,12161,3947,3906,11759,12104,3850,10697,11931,11955,12117,3901,10887,11986,12060,12116,12160,3569,11769,11918,11994,12044,3907,3585,10884,10953,11034,11094,11951,12012,12258,12332,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,12005,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,12100,12269,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,3280,11974,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,12071,12167,12170,12233,12262,3361,10501,10756,10800,11083,11155,11321,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,12008,12148,12188,12194,12281,12284,3266,10528,10558,11112,11662,12296,3305,3297,3718,3658,10215,11487,11515,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,3224,10705,10776,11516,11667,11868,3680,4028,4480,3689,3726,4459,4462,3180,3181,4461,4464,3697,3519,11480,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,11194,3913,3807,11191,11540,11544,11604,12218,12226,3647,10816,10822,10839,11795,12011,12277,3506,11052,12145,12152,12223,12272,3982,3649,10903,11058,11088,11099,12110,12222,12266,3578,3478,10493,10496,10561,10735,4498,11481,4499,10619,10714,11037,11181,11318,12079,12086,12133,4089,10688,12113,12125,3989,3679,4496,10188,10191,10516,10519,11357,11541,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,842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% 173.53/173.47 cnf(12359,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x123591),x123592),f189(f860(x123591,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12360,plain,
% 173.53/173.47 (P22(f312(f312(f314(f859(f853(x123601),f853(x123601))),f312(f312(f239(f853(x123601),f853(x123601)),f127(x123601)),f127(x123601))),f154(x123601,x123602)))),
% 173.53/173.47 inference(rename_variables,[],[3984])).
% 173.53/173.47 cnf(12365,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x123651),x123652),f189(f860(x123651,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12368,plain,
% 173.53/173.47 (E(f312(f190(f853(x123681)),f312(f164(x123681),x123682)),f312(f190(f853(x123681)),x123682))),
% 173.53/173.47 inference(rename_variables,[],[3216])).
% 173.53/173.47 cnf(12371,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x123711),x123712),f189(f860(x123711,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12378,plain,
% 173.53/173.47 (~P22(f312(f312(f314(f859(f853(x123781),f853(x123781))),f312(f312(f239(f853(x123781),f853(x123781)),x123782),x123782)),f143(x123781,f149(x123781,f127(f860(x123781,a852))))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,10943,11989,12092,12181,12219,12227,12240,3453,3454,3766,3173,4430,3076,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,11967,12157,4359,11219,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,12053,12211,4404,10332,10423,3261,3415,2804,2809,2821,2824,2825,2826,2830,2831,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2885,2888,2889,2891,2892,2895,2897,2941,2950,2956,2958,2959,2963,2984,3098,4380,3543,3245,3930,3136,11493,12243,12247,12251,3145,3257,3661,3971,3038,4400,3722,11253,3106,3067,10172,3061,3046,3051,3082,3216,11732,11941,12076,12292,3262,10700,12054,3134,3135,3155,10376,3309,4492,3838,4420,10169,10329,11308,12207,12244,4429,12215,3192,11588,4482,10875,10948,11163,11166,3310,3101,3102,10234,10531,3367,3016,3120,11243,3984,12230,12360,3840,10881,11010,11061,12191,12197,12306,12309,12335,4501,10803,11015,11120,11139,11169,11175,12139,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,12095,12136,12214,3568,4266,4267,4417,11234,3510,3714,4105,3760,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,12022,3653,11484,3187,3284,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,12142,4488,11360,11393,11430,11464,3640,3416,3790,3230,3232,3205,4469,4414,3594,4120,3400,4489,3978,11134,3528,3244,11607,12061,12161,3947,3906,11759,12104,3850,10697,11931,11955,12117,3901,10887,11986,12060,12116,12160,3569,11769,11918,11994,12044,3907,3585,10884,10953,11034,11094,11951,12012,12258,12332,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,12005,12164,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,12100,12269,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,3280,11974,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,12071,12167,12170,12233,12262,12295,3361,10501,10756,10800,11083,11155,11321,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,12008,12148,12188,12194,12281,12284,12299,12359,12365,3266,10528,10558,11112,11662,12296,3305,3297,3718,3658,10215,11487,11515,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,3224,10705,10776,11516,11667,11868,3680,4028,4480,3689,3726,4459,4462,3180,3181,4461,4464,3697,3519,11480,4125,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,11194,3913,3807,11191,11540,11544,11604,12218,12226,3647,10816,10822,10839,11795,12011,12277,3506,11052,12145,12152,12223,12272,3982,3649,10903,11058,11088,11099,12110,12222,12266,3578,3478,10493,10496,10561,10735,4498,11481,4499,10619,10714,11037,11181,11318,12079,12086,12133,4089,10688,12113,12125,3989,3679,4496,10188,10191,10516,10519,11357,11541,4497,11461,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048,6049,6050,6051,6086,6102,6140,6157,6193,6194,6196,6216,6217,6219,6222,6223,6233,6242,6260,6279,6280,6286,6296,6306,6330,6335,6337,6351,6352,6355,6356,6358,6360,6361,6362,6364,6366,6369,6375,6376,6377,6378,6384,6386,6391,6426,6429,6442,6445,6446,6447,6448,6482,6487,6489,6494,6495,6503,6507,6520,6544,6545,6546,6547,6559,6563,6576,6583,6587,6589,6638,6639,6640,6645,6648,6679,6681,6683,6685,6688,6693,6706,6715,6748,6751,6752,6765,6766,6767,6768,6784,6785,6801,6822,6823,6829,6850,6863,6865,6866,6868,6870,6871,6878,6896,6910,6911,6916,6917,6918,6919,6921,6923,6956,6957,6969,6976,6978,6979,6980,7009,7018,7029,7038,7051,7052,7057,7059,7060,7066,7075,7089,7123,7125,7140,7148,7189,7194,7219,7264,7298,7311,7327,7358,7359,7362,7363,7387,7410,7427,7430,7431,7441,7460,7461,7463,7465,7467,7469,7516,7520,7521,7552,7554,7555,7556,7561,7583,7602,7612,7621,7633,7634,7636,7656,7665,7666,7689,7708,7756,7757,7799,7808,7830,7847,7848,7911,7912,7913,7938,7971,7978,7980,7988,7997,8001,8036,8042,8049,8063,8086,8109,8153,8183,8195,8213,8216,8251,8271,8338,8339,8344,8346,8364,8452,8453,8454,8455,8486,8513,8538,8580,8598,8655,8698,8701,8714,8721,8757,8778,8802,8803,8820,8821,8967,8986,8996,9020,9022,9025,9029,9032,9033,9064,9070,9082,9131,9151,9170,9205,9206,9212,9248,9271,9276,9312,9319,9323,9326,9327,9342,9356,9365,9376,9389,9390,9394,9396,9420,9538,9581,9625,9669,9785,9786])).
% 173.53/173.47 cnf(12380,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x123801),x123801))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12383,plain,
% 173.53/173.47 (P22(f312(f312(f314(x123831),x123832),f235(f860(x123831,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(12390,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x123901,a845)),x123902),x123902))),
% 173.53/173.47 inference(rename_variables,[],[3506])).
% 173.53/173.47 cnf(12393,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x123931),x123932),f189(f860(x123931,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12396,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x123961)),x123962)))),
% 173.53/173.47 inference(rename_variables,[],[3679])).
% 173.53/173.47 cnf(12399,plain,
% 173.53/173.47 (E(f37(x123991,x123992,x123993,x123994,x123995,x123996,x123997,x123998,x123999,a23),x123992)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12401,plain,
% 173.53/173.47 (E(f37(x124011,x124012,x124013,x124014,x124015,x124016,x124017,x124018,x124019,a23),x124012)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12405,plain,
% 173.53/173.47 (E(f37(x124051,x124052,x124053,x124054,x124055,x124056,x124057,x124058,x124059,a23),x124052)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12407,plain,
% 173.53/173.47 (E(f37(x124071,x124072,x124073,x124074,x124075,x124076,x124077,x124078,x124079,a23),x124072)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12412,plain,
% 173.53/173.47 (P41(x124121,f149(x124121,x124122))),
% 173.53/173.47 inference(rename_variables,[],[3076])).
% 173.53/173.47 cnf(12421,plain,
% 173.53/173.47 (P19(x124211,x124211,f5(x124211),x124212)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12422,plain,
% 173.53/173.47 (E(f37(x124221,x124222,x124223,x124224,x124225,x124226,x124227,x124228,x124229,a23),x124222)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12424,plain,
% 173.53/173.47 (P19(x124241,x124241,f5(x124241),x124242)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12430,plain,
% 173.53/173.47 (E(f37(x124301,x124302,x124303,x124304,x124305,x124306,x124307,x124308,x124309,a23),x124302)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12432,plain,
% 173.53/173.47 (E(f37(x124321,x124322,x124323,x124324,x124325,x124326,x124327,x124328,x124329,a23),x124322)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12434,plain,
% 173.53/173.47 (E(f37(x124341,x124342,x124343,x124344,x124345,x124346,x124347,x124348,x124349,a23),x124342)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12436,plain,
% 173.53/173.47 (P34(x124361,f2(a852),f312(f312(f312(f100(x124361),x124362),f312(a27,x124363)),x124364))),
% 173.53/173.47 inference(rename_variables,[],[3576])).
% 173.53/173.47 cnf(12444,plain,
% 173.53/173.47 (E(f37(x124441,x124442,x124443,x124444,x124445,x124446,x124447,x124448,x124449,a23),x124442)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12446,plain,
% 173.53/173.47 (P55(x124461,f189(f860(x124461,a845)),x124462)),
% 173.53/173.47 inference(rename_variables,[],[3222])).
% 173.53/173.47 cnf(12450,plain,
% 173.53/173.47 (P50(x124501,x124502,f237(x124501,x124502))),
% 173.53/173.47 inference(rename_variables,[],[3172])).
% 173.53/173.47 cnf(12452,plain,
% 173.53/173.47 (P50(x124521,x124522,f237(x124521,x124522))),
% 173.53/173.47 inference(rename_variables,[],[3172])).
% 173.53/173.47 cnf(12459,plain,
% 173.53/173.47 (E(f189(f860(f859(x124591,x124591),a845)),f237(x124591,f189(f860(x124591,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3275])).
% 173.53/173.47 cnf(12465,plain,
% 173.53/173.47 (E(f37(x124651,x124652,x124653,x124654,x124655,x124656,x124657,x124658,x124659,a23),x124652)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12467,plain,
% 173.53/173.47 (P36(x124671,x124672,x124673,f180(x124671,x124672,x124674,x124673))),
% 173.53/173.47 inference(rename_variables,[],[3766])).
% 173.53/173.47 cnf(12469,plain,
% 173.53/173.47 (P36(x124691,x124692,x124693,f180(x124691,x124692,x124694,x124693))),
% 173.53/173.47 inference(rename_variables,[],[3766])).
% 173.53/173.47 cnf(12471,plain,
% 173.53/173.47 (P36(x124711,x124712,x124713,f180(x124711,x124712,x124714,x124713))),
% 173.53/173.47 inference(rename_variables,[],[3766])).
% 173.53/173.47 cnf(12473,plain,
% 173.53/173.47 (P36(x124731,x124732,x124733,f180(x124731,x124732,x124734,x124733))),
% 173.53/173.47 inference(rename_variables,[],[3766])).
% 173.53/173.47 cnf(12475,plain,
% 173.53/173.47 (E(f37(x124751,x124752,x124753,x124754,x124755,x124756,x124757,x124758,x124759,a23),x124752)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12477,plain,
% 173.53/173.47 (P18(x124771,x124772,f189(f860(f851(x124771),a845)))),
% 173.53/173.47 inference(rename_variables,[],[3260])).
% 173.53/173.47 cnf(12483,plain,
% 173.53/173.47 (P11(x124831,f860(x124831,a845),f289(x124831))),
% 173.53/173.47 inference(rename_variables,[],[3177])).
% 173.53/173.47 cnf(12488,plain,
% 173.53/173.47 (P37(x124881,x124882,f127(x124881),f127(x124881))),
% 173.53/173.47 inference(rename_variables,[],[3453])).
% 173.53/173.47 cnf(12490,plain,
% 173.53/173.47 (P37(x124901,x124902,f127(x124901),f127(x124901))),
% 173.53/173.47 inference(rename_variables,[],[3453])).
% 173.53/173.47 cnf(12494,plain,
% 173.53/173.47 (P54(x124941,x124941,f237(x124941,x124942))),
% 173.53/173.47 inference(rename_variables,[],[3173])).
% 173.53/173.47 cnf(12502,plain,
% 173.53/173.47 (E(f37(x125021,x125022,x125023,x125024,x125025,x125026,x125027,x125028,x125029,a23),x125022)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12507,plain,
% 173.53/173.47 (P45(x125071,x125072,x125073,x125074,f189(f860(x125071,a845)),x125074)),
% 173.53/173.47 inference(rename_variables,[],[4149])).
% 173.53/173.47 cnf(12510,plain,
% 173.53/173.47 (P45(x125101,x125102,x125103,x125104,f189(f860(x125101,a845)),x125104)),
% 173.53/173.47 inference(rename_variables,[],[4149])).
% 173.53/173.47 cnf(12514,plain,
% 173.53/173.47 (P42(x125141,f192(x125141))),
% 173.53/173.47 inference(rename_variables,[],[3035])).
% 173.53/173.47 cnf(12528,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x125281),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12531,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x125311),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12538,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x125381)),f312(f88(a1),f312(f114(a1),x125382))))),
% 173.53/173.47 inference(rename_variables,[],[4494])).
% 173.53/173.47 cnf(12548,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x125481),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12551,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x125511),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12554,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125541,x125542)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12557,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125571,x125572)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12560,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125601,x125602)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12563,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125631,x125632)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12570,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x125701))),f312(f114(a1),x125702)))),
% 173.53/173.47 inference(rename_variables,[],[3680])).
% 173.53/173.47 cnf(12573,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x125731),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12574,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x125741),x125741))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12581,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x125811),f312(a126,x125811)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12584,plain,
% 173.53/173.47 (P22(f312(f312(f314(x125841),f312(x125842,x125843)),f312(f290(x125844,x125841,x125842),f235(f860(x125844,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12585,plain,
% 173.53/173.47 (~E(f312(a126,x125851),f2(a852))),
% 173.53/173.47 inference(rename_variables,[],[4398])).
% 173.53/173.47 cnf(12590,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x125901),x125901))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12593,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125931,x125932)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12596,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x125961,x125962)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12599,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x125991),x125991))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12612,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x126121),f312(a126,x126121)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12617,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f54(a852,x126171,x126172)),x126171))),
% 173.53/173.47 inference(rename_variables,[],[3658])).
% 173.53/173.47 cnf(12624,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x126241),f312(a126,x126241)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12625,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x126251),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12634,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x126341)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(12635,plain,
% 173.53/173.47 (P22(f312(f235(f860(x126351,a845)),x126352))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(12638,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x126381)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(12639,plain,
% 173.53/173.47 (P22(f312(f235(f860(x126391,a845)),x126392))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(12642,plain,
% 173.53/173.47 (P22(f312(f235(f860(x126421,a845)),x126422))),
% 173.53/173.47 inference(rename_variables,[],[3266])).
% 173.53/173.47 cnf(12653,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x126531),x126532),f189(f860(x126531,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12654,plain,
% 173.53/173.47 (P22(f312(f70(x126541),f189(f860(x126541,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12663,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x126631))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(12666,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x126661),f312(a126,x126661)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12667,plain,
% 173.53/173.47 (~E(f312(a126,x126671),x126671)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12670,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x126701),x126702),f189(f860(x126701,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12673,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x126731),x126732),f189(f860(x126731,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12676,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x126761),x126761))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12683,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x126831),x126831))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12686,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x126861),x126861))),
% 173.53/173.47 inference(rename_variables,[],[4468])).
% 173.53/173.47 cnf(12687,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x126871),f312(a126,x126871)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12690,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x126901),x126901))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12695,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x126951),x126951))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12698,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x126981),x126981))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12701,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x127011),x127011))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12704,plain,
% 173.53/173.47 (E(f312(f312(f21(f860(x127041,a845)),f189(f860(x127041,a845))),x127042),f189(f860(x127041,a845)))),
% 173.53/173.47 inference(rename_variables,[],[3480])).
% 173.53/173.47 cnf(12705,plain,
% 173.53/173.47 (P22(f312(f70(x127051),f189(f860(x127051,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12708,plain,
% 173.53/173.47 (E(f312(f312(f21(f860(x127081,a845)),f189(f860(x127081,a845))),x127082),f189(f860(x127081,a845)))),
% 173.53/173.47 inference(rename_variables,[],[3480])).
% 173.53/173.47 cnf(12709,plain,
% 173.53/173.47 (P22(f312(f70(x127091),f189(f860(x127091,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12712,plain,
% 173.53/173.47 (E(f312(f312(f21(f860(x127121,a845)),f189(f860(x127121,a845))),x127122),f189(f860(x127121,a845)))),
% 173.53/173.47 inference(rename_variables,[],[3480])).
% 173.53/173.47 cnf(12713,plain,
% 173.53/173.47 (P22(f312(f70(x127131),f189(f860(x127131,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12716,plain,
% 173.53/173.47 (E(f312(f312(f21(f860(x127161,a845)),f189(f860(x127161,a845))),x127162),f189(f860(x127161,a845)))),
% 173.53/173.47 inference(rename_variables,[],[3480])).
% 173.53/173.47 cnf(12717,plain,
% 173.53/173.47 (P22(f312(f70(x127171),f189(f860(x127171,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12721,plain,
% 173.53/173.47 (E(f37(x127211,x127212,x127213,x127214,x127215,x127216,x127217,x127218,x127219,a23),x127212)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12726,plain,
% 173.53/173.47 (E(f312(f312(f21(f860(x127261,a845)),f189(f860(x127261,a845))),x127262),f189(f860(x127261,a845)))),
% 173.53/173.47 inference(rename_variables,[],[3480])).
% 173.53/173.47 cnf(12727,plain,
% 173.53/173.47 (P22(f312(f70(x127271),f189(f860(x127271,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12731,plain,
% 173.53/173.47 (P22(f312(f70(x127311),f189(f860(x127311,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3280])).
% 173.53/173.47 cnf(12734,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x127341),x127341))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12740,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x127401),x127401))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12743,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x127431),f312(a126,x127431)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12746,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x127461),x127461))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12749,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x127491),f312(a126,x127491)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12764,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x127641),x127641))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12769,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x127691),x127692),f189(f860(x127691,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12780,plain,
% 173.53/173.47 (P22(f312(f312(f314(x127801),x127802),f235(f860(x127801,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(12786,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x127861,a845)),f312(f168(x127861),f312(f132(x127861,x127862),x127863))),f312(f168(x127861),x127863)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(12792,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x127921),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12793,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x127931),x127931))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12797,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x127971),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12798,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x127981),x127981))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12803,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x128031,a845)),x128032),f235(f860(x128031,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12808,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x128081),x128081))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12815,plain,
% 173.53/173.47 (E(f312(f312(f16(x128151,x128152),x128153),x128154),x128153)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(12818,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x128181,a845)),f312(f168(x128181),f166(x128181,x128182,x128183))),f312(f168(x128181),x128183)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(12822,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x128221),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12823,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x128231),x128231))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12827,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a852),x128271),f2(a852)))),
% 173.53/173.47 inference(rename_variables,[],[4472])).
% 173.53/173.47 cnf(12828,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x128281),x128281))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(12831,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x128311),x128311))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12833,plain,
% 173.53/173.47 (~P22(f312(f312(f227(f860(a852,a845)),f283(a852,f312(a126,x128331),f312(a126,x128331))),f283(a852,x128332,x128331)))),
% 173.53/173.47 inference(scs_inference,[],[4460,3446,10943,11989,12092,12181,12219,12227,12240,12289,12421,3453,12057,12488,12490,3454,12120,3766,10842,12467,12469,12471,3172,12450,12452,3173,12494,4430,4149,12507,12510,3177,12483,3013,3035,12514,3076,12412,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,11967,12157,12348,12399,12401,12405,12407,12422,12430,12432,12434,12444,12465,12475,12502,4359,11219,3508,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,12053,12211,12263,4404,10332,10423,3261,3222,12446,3415,4398,2804,2809,2821,2824,2825,2826,2830,2831,2839,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2885,2888,2889,2891,2892,2895,2897,2903,2907,2915,2926,2937,2941,2950,2955,2956,2957,2958,2959,2960,2963,2984,3098,3075,4380,3543,3185,3245,3930,3157,3530,3781,4371,3136,11493,12243,12247,12251,3145,3257,3661,3971,3038,4400,4418,3722,11253,3260,12477,3106,3067,10172,3576,12436,3061,3873,3583,4345,3046,3025,3051,3082,3216,11732,11941,12076,12292,12368,3262,10700,12054,3134,3135,3155,10376,3309,4492,10304,3838,4420,10169,10329,11308,12207,12244,4429,12215,3192,11588,11591,4482,10875,10948,11163,11166,3310,3529,3275,12459,3101,3102,10234,10531,3367,3092,3016,3120,11243,3984,12230,12360,3840,10881,11010,11061,12191,12197,12306,12309,12335,4501,10803,11015,11120,11139,11169,11175,12139,4502,10917,11018,11123,4503,11021,4504,11075,4505,3119,3408,12095,12136,12214,3568,4266,4267,4417,11234,3510,3546,3714,4105,3480,12704,12708,12712,12716,12726,3760,12089,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,12022,12339,12581,12612,12624,12666,12687,12743,12749,3653,11484,3187,3284,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,12142,12234,12528,12531,12548,12551,12573,12625,12792,12797,12822,4488,11360,11393,11430,11464,12634,12638,3640,3416,3417,12554,12557,12560,12563,12593,3790,3230,3232,3205,4469,3100,4414,3594,4120,3908,3400,4489,3978,11134,3528,3244,11607,12061,12161,12319,3947,3906,11759,12104,3850,10697,11931,11955,12117,12342,3901,10887,11986,12060,12116,12160,3569,11769,11918,11994,12044,3870,3907,3585,10884,10953,11034,11094,11951,12012,12258,12332,12345,4493,10643,11026,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,12005,12164,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,12100,12269,12312,12574,12599,12676,12683,12690,12695,12698,12701,12734,12746,12808,12831,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,11863,12590,12740,12764,12793,12798,12823,3280,11974,12654,12705,12709,12713,12717,12727,12731,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,12071,12167,12170,12233,12262,12295,12380,12686,3361,10501,10756,10800,11083,11155,11321,12210,12383,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,12008,12148,12188,12194,12281,12284,12299,12359,12365,12371,12393,12653,12670,12673,3266,10528,10558,11112,11662,12296,12313,12635,12639,12642,3305,3297,3718,3658,10215,11487,11515,12617,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,3224,10705,10776,11516,11667,11868,12101,3680,11610,12570,4028,3422,4480,3689,3726,4459,4462,4463,3180,3181,4461,4464,3697,3519,11480,4125,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,11194,3913,12128,3807,11191,11540,11544,11604,12218,12226,12305,3647,10816,10822,10839,11795,12011,12277,3506,11052,12145,12152,12223,12272,12280,3982,3649,10903,11058,11088,11099,12110,12222,12266,3578,11600,3478,10493,10496,10561,10735,3477,4498,11481,4494,12538,4499,10619,10714,11037,11181,11318,12079,12086,12133,12329,4089,10688,12113,12125,3989,3679,12396,4496,10188,10191,10516,10519,11357,11541,12338,4497,11461,11554,3651,10490,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048,6049,6050,6051,6086,6102,6140,6157,6193,6194,6196,6216,6217,6219,6222,6223,6233,6242,6260,6279,6280,6286,6296,6306,6330,6335,6337,6351,6352,6355,6356,6358,6360,6361,6362,6364,6366,6369,6375,6376,6377,6378,6384,6386,6391,6426,6429,6442,6445,6446,6447,6448,6482,6487,6489,6494,6495,6503,6507,6520,6544,6545,6546,6547,6559,6563,6576,6583,6587,6589,6638,6639,6640,6645,6648,6679,6681,6683,6685,6688,6693,6706,6715,6748,6751,6752,6765,6766,6767,6768,6784,6785,6801,6822,6823,6829,6850,6863,6865,6866,6868,6870,6871,6878,6896,6910,6911,6916,6917,6918,6919,6921,6923,6956,6957,6969,6976,6978,6979,6980,7009,7018,7029,7038,7051,7052,7057,7059,7060,7066,7075,7089,7123,7125,7140,7148,7189,7194,7219,7264,7298,7311,7327,7358,7359,7362,7363,7387,7410,7427,7430,7431,7441,7460,7461,7463,7465,7467,7469,7516,7520,7521,7552,7554,7555,7556,7561,7583,7602,7612,7621,7633,7634,7636,7656,7665,7666,7689,7708,7756,7757,7799,7808,7830,7847,7848,7911,7912,7913,7938,7971,7978,7980,7988,7997,8001,8036,8042,8049,8063,8086,8109,8153,8183,8195,8213,8216,8251,8271,8338,8339,8344,8346,8364,8452,8453,8454,8455,8486,8513,8538,8580,8598,8655,8698,8701,8714,8721,8757,8778,8802,8803,8820,8821,8967,8986,8996,9020,9022,9025,9029,9032,9033,9064,9070,9082,9131,9151,9170,9205,9206,9212,9248,9271,9276,9312,9319,9323,9326,9327,9342,9356,9365,9376,9389,9390,9394,9396,9420,9538,9581,9625,9669,9785,9786,9845,9915,9989,10004,10009,3,2558,2562,2564,2571,2576,2577,2578,2581,2582,2588,2589,2590,2593,2594,2597,2598,2599,2600,2603,2604,2605,2608,2609,2610,2611,2613,2614,2618,2619,2623,2624,2625,2626,2628,2638,2640,2650,2651,2653,2654,2660,2661,2662,2663,2664,2682,2683,2684,2685,2690,2692,2697,2708,2710,2711,2720,2721,2722,2724,2727,2728,2729,2731,2734,2735,2736,2738,2739,2747,2748,2767,2782,5219,5391,5397,5398,5472,5518,5547,5576,5652,5654,5660,5717,5718,5719,5720,5726,5755,5886,5938,5957,5991,6028,6173,6180,6214,6215,6231,6235,6237,6244,6245,6246,6247,6248,6249,6250,6251,6332,6398,6399,6480,6514,6515,6556,6557,6694,6723,6775,6776,6780,6802,6827,6835,6837,6886,6914,6915,6931,6932,6933,6968,7012,7013,7112,7170,7171,7172,7173,7186,7213,7269,7270,7278,7286,7288,7300,7330,7331,7332,7333,7475,7476,7483,7485,7486,7487,7697,7699,7700,7716,7755,7826,7866,7922,7943,7944,7959,8021,8123,8193,8194,8196,8234,8296,8297,8396,8397])).
% 173.53/173.47 cnf(12834,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x128341),x128341))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12837,plain,
% 173.53/173.47 (~P22(f312(f312(f227(a852),f312(a126,x128371)),x128371))),
% 173.53/173.47 inference(rename_variables,[],[4481])).
% 173.53/173.47 cnf(12843,plain,
% 173.53/173.47 (P22(f312(f312(f314(x128431),f312(x128432,x128433)),f312(f290(x128434,x128431,x128432),f235(f860(x128434,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12844,plain,
% 173.53/173.47 (P19(x128441,x128441,f5(x128441),x128442)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12848,plain,
% 173.53/173.47 (P22(f312(f312(f314(x128481),x128482),f235(f860(x128481,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(12849,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x128491),x128492),f189(f860(x128491,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12853,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x128531,a845)),x128532),f235(f860(x128531,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12854,plain,
% 173.53/173.47 (P19(x128541,x128541,f5(x128541),x128542)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12858,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x128581,a845)),x128582),f235(f860(x128581,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3585])).
% 173.53/173.47 cnf(12859,plain,
% 173.53/173.47 (P19(x128591,x128591,f5(x128591),x128592)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12866,plain,
% 173.53/173.47 (P19(x128661,x128661,f5(x128661),x128662)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12869,plain,
% 173.53/173.47 (~P22(f312(f312(f228(f860(x128691,a845)),x128692),f189(f860(x128691,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4493])).
% 173.53/173.47 cnf(12872,plain,
% 173.53/173.47 (P19(x128721,x128721,f5(x128721),x128722)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12875,plain,
% 173.53/173.47 (P19(x128751,x128751,f5(x128751),x128752)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12886,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x128861,a845)),f189(f860(x128861,a845))),x128862))),
% 173.53/173.47 inference(rename_variables,[],[3649])).
% 173.53/173.47 cnf(12890,plain,
% 173.53/173.47 (E(f37(x128901,x128902,x128903,x128904,x128905,x128906,x128907,x128908,x128909,a23),x128902)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12894,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x128941),x128942),f189(f860(x128941,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12897,plain,
% 173.53/173.47 (~P22(f312(f312(f228(a1),f312(f114(a1),x128971)),f2(a1)))),
% 173.53/173.47 inference(rename_variables,[],[4488])).
% 173.53/173.47 cnf(12898,plain,
% 173.53/173.47 (~E(f312(a126,x128981),x128981)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12902,plain,
% 173.53/173.47 (P22(f312(f312(f314(x129021),f312(x129022,x129023)),f312(f290(x129024,x129021,x129022),f235(f860(x129024,a845)))))),
% 173.53/173.47 inference(rename_variables,[],[3807])).
% 173.53/173.47 cnf(12903,plain,
% 173.53/173.47 (P19(x129031,x129031,f5(x129031),x129032)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(12906,plain,
% 173.53/173.47 (P22(f312(f312(f314(x129061),x129062),f235(f860(x129061,a845))))),
% 173.53/173.47 inference(rename_variables,[],[3361])).
% 173.53/173.47 cnf(12913,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x129131),x129132),f189(f860(x129131,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12916,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x129161),x129162),f189(f860(x129161,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12919,plain,
% 173.53/173.47 (E(f37(x129191,x129192,x129193,x129194,x129195,x129196,x129197,x129198,x129199,a23),x129192)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(12921,plain,
% 173.53/173.47 (~E(f312(a126,x129211),x129211)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12925,plain,
% 173.53/173.47 (E(f312(f312(f16(x129251,x129252),x129253),x129254),x129253)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(12928,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x129281),f312(a126,x129281)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12929,plain,
% 173.53/173.47 (~E(f312(a126,x129291),x129291)),
% 173.53/173.47 inference(rename_variables,[],[4386])).
% 173.53/173.47 cnf(12932,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x129321),f312(a126,f312(f312(f89(a852),x129322),x129321))))),
% 173.53/173.47 inference(rename_variables,[],[3651])).
% 173.53/173.47 cnf(12933,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x129331),f312(a126,x129331)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(12942,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x129421)))),
% 173.53/173.47 inference(rename_variables,[],[3305])).
% 173.53/173.47 cnf(12947,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x129471))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(12948,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x129481),x129481))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(12951,plain,
% 173.53/173.47 (~E(f312(a126,x129511),f2(a852))),
% 173.53/173.47 inference(rename_variables,[],[4398])).
% 173.53/173.47 cnf(12956,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x129561),x129562),f189(f860(x129561,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(12959,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x129591,x129592)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12960,plain,
% 173.53/173.47 (E(f312(f312(f226(a852),f312(a126,x129601)),f312(a126,x129602)),f312(a126,f312(f312(f226(a852),x129601),x129602)))),
% 173.53/173.47 inference(rename_variables,[],[3379])).
% 173.53/173.47 cnf(12963,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x129631,x129632)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12964,plain,
% 173.53/173.47 (E(f312(f312(f225(a852),f312(a126,x129641)),f312(a126,x129642)),f312(a126,f312(f312(f225(a852),x129641),x129642)))),
% 173.53/173.47 inference(rename_variables,[],[3378])).
% 173.53/173.47 cnf(12967,plain,
% 173.53/173.47 (P22(f312(f70(a852),f284(a852,x129671,x129672)))),
% 173.53/173.47 inference(rename_variables,[],[3417])).
% 173.53/173.47 cnf(12975,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x129751,a845)),f312(f168(x129751),f312(f132(x129751,x129752),x129753))),f312(f168(x129751),x129753)))),
% 173.53/173.47 inference(rename_variables,[],[3850])).
% 173.53/173.47 cnf(12976,plain,
% 173.53/173.47 (E(f312(f312(f16(x129761,x129762),x129763),x129764),x129763)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(12979,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x129791,a845)),f312(f168(x129791),f312(f312(f169(x129791),x129792),x129793))),f312(f168(x129791),x129793)))),
% 173.53/173.47 inference(rename_variables,[],[3896])).
% 173.53/173.47 cnf(12980,plain,
% 173.53/173.47 (E(f312(f312(f16(x129801,x129802),x129803),x129804),x129803)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(12984,plain,
% 173.53/173.47 (E(f312(f312(f16(x129841,x129842),x129843),x129844),x129843)),
% 173.53/173.47 inference(rename_variables,[],[3192])).
% 173.53/173.47 cnf(12997,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x129971)))),
% 173.53/173.47 inference(rename_variables,[],[3305])).
% 173.53/173.47 cnf(13000,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x130001),x130002),f189(f860(x130001,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(13003,plain,
% 173.53/173.47 (~P22(f312(f312(f314(x130031),x130032),f189(f860(x130031,a845))))),
% 173.53/173.47 inference(rename_variables,[],[4484])).
% 173.53/173.47 cnf(13004,plain,
% 173.53/173.47 (E(f37(x130041,x130042,x130043,x130044,x130045,x130046,x130047,x130048,x130049,a23),x130042)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13005,plain,
% 173.53/173.47 (P19(x130051,x130051,f5(x130051),x130052)),
% 173.53/173.47 inference(rename_variables,[],[3446])).
% 173.53/173.47 cnf(13009,plain,
% 173.53/173.47 (E(f37(x130091,x130092,x130093,x130094,x130095,x130096,x130097,x130098,x130099,a23),x130092)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13015,plain,
% 173.53/173.47 (E(f37(x130151,x130152,x130153,x130154,x130155,x130156,x130157,x130158,x130159,a23),x130152)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13016,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x130161),x130161))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(13019,plain,
% 173.53/173.47 (E(f37(x130191,x130192,x130193,x130194,x130195,x130196,x130197,x130198,x130199,a23),x130192)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13020,plain,
% 173.53/173.47 (P22(f312(f312(f227(a1),x130201),x130201))),
% 173.53/173.47 inference(rename_variables,[],[3204])).
% 173.53/173.47 cnf(13023,plain,
% 173.53/173.47 (E(f37(x130231,x130232,x130233,x130234,x130235,x130236,x130237,x130238,x130239,a23),x130232)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13027,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x130271),f312(a126,x130271)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(13029,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x130291),x130291))),
% 173.53/173.47 inference(rename_variables,[],[3203])).
% 173.53/173.47 cnf(13030,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x130301))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(13033,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),x130331),f312(a126,x130331)))),
% 173.53/173.47 inference(rename_variables,[],[3272])).
% 173.53/173.47 cnf(13036,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x130361))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(13040,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x130401))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(13041,plain,
% 173.53/173.47 (P22(f312(f312(f228(a852),f2(a852)),f312(a126,x130411)))),
% 173.53/173.47 inference(rename_variables,[],[3284])).
% 173.53/173.47 cnf(13042,plain,
% 173.53/173.47 (E(f37(x130421,x130422,x130423,x130424,x130425,x130426,x130427,x130428,x130429,a23),x130422)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13047,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),f2(a852)),x130471))),
% 173.53/173.47 inference(rename_variables,[],[3224])).
% 173.53/173.47 cnf(13049,plain,
% 173.53/173.47 (E(f37(x130491,x130492,x130493,x130494,x130495,x130496,x130497,x130498,x130499,a23),x130492)),
% 173.53/173.47 inference(rename_variables,[],[4358])).
% 173.53/173.47 cnf(13119,plain,
% 173.53/173.47 (P22(f312(f312(f228(a1),f2(a1)),f312(f84(a1),f87(a1))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3428,3446,10943,11989,12092,12181,12219,12227,12240,12289,12421,12424,12844,12854,12859,12866,12872,12875,12903,13005,3453,12057,12488,12490,3454,12120,3766,10842,12467,12469,12471,12473,3172,12450,12452,3173,12494,4430,4149,12507,12510,3177,12483,3013,3035,12514,3076,12412,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,11967,12157,12348,12399,12401,12405,12407,12422,12430,12432,12434,12444,12465,12475,12502,12721,12890,12919,13004,13009,13015,13019,13023,13042,13049,4359,11219,3508,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,12053,12211,12263,12667,12898,12921,12929,4404,10332,10423,3261,3222,12446,3415,4398,12585,12951,2804,2809,2818,2821,2822,2824,2825,2826,2830,2831,2839,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2885,2888,2889,2891,2892,2895,2897,2903,2907,2915,2923,2926,2933,2937,2938,2941,2945,2950,2955,2956,2957,2958,2959,2960,2963,2984,3098,3075,4380,3543,3185,3245,3930,3157,3530,3781,4371,3136,11493,12243,12247,12251,3145,3257,3661,3971,3037,3038,4400,4418,3722,11253,3260,12477,3106,3067,10172,3576,12436,3061,3873,3083,3583,4345,3046,3025,3051,3082,3216,11732,11941,12076,12292,12368,3262,10700,12054,3134,3135,3155,10376,3309,4492,10304,3838,4420,10169,10329,11308,12207,12244,12248,4429,12215,3192,11588,11591,12815,12925,12976,12980,12984,4482,10875,10948,11163,11166,3188,3310,3529,3300,3275,12459,3101,3102,10234,10531,4466,3367,3092,3016,3144,3120,11243,3984,12230,12360,3840,10881,11010,11061,12191,12197,12306,12309,12335,4501,10803,11015,11120,11139,11169,11175,12139,4502,10917,11018,11123,4503,11021,11072,4504,11075,4505,3119,3408,12095,12136,12214,3568,4266,4267,3391,4417,11234,3510,3546,3714,4105,3480,12704,12708,12712,12716,12726,3760,12089,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,12022,12339,12581,12612,12624,12666,12687,12743,12749,12928,12933,13027,13033,3653,11484,3187,3284,11601,13041,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,12142,12234,12528,12531,12548,12551,12573,12625,12792,12797,12822,12827,4488,11360,11393,11430,11464,12634,12638,12897,3640,3416,3417,12554,12557,12560,12563,12593,12596,12959,12963,12967,3419,3790,3378,12964,3379,12960,3230,3232,3205,4469,3100,4414,3594,4120,3908,3400,4489,3978,11134,3528,3244,11607,12061,12161,12319,3947,3906,11759,12104,3850,10697,11931,11955,12117,12342,12786,12975,3896,12979,3901,10887,11986,12060,12116,12160,12818,3902,3569,11769,11918,11994,12044,3870,3907,3585,10884,10953,11034,11094,11951,12012,12258,12332,12345,12803,12853,12858,4493,10643,11026,12869,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,12005,12164,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,12100,12269,12312,12574,12599,12676,12683,12690,12695,12698,12701,12734,12746,12808,12831,12834,12948,13029,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,11863,12590,12740,12764,12793,12798,12823,12828,13016,13020,3280,11974,12654,12705,12709,12713,12717,12727,12731,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,12071,12167,12170,12233,12262,12295,12380,12686,3361,10501,10756,10800,11083,11155,11321,12210,12383,12780,12848,12906,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,12008,12148,12188,12194,12281,12284,12299,12359,12365,12371,12393,12653,12670,12673,12769,12849,12894,12913,12916,12956,13000,13003,3266,10528,10558,11112,11662,12296,12313,12635,12639,12642,3305,12942,12997,3297,3718,3658,10215,11487,11515,12617,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,12837,3224,10705,10776,11516,11667,11868,12101,12663,12947,13030,13036,13040,13047,3680,11610,12570,4028,3422,4480,3689,3726,4459,4462,4463,3180,3181,4461,4464,4204,3697,3519,11480,11566,4125,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,11194,3913,12128,3807,11191,11540,11544,11604,12218,12226,12305,12584,12843,12902,3647,10816,10822,10839,11795,12011,12277,12302,3506,11052,12145,12152,12223,12272,12280,12390,3982,3649,10903,11058,11088,11099,12110,12222,12266,12316,12886,3578,11600,3478,10493,10496,10561,10735,3477,4498,11481,4494,12538,4499,10619,10714,11037,11181,11318,12079,12086,12133,12329,4089,10688,12113,12125,12151,3989,3679,12396,4496,10188,10191,10516,10519,11357,11541,12338,4497,11461,11554,3651,10490,10732,12932,3920,4508,4509,4517,4522,4529,4545,4594,4596,4630,4647,4656,4657,4697,4725,4730,4813,4838,4839,4875,4902,4903,4920,4921,4934,4937,4958,4965,4982,4985,4986,4987,4992,4993,5016,5042,5043,5053,5058,5066,5111,5112,5120,5130,5134,5136,5146,5148,5154,5157,5172,5179,5182,5183,5187,5221,5233,5240,5242,5243,5246,5247,5248,5255,5257,5259,5263,5264,5265,5272,5276,5277,5278,5286,5290,5295,5307,5315,5327,5329,5337,5338,5342,5346,5369,5372,5378,5388,5389,5404,5437,5443,5459,5460,5463,5484,5492,5493,5498,5499,5509,5511,5524,5528,5539,5540,5541,5543,5559,5564,5577,5578,5587,5594,5606,5609,5610,5616,5617,5618,5621,5622,5627,5664,5665,5668,5671,5672,5674,5676,5678,5683,5690,5703,5721,5722,5731,5732,5737,5742,5744,5747,5791,5803,5811,5814,5818,5826,5829,5836,5850,5856,5874,5877,5889,5923,5924,5937,5958,5977,5978,5981,5994,5996,5997,5999,6011,6014,6015,6017,6020,6021,6032,6037,6039,6044,6083,6084,6091,6101,6142,6144,6146,6148,6154,6156,6158,6164,6166,6172,6175,6183,6190,6191,6192,6198,6220,6226,6230,6267,6268,6271,6272,6273,6274,6275,6276,6277,6285,6315,6316,6323,6326,6327,6347,6367,6370,6381,6382,6388,6401,6418,6419,6420,6430,6524,6548,6595,6610,6619,6620,6621,6622,6643,6644,6651,6662,6665,6667,6669,6670,6671,6673,6687,6696,6698,6699,6711,6714,6762,6772,6774,6778,6792,6793,6831,6839,6844,6874,6913,6965,6997,7048,7072,7081,7085,7137,7147,7193,7195,7212,7220,7223,7224,7245,7251,7252,7301,7310,7313,7328,7378,7379,7383,7425,7426,7444,7512,7532,7553,7576,7591,7606,7615,7624,7625,7655,7657,7659,7668,7706,7718,7744,7798,7828,7859,7903,7919,7935,7936,8013,8068,8085,8110,8130,8150,8155,8243,8257,8259,8264,8280,8284,8300,8303,8324,8335,8337,8354,8360,8363,8389,8403,8404,8419,8420,8425,8426,8427,8428,8429,8448,8449,8450,8460,8461,8475,8477,8491,8495,8497,8498,8499,8506,8510,8534,8535,8564,8577,8581,8599,8621,8622,8623,8624,8637,8638,8661,8671,8680,8681,8682,8683,8685,8705,8706,8717,8760,8766,8772,8785,8787,8789,8792,8793,8797,8806,8892,8923,8924,8925,8940,8956,8962,8988,8989,9031,9034,9059,9102,9103,9104,9120,9146,9159,9165,9169,9192,9193,9220,9279,9315,9316,9317,9343,9344,9360,9377,9383,9401,9422,9444,9451,9452,9453,9454,9469,9471,9476,9509,9510,9516,9555,9556,9584,9595,9605,9607,9608,9618,9632,9661,9692,9698,9756,9802,9803,9815,9816,9836,9841,9864,9869,9888,9938,10068,10084,2,8,9,4532,4533,4551,4582,4583,4585,4614,4622,4623,4634,4685,4687,4729,4758,4854,4855,4868,4890,4940,4941,4944,4945,4947,4949,4961,4962,4972,4983,4984,4990,5009,5010,5030,5035,5036,5037,5038,5041,5049,5052,5059,5060,5061,5126,5132,5133,5140,5169,5180,5185,5201,5204,5220,5227,5228,5229,5237,5252,5253,5254,5261,5268,5269,5282,5283,5284,5285,5287,5288,5291,5292,5293,5294,5323,5324,5325,5333,5334,5335,5336,5383,5385,5387,5422,5424,5425,5427,5428,5430,5431,5433,5442,5447,5449,5450,5451,5452,5453,5454,5461,5471,5475,5476,5487,5503,5504,5507,5517,5520,5521,5522,5551,5561,5579,5580,5588,5589,5591,5593,5629,5634,5636,5691,5723,5724,5728,5733,5734,5735,5736,5743,5753,5754,5756,5757,5765,5772,5788,5817,5832,5835,5837,5846,5848,5867,5868,5869,5872,5873,5893,5907,5908,5939,5940,5960,5963,5985,5990,6012,6016,6023,6031,6036,6038,6048,6049,6050,6051,6086,6102,6140,6157,6193,6194,6196,6216,6217,6219,6222,6223,6233,6242,6260,6279,6280,6286,6296,6306,6330,6335,6337,6351,6352,6355,6356,6358,6360,6361,6362,6364,6366,6369,6375,6376,6377,6378,6384,6386,6391,6426,6429,6442,6445,6446,6447,6448,6482,6487,6489,6494,6495,6503,6507,6520,6544,6545,6546,6547,6559,6563,6576,6583,6587,6589,6638,6639,6640,6645,6648,6679,6681,6683,6685,6688,6693,6706,6715,6748,6751,6752,6765,6766,6767,6768,6784,6785,6801,6822,6823,6829,6850,6863,6865,6866,6868,6870,6871,6878,6896,6910,6911,6916,6917,6918,6919,6921,6923,6956,6957,6969,6976,6978,6979,6980,7009,7018,7029,7038,7051,7052,7057,7059,7060,7066,7075,7089,7123,7125,7140,7148,7189,7194,7219,7264,7298,7311,7327,7358,7359,7362,7363,7387,7410,7427,7430,7431,7441,7460,7461,7463,7465,7467,7469,7516,7520,7521,7552,7554,7555,7556,7561,7583,7602,7612,7621,7633,7634,7636,7656,7665,7666,7689,7708,7756,7757,7799,7808,7830,7847,7848,7911,7912,7913,7938,7971,7978,7980,7988,7997,8001,8036,8042,8049,8063,8086,8109,8153,8183,8195,8213,8216,8251,8271,8338,8339,8344,8346,8364,8452,8453,8454,8455,8486,8513,8538,8580,8598,8655,8698,8701,8714,8721,8757,8778,8802,8803,8820,8821,8967,8986,8996,9020,9022,9025,9029,9032,9033,9064,9070,9082,9131,9151,9170,9205,9206,9212,9248,9271,9276,9312,9319,9323,9326,9327,9342,9356,9365,9376,9389,9390,9394,9396,9420,9538,9581,9625,9669,9785,9786,9845,9915,9989,10004,10009,3,2558,2562,2564,2571,2576,2577,2578,2581,2582,2588,2589,2590,2593,2594,2597,2598,2599,2600,2603,2604,2605,2608,2609,2610,2611,2613,2614,2618,2619,2623,2624,2625,2626,2628,2638,2640,2650,2651,2653,2654,2660,2661,2662,2663,2664,2682,2683,2684,2685,2690,2692,2697,2708,2710,2711,2720,2721,2722,2724,2727,2728,2729,2731,2734,2735,2736,2738,2739,2747,2748,2767,2782,5219,5391,5397,5398,5472,5518,5547,5576,5652,5654,5660,5717,5718,5719,5720,5726,5755,5886,5938,5957,5991,6028,6173,6180,6214,6215,6231,6235,6237,6244,6245,6246,6247,6248,6249,6250,6251,6332,6398,6399,6480,6514,6515,6556,6557,6694,6723,6775,6776,6780,6802,6827,6835,6837,6886,6914,6915,6931,6932,6933,6968,7012,7013,7112,7170,7171,7172,7173,7186,7213,7269,7270,7278,7286,7288,7300,7330,7331,7332,7333,7475,7476,7483,7485,7486,7487,7697,7699,7700,7716,7755,7826,7866,7922,7943,7944,7959,8021,8123,8193,8194,8196,8234,8296,8297,8396,8397,8398,8399,8542,8751,8774,8775,8824,8853,8868,8926,8927,9041,9074,9097,9132,9175,9332,9363,9619,9814,9872,9875,5544,5952,6313,6314,6402,6421,6422,6473,6826,7047,8470,8692,8881,8882,8953,8954,9222,9223,9224,9225,9423,9688,9998,10052,10053,6383,7265,7517,7518,8287,8288,8741,8758,9552,9689,10051,4555,4586,4588,4589,4648,4658,4791,4805,4806,4836,4837,4867,4919,4979,5039,5091,5119,5155,5158,5162,5164,5165,5190,5260,5281,5412,5479,5480,5602])).
% 173.53/173.47 cnf(13147,plain,
% 173.53/173.47 (~P22(f312(f70(x131471),f48(f860(x131471,a845),f235(f860(f860(x131471,a845),a845)))))),
% 173.53/173.47 inference(scs_inference,[],[4460,3428,3446,10943,11989,12092,12181,12219,12227,12240,12289,12421,12424,12844,12854,12859,12866,12872,12875,12903,13005,3453,12057,12488,12490,3454,12120,3766,10842,12467,12469,12471,12473,3172,12450,12452,3173,12494,4430,4149,12507,12510,3177,12483,3013,3035,12514,3076,12412,4382,3553,4358,10102,10105,10114,10178,10181,10271,10274,10555,10566,10825,10828,11200,11203,11218,11222,11267,11270,11273,11276,11286,11329,11344,11371,11374,11385,11390,11396,11454,11496,11499,11502,11512,11551,11633,11967,12157,12348,12399,12401,12405,12407,12422,12430,12432,12434,12444,12465,12475,12502,12721,12890,12919,13004,13009,13015,13019,13023,13042,13049,4359,11219,3508,4386,10099,10108,10111,10121,10132,10143,10242,10245,10248,10351,10461,10751,10928,10931,11126,11206,11213,11229,11279,11282,11305,11399,11447,11467,11742,11770,11790,11838,11952,11970,12037,12053,12211,12263,12667,12898,12921,12929,4404,10332,10423,3261,3222,12446,3415,4398,12585,12951,2804,2809,2818,2821,2822,2824,2825,2826,2830,2831,2839,2840,2845,2848,2852,2854,2861,2863,2864,2871,2872,2874,2876,2885,2888,2889,2891,2892,2895,2897,2903,2907,2915,2923,2926,2933,2937,2938,2941,2945,2950,2955,2956,2957,2958,2959,2960,2963,2984,3098,3075,4380,3543,3185,3245,3930,3157,3530,3781,4371,3136,11493,12243,12247,12251,3145,3257,3661,3971,3037,3038,4400,4418,3722,11253,3260,12477,3106,3067,10172,3576,12436,3061,3873,3083,3583,4345,3046,3025,3051,3082,3216,11732,11941,12076,12292,12368,3262,10700,12054,3134,3135,3155,10376,3309,4492,10304,3838,4420,10169,10329,11308,12207,12244,12248,4429,12215,3192,11588,11591,12815,12925,12976,12980,12984,4482,10875,10948,11163,11166,3188,3310,3529,3300,3275,12459,3101,3102,10234,10531,4466,3367,3092,3016,3144,3120,11243,3984,12230,12360,3840,10881,11010,11061,12191,12197,12306,12309,12335,4501,10803,11015,11120,11139,11169,11175,12139,4502,10917,11018,11123,4503,11021,11072,4504,11075,4505,3119,3408,12095,12136,12214,3568,4266,4267,3391,4417,11234,3510,3546,3714,4105,3480,12704,12708,12712,12716,12726,3760,12089,3394,3642,3272,10253,10369,10440,10484,10487,10534,10616,10865,11766,11810,11887,11948,12019,12022,12339,12581,12612,12624,12666,12687,12743,12749,12928,12933,13027,13033,3653,11484,3187,3284,11601,13041,3475,4472,10146,10149,10175,10627,10640,10761,11184,11246,11649,11657,11890,11893,11980,12142,12234,12528,12531,12548,12551,12573,12625,12792,12797,12822,12827,4488,11360,11393,11430,11464,12634,12638,12897,3640,3416,3417,12554,12557,12560,12563,12593,12596,12959,12963,12967,3419,3790,3378,12964,3379,12960,3230,3232,3205,4469,3100,4414,3594,4120,3908,3400,4489,3978,11134,3528,3244,11607,12061,12161,12319,3947,3906,11759,12104,3850,10697,11931,11955,12117,12342,12786,12975,3896,12979,3901,10887,11986,12060,12116,12160,12818,3902,3569,11769,11918,11994,12044,3870,3907,3585,10884,10953,11034,11094,11951,12012,12258,12332,12345,12803,12853,12858,4493,10643,11026,12869,3202,10264,10358,10437,10541,11336,11343,11550,11560,11572,11632,11735,11741,12005,12164,3203,10603,10646,10649,10682,10708,10745,10783,10819,11813,11816,11819,11822,12025,12028,12031,12034,12100,12269,12312,12574,12599,12676,12683,12690,12695,12698,12701,12734,12746,12808,12831,12834,12948,13029,3204,10345,10546,10622,10748,11402,11443,11636,11652,11745,11756,11777,11782,11798,11825,11843,11858,11863,12590,12740,12764,12793,12798,12823,12828,13016,13020,3280,11974,12654,12705,12709,12713,12717,12727,12731,4468,10212,10297,10348,10432,10664,10711,10721,11409,11511,11531,11534,11537,11557,11693,11696,11699,11702,11789,11809,11828,11837,11902,11905,11908,11911,11981,12068,12071,12167,12170,12233,12262,12295,12380,12686,3361,10501,10756,10800,11083,11155,11321,12210,12383,12780,12848,12906,4484,10673,10685,10792,10810,10813,10878,10967,10975,10991,11029,11046,11055,11091,11129,11149,11152,11178,11585,11613,11896,11899,11936,11975,12008,12148,12188,12194,12281,12284,12299,12359,12365,12371,12393,12653,12670,12673,12769,12849,12894,12913,12916,12956,13000,13003,3266,10528,10558,11112,11662,12296,12313,12635,12639,12642,3305,12942,12997,3297,3718,3658,10215,11487,11515,12617,4481,10166,10522,10525,10970,10988,11446,11453,11545,11668,11705,11708,11711,11714,12837,3224,10705,10776,11516,11667,11868,12101,12663,12947,13030,13036,13040,13047,3680,11610,12570,4028,3422,4480,3689,3726,4459,4462,4463,3180,3181,4461,4464,4204,3697,3519,11480,11566,4125,4495,10137,10140,10394,10443,10448,10850,11315,11569,11671,4500,11049,11160,11194,3913,12128,3807,11191,11540,11544,11604,12218,12226,12305,12584,12843,12902,3647,10816,10822,10839,11795,12011,12277,12302,3506,11052,12145,12152,12223,12272,12280,12390,3982,3649,10903,11058,11088,11099,12110,12222,12266,12316,12886,3578,11600,3478,10493,10496,10561,10735,3477,4498,11481,4494,12538,4499,10619,10714,11037,11181,11318,12079,12086,12133,12329,4089,10688,12113,12125,12151,3989,3679,12396,4496,10188,10191,10516,10519,11357,11541,12338,4497,11461,11554,3651,10490,10732,12932,3920,4508,4509,4517,4522,4529,454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246,6247,6248,6249,6250,6251,6332,6398,6399,6480,6514,6515,6556,6557,6694,6723,6775,6776,6780,6802,6827,6835,6837,6886,6914,6915,6931,6932,6933,6968,7012,7013,7112,7170,7171,7172,7173,7186,7213,7269,7270,7278,7286,7288,7300,7330,7331,7332,7333,7475,7476,7483,7485,7486,7487,7697,7699,7700,7716,7755,7826,7866,7922,7943,7944,7959,8021,8123,8193,8194,8196,8234,8296,8297,8396,8397,8398,8399,8542,8751,8774,8775,8824,8853,8868,8926,8927,9041,9074,9097,9132,9175,9332,9363,9619,9814,9872,9875,5544,5952,6313,6314,6402,6421,6422,6473,6826,7047,8470,8692,8881,8882,8953,8954,9222,9223,9224,9225,9423,9688,9998,10052,10053,6383,7265,7517,7518,8287,8288,8741,8758,9552,9689,10051,4555,4586,4588,4589,4648,4658,4791,4805,4806,4836,4837,4867,4919,4979,5039,5091,5119,5155,5158,5162,5164,5165,5190,5260,5281,5412,5479,5480,5602,5603,5625,5626,5630,5680,5686,5695,5701,5768,5844,5913,5974,5995,6160])).
% 173.53/173.47 cnf(13280,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x132801,a845)),f312(f168(x132801),f166(x132801,x132802,x132803))),f312(f168(x132801),x132803)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(13322,plain,
% 173.53/173.47 (E(f312(x133221,f739(f312(x133221,x133222),f312(f219(x133223),x133222),x133221,x133224,x133223)),f312(x133221,x133222))),
% 173.53/173.47 inference(rename_variables,[],[11001])).
% 173.53/173.47 cnf(13333,plain,
% 173.53/173.47 (E(f312(x133331,f739(f312(x133331,x133332),f312(f219(x133333),x133332),x133331,x133334,x133333)),f312(x133331,x133332))),
% 173.53/173.47 inference(rename_variables,[],[11001])).
% 173.53/173.47 cnf(13336,plain,
% 173.53/173.47 (P22(f312(f312(f227(a852),x133361),f312(f312(f90(a852),x133361),x133361)))),
% 173.53/173.47 inference(rename_variables,[],[3478])).
% 173.53/173.47 cnf(13363,plain,
% 173.53/173.47 (P22(f312(f312(f227(f860(x133631,a845)),f312(f168(x133631),f166(x133631,x133632,x133633))),f312(f168(x133631),x133633)))),
% 173.53/173.47 inference(rename_variables,[],[3901])).
% 173.53/173.47 cnf(13408,plain,
% 173.53/173.47 ($false),
% 173.53/173.47 inference(scs_inference,[],[3947,3790,4498,3840,4461,3297,4501,4484,3284,3901,13280,13363,3807,3025,4420,3224,3506,3578,3478,13336,3568,4494,4499,13119,11404,12355,11001,13322,13333,10565,10854,12833,10578,11518,12144,11623,11625,10572,10987,10809,10812,11930,11148,12378,13147,11041,2976,6039,8534,8892,8389,9102,5511,6670,4555,5242,5974,8792,5243,5695,4921,7840,8682,5221,7378,6183,5686,5606,6773,6621,5981,4588,6774,9189,4867,5826,5463,9316,5281,6160,6662,7624,8257,8259,8638,8706,6778,5164,7328,4903,5329,7859,8797,9146,8335,2,5492,5609,6327,7828,5618,5626,6273,4630]),
% 173.53/173.47 ['proof']).
% 173.53/173.48 % SZS output end Proof
% 173.53/173.48 % Total time :153.810000s
%------------------------------------------------------------------------------